Imaging of Defects in Girth Welds using Inverse Wave Field

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1 Imaging of Defects in Girth Welds using Inverse Wave Field Extrapolation of Ultrasonic Data Niels Prtzgen

2 Imaging of Defects in Girth Welds using Inverse Wave Field Extrapolation of Ultrasonic Data PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties, in het openbaar te verdedigen op dinsdag 6 november 2007 om 10:00 uur door Niels PORTZGEN natuurkundig ingenieur geboren te Terneuzen

3 Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. ir. A. Gisolf Toegevoegd promotor: Dr. ir. D.J. Verschuur Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof. dr. ir. A. Gisolf, Technische Universiteit Delft, promotor Dr. ir. D.J. Verschuur, Technische Universiteit Delft, toegevoegd promotor Prof. dr. ir. C.P.A. Wapenaar, Technische Universiteit Delft Prof. dr. H.P. Urbach, Technische Universiteit Delft Prof. dr. A. Erhard, BAM Berlin Dr. ir. G. Blacquiere, TNO Dr. ir. M. Lorenz Shell Global Solutions ISBN 978-90-9022387-2 c Copyright 2007, by N. Portzgen, Laboratory of Acoustical Imaging and Sound Control, Faculty of Applied Sciences, Delft University of Technology, Delft, The Netherlands. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the author N. Portzgen, Faculty of Applied Sciences, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands. SUPPORT The research for this thesis was financially supported by RTD bv. and by a subsidy within the Dutch Technologische Samenwerking program. Typesetting system: LATEX. Printed in The Netherlands by Gildeprint, Enschede.

4 To my sons Thijs and Daan Maybe some day you will understand this

5 Contents 1 Introduction 5 1.1 Non-destructive inspection techniques . . . . . . . . . . . . . . . . . . . . . 5 1.2 Conventional defect sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Automated girth weld inspection based on zone discrimination . . . . . . . 10 1.4 Ultrasonic arrays in NDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 The use of arrays in seismic exploration . . . . . . . . . . . . . . . . . . . . 15 1.6 Outline and objectives of this thesis . . . . . . . . . . . . . . . . . . . . . . 17 2 Wave theory and imaging 19 2.1 Introduction of the imaging philosophy . . . . . . . . . . . . . . . . . . . . . 19 2.2 The Rayleigh II integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Wave field extrapolation in elastic media . . . . . . . . . . . . . . . . . . . . 23 2.4 The imaging condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 An example of imaging with simulated acoustic data . . . . . . . . . . . . . 25 2.6 2D imaging implementation using the matrix notation . . . . . . . . . . . . 29 2.7 2D Zero offset imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.8 3D imaging with linear arrays, the two pass method . . . . . . . . . . . . . 34 3 Application of imaging techniques for weld inspection 39 3.1 Properties of girth welds in pipelines and defects . . . . . . . . . . . . . . . 39 3.2 Rejection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3 Spatial and temporal sampling . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4 Resolution analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6 2 CONTENTS 4 2D imaging results from measured data 55 4.1 Imaging a bore hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Imaging of embedded lack of fusion defects . . . . . . . . . . . . . . . . . . 59 4.3 Imaging surface breaking defects and porosity . . . . . . . . . . . . . . . . . 62 4.4 Imaging cold lap and lack of cross penetration defects . . . . . . . . . . . . 66 5 3D imaging results from measured data 69 5.1 3D imaging of a round bottom hole . . . . . . . . . . . . . . . . . . . . . . . 71 5.2 3D imaging of three inclined cylinders with round bottom holes . . . . . . . 75 5.3 3D imaging of a planar inclined slit . . . . . . . . . . . . . . . . . . . . . . . 80 5.4 3D imaging of a buried reflector in a weld . . . . . . . . . . . . . . . . . . . 85 6 Artifacts and their removal 91 6.1 Derivation of the location of artifacts . . . . . . . . . . . . . . . . . . . . . . 91 6.2 Analysis of the positioning of leaked L-L energy in the L-T image of a point scatterer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3 Suppression of artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7 Conclusion 109 7.1 General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.2 Conclusion on the 2D imaging of defect like reflectors . . . . . . . . . . . . 110 7.3 Conclusion on the 3D imaging results . . . . . . . . . . . . . . . . . . . . . 111 7.4 Conclusions on the appearance and suppression of L-L leakage artifacts in L-T images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 8 Discussion and recommendations 113 8.1 Discussion on the resolution, a gap in the aperture . . . . . . . . . . . . . . 113 8.2 Imaging of LL-L arrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 8.3 Recommendations for further research . . . . . . . . . . . . . . . . . . . . . 121 8.4 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 A High frequency approximation 129 B Derivation of the locus curves of L-L leakage artifacts in L-T images 131 C Technical drawings of test pieces 133 D Symbols and Abbreviations 137 D.1 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 D.2 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Summary 141 Samenvatting 143

7 CONTENTS 3 Curriculum vitae 145 Acknowledgements 147

8 4 CONTENTS

9 1 Introduction 1.1 Non-destructive inspection techniques Non-destructive inspection (NDI) methods are used in a wide range of application fields. In general, the objective of NDI methods is to inspect the inside of an object without damaging it. NDI makes a substantial contribution to safety, the economy and the en- vironment. In many cases, imperfections like small cracks, corrosion or imperfections in welds caused near accidents or accidents which lead to sometimes environmental disasters, economic failure and even fatalities. Therefore, governments developed regulations to set a standard for the quality of newly constructed objects in the petrochemical industry such as pressure vessels, pipe lines and storage tanks, or in the aviation industry such as aero-plane wings. In addition, regulations were made for the maintenance of those objects. A simple NDI method is visual inspection. Just by carefully looking at an object something can be said about the quality of the manufacturing of it while the shape and condition of the object remains unchanged. A shortcoming of visual inspection is, of course, that in many cases the interior of an object cannot be inspected. Other non-destructive methods have been developed to measure the condition of the interior of the object from the outside. Those NDI methods are usually based on: Radiography Electromagnetism or permanent magnetism Dye or magnetic particle fluid penetrant Ultrasonic waves

10 6 Introduction All these methods can be used to measure parameters that are related to the physical prop- erties of materials. The applications for which a certain NDI method is suitable depend on the physical principles involved. In general, all NDI methods have got their weak and strong points concerning inspection speed, resolution, safety, accuracy and probability of detection of inhomogeneities. A useful table that summarizes the advantages and disad- vantages of the major NDI methods can be found in Lorenz [1993]. In this thesis, the application of interest is girth weld inspection. The non-destructive technique for the inspection of girth welds is based on ultrasonic wave propagation. An ultrasonic transducer transmits a wave field that is scattered by inhomogeneities in the ob- ject of interest, after which the scattered wave field is measured by one or more receivers, which often are the same transducer. To judge the condition of an object from these measurements, the raw data has to be pro- cessed interpreted. After data analysis it can be concluded if an inhomogeneity is present. An inhomogeneity may not necessarily be unacceptable. Throughout this thesis, the term defect will be used for all unacceptable inhomogeneities. A thorough understanding of the physical principles of the used NDI method will improve the results of the interpretation. 1.2 Conventional defect sizing In ultrasonic NDI a wave field usually is generated with the use of piezo electric crystals or composites. When such a crystal is exposed to a mechanical vibration, an electric potential is generated. Vise versa, a mechanical vibration is generated when the crystal is subjected to an electric potential. Crystals with these characteristics are called transducers. In practice, the crystal is exposed to a short potential pulse causing the crystal to vibrate with a frequency bandwidth and directivity pattern characteristic for the crystal design. Directly after the pulse, the potential over the crystal is measured during a limited time. When waves reflect or diffract at medium boundaries, a response signal is recorded. This signal is the basis of any ultrasonic NDI measurement. In NDI the recorded signal is called an A-scan, where in seismic exploration it is often called a trace. The physical parameter that is measured directly is a voltage caused by the strain in the piezo-electric material. The amplitude of the signal usually is related to a reference value and presented as a percentage of the full screen height (FSH). When ultrasonic responses are measured the results have to be evaluated. A response can be caused by an inhomogeneity or by the boundaries defined by the geometry of the object (see figure 1.1). In case of ultrasonic inspection techniques, responses caused by the ir- regular geometry of boundaries can usually be identified. Before the inspection starts, the geometry of the weld and the materials the weld and the pipe consist of, are known. Loca- tions that cause responses are, for example, the weld reinforcements (cap and root), clad layers or buffer zones. Since the positions of those locations are known, the concomitant signals can be identified by their travel times. Sometimes the travel time from a defect to the receiver is almost the same as the travel time from a boundary to the receiver. In this case the defects responses are masked. In case signals are identified as not geometry related, the response must be caused by

11 1.2 Conventional defect sizing 7 cap geometry lack of fusion defect Figure 1.1: Cross section of a narrow gap weld. The cap of the weld can cause ultrasonic responses. This weld contains a lack of fusion defect. an inhomogeneity. The acceptance or rejection of the weld on the basis of the detection of an inhomogeneity depends on established codes that prescribe acceptance criteria. Most codes for weld inspection are based on radiographic inspection because this was the first NDI method that was used. The acceptance criteria in earlier codes are based on good workmanship, later codes are based on fracture mechanics or engineering critical assess- ment (ECA). Good workmanship codes are mainly meant as a guidance to contracting parties in the industry and are usually conservative. Codes based on ECA contain fitness for purpose criteria. As a consequence, defect characterization is dictated by the result of the assessment and must be as accurate as possible. To apply the acceptance criteria, the NDI results must be evaluated according to code requirements. The evaluation requirements are different for most codes. Some codes re- quire an evaluation and rejection based on the amplitude height of the signal (NEN3650 [1992], DNV [1996]), while other codes only prescribe rejection criteria based on maximum defect length and height (BS [1996], API [1999]). Evaluation based on amplitudes can be applied directly, since the result of an ultrasonic measurements contains the amplitude information. In case defect height and length are subjected to the criteria, the information must be extracted from the amplitudes and temporal information of the ultrasonic signals. Defect sizing based on amplitude height of the ultrasonic signal usually is done with the help of a reference reflector with known characteristics and dimensions. Commonly used re- flectors are bore holes, flat bottomed holes or notches. Relationships have been established to calculate a reflectors diameter from the measured amplitude, given the probe charac- teristics, the distance of the reflector and the calibration amplitude. Diagrams are made from relationships, known as AVG curves (Amplitude Verstarkung Grosse), DAC curves (Distance Amplitude Correction) or sizing curves (Krautkramer [1977]). In practice, an amplitude caused by a defect will be compared to the amplitude of a reference defect.

12 8 Introduction Then the dimensions of the reference defect with the corresponding amplitude obtained from the curve, are use as defect size. Amplitude based sizing has got some disadvantages: By using the dimensions of a corresponding reference reflector, the assumption is made that the shape of the defect is identical to the shape of the reference defect. The amplitude of a reflected signal is highly dependent on the orientation of the defect. The consequence can be that a large defect under a certain orientation is accepted because the amount of received energy is much lower than the total reflected energy. Because the assumptions made in amplitude based sizing do no always hold in practice and can result in large defect size variations, as described by Lozev [2005], acceptance criteria must be conservative. Defect sizing with temporal information is based on the travel times from waves that are diffracted at defect tips, the most common method is the time of flight diffraction method (ToFD), see e.g. Ravenscroft [1991] and Ogilvy [1983]. The transmitting and receiving transducers are placed in a pitch-catch configuration. The travel time from source to de- fect tip to receiver contains the location information of the defect. The ToFD technique is less dependent on defect orientation. When diffractions caused by the upper tip and lower tip are measured, reasonably accurate sizing is possible, depending on the frequency bandwidth of the signal. A disadvantage of the technique is the dead zone caused by the direct wave traveling just below the surface, also called the lateral wave. Cracks connected to the surface are obscured by the lateral wave (Erhard and Ewert [1999]). The ToFD technique is widely accepted and special standards are available. In most practical situations a combination of pulse-echo techniques and ToFD techniques is used to increase the probability of detection of defects and to improve sizing by com- bining the results. Good results have been obtained with both the pulse-echo technique and ToFD techniques in controlled laboratory and field circumstances. Still, those results involve interpretation by experienced operators, because they do not directly show the de- fects location, orientation, shape and size. Pattern recognition and neural networks have been applied for uniform interpretation, such as described by Moura [2004]. However, the success of these techniques depends on training that does not involve the physics of wave propagation. Advanced ultrasonic techniques have been studied and applied to make an image of a defect illustrating the defects characteristics. Phased array sectorial scans are used suc- cessfully in medical imaging, such as described by Wells [2000], Fenster [2001], Jesse and Smith [2002]. With the development and miniaturization of ultrasonic array equipment, sectorial scans have become popular for industrial applications (e.g. R/D-Tech [2004]). However, the same drawbacks regarding defect shape and orientation remain. In summary, none of the techniques discussed above provide a complete unambiguous solution for defect characterization and sizing. They all have their own merits and draw- backs concerning probability of detection, sizing capabilities and practical usage. Due to the drawbacks, combinations of techniques are used for more reliable detection and assess- ment. Furthermore, acceptance criteria contain a certain amount of conservatism. The

13 1.2 Conventional defect sizing 9 need for conservatism can be minimized by accurate failure analysis and by accurate sizing of detected defects. Minimizing the need for conservatism will lead to lower repair rates and thus substantial economic benefit. Defect sizing still dictates the extend of conservatism. In addition, with the development of more efficient and faster computers, numerical fracture mechanics analysis has improved. Ultrasonic imaging, as presented in this thesis, aims for accurate and unambiguous defect characterization and sizing. We will introduce in chapter 2 an imaging approach that has been developed in seismic exploration. With the develop- ment of ultrasonic arrays we will see that this approach becomes feasible for the imaging of defects from ultrasonic data. One of the techniques that aims for better characterization of the inhomogeneities is the synthetic aperture focussing technique (SAFT), as described by Lorenz [1993]. The SAFT technique was originally developed for radar applications. With the SAFT technique multi- ple pulse-echo measurements are taken whereby the distances between the transmitter and receiver are varied. Two single element transducers are used for each measurement, the locations of the transducers are usually stored by using an encoder. If an inhomogeneity is present, signals caused by the inhomogeneity will arrive at different times depending on: the transmitter-receiver separation, the distance between the transducers and the inhomogeneity, the wall thickness of the inspected object, the wave mode (transversal or longitudinal or indirect insonification via boundaries). The arrival times can be determined for each combination. For a point of interest all scans can be compensated for certain travel times by applying phase shifts. After the compen- sation of the travel times, the scans are added and the amplitude at zero time is used as contribution for that point in a defined image space. If the inhomogeneity was present at the chosen point, the signals caused by the inhomogeneity will all be shifted to zero time and the amplitudes will add constructively resulting in a large contribution. Usually, only one path is regarded in SAFT. Multi-SAFT, as presented by Lorenz [1993], also takes different modes into account to increase the spatial bandwidth. The orientation and size of the defect appear after the contributions of all points in the image space are calculated. The principle of filling an image space is unique in the ultrasonic application field. Despite its good potential, the SAFT technique is not regarded as a standard ultrasonic inspection technique, nor is it described in codes. In addition, the data collection and processing can be time consuming. In the next section, the application of NDI on girth welds will be discussed. This applica- tion will be the focus of this thesis. Girth weld inspection can be done in an automated ultrasonic set-up. The inspection philosophy will be discussed in the next section.

14 10 Introduction zone 1 cap 2 3rd fill 3 2nd fill 4 1st fill 5 hot pass 6 lcp 7 root Figure 1.2: The automated ultrasonic girth weld inspection approach is based on zone dis- crimination. Each zone is inspected with a dedicated ultrasonic set-up. 1.3 Automated girth weld inspection based on zone discrimi- nation A well known application for NDI is girth weld inspection. Traditionally, girth welds were inspected with radiography. However, with advances in ultrasonic technology, ultrasonic inspection is now a well accepted inspection method. The first ultrasonic inspection meth- ods were based on moving an ultrasonic probe with a particular angle (usually 45 , 60 and 70 ) towards and from the weld in a so called Meander movement. This inspec- tion method has been automated resulting in a mechanized scanner with several ultrasonic probes to cover the entire weld volume. Mechanized ultrasonic inspection of girth welds can be considered as a reliable alternative for radiography (see de Raad and Dijkstra [1995] and de Raad and Dijkstra [1998]). The inspection method for automated ultrasonic testing (AUT) is based on zone discrimi- nation for full coverage of the weld and heat affected zones (see Dube et al. [1998] or Findlay and van der Ent [2001]). A complete overview of AUT and zone discrimination is given by Ginzel [2006]. The weld is divided into zones of typically 1- 3 mm height. Each zone is then inspected with an dedicated ultrasonic beam, generated by a probe that is fixed in a frame called the probe pan. The probe pan is fixed to a carrier that can be mounted on a band attached to the pipe circumference. The carrier moves once around the entire cir- cumference during the weld inspection (see figure 1.3). The probes are optimized to reflect defects at the fusion face. Depending on the weld configuration, single crystal probes can be used for a perpendicular insonification, whereas steep fusion faces are inspected with a dual crystal probe in a so called tandem configuration. The near surface zones are usually not insonified by a configuration that is aimed in the direction of the fusion face. Here, the ultrasound will reflect as a result of the interaction with the defect and the surface (corner reflection). Defect sizing is usually based on amplitude height evaluation as described in section 1.2. Therefore, a calibration block is needed that contains reference reflectors like float-bottom holes of 2-3 mm in diameter typically (see figure 1.4). For surface defects, notches are

15 1.3 Automated girth weld inspection based on zone discrimination 11 Figure 1.3: Automated ultrasonic testing system. The weld is inspected with zone discrim- ination, whereby each zone is examined by a dedicated ultrasonic beam. The ultrasonic probes are mounted into a frame. The frame is fixed to a carrier that moves around the circumference during inspection. used. Once the position of the probes are optimized, the gain will be adjusted such that the amplitude reaches 80% full screen height (FSH). With the computer, a time gate will be placed over the calibration signal so that only the information in the time gate will be stored. The data display of AUT is done with strip charts (see figure 1.5). Each column of a strip chart contains the recordings of the highest amplitude and the position within the gate of a certain probe. Some columns record the full digitized signal within the gate. These columns are referred to as mapping channels and aim to detect volumetric flaws such as porosity or inclusions. In addition, signals caused by the cap and root re-enforcements can be monitored. The top of the column represents the start position and the end of the column represents the end position around the circumference of the pipe. During an inspection the real-time view resembles a waterfall of data building up from the top of the screen to the bottom. In the presence of a defect, an amplitude will appear in the column that corresponds to the inspected zone. Interpretation of strip charts is not straight forward and requires operator experience. In addition, defect characterization and sizing accuracy is questionable, as described by

16 12 Introduction flat bottom holes notches Figure 1.4: The sensitivity of the automated ultrasonic inspection system is set with the use of calibration reflectors in a special designed calibration block. Figure 1.5: Typical strip chart data presentation of the automated ultrasonic inspection of a girth weld with the zone discrimination method.

17 1.4 Ultrasonic arrays in NDI 13 Ginzel [2000], Gross et al. [2001], Morgan [2002] and Heckauser [2006]. The improvement of this methodology forms a substantial objective of this thesis. 1.4 Ultrasonic arrays in NDI In section 1.2 several ultrasonic NDI techniques for detection and sizing of defects were discussed and in section 1.3 an application was presented. All techniques make use of ul- trasonic beams with a certain angle, beam spread, focal point, frequency and wave mode. When the pulse echo technique is applied, the beam characteristics are dictated by the defects of interest (a more detailed discussion is given in section 3.1). As discussed in the previous section, in an automated inspection setup for the inspection of girth welds, multiple probe configurations are use for the inspection of the entire volume of the weld. The weld configuration is usually different from project to project. This requires the man- ufacturing of new probes for almost each project. All the probes are fixed in a frame. The positions in the frame must be optimized for each probe, making the setup labor intensive. The number of probes and the setup time for automated ultrasonic testing systems can be reduced with the use of ultrasonic array technology, as described by Portzgen et al. [2002], Moles et al. [2005] and Huang et al. [2004]. The characteristics of beams generated by ultrasonic arrays can be controlled with a computer, within certain limits. One array probe can even be used to replace all the single crystal probes in an automated inspection setup. An array probe consists of typically 32 to 64 crystal elements which have a size in the order of half the wavelength of the center frequency of the crystal. The center frequency is typically between 1 and 10 MHz and the element size 0.3mm - 2mm. Each element is connected to the ultrasonic hardware and can be fired individually. The directivity pattern of a single element resembles the directivity pattern of a dipole source. When adjacent elements are fired simultaneously, the resulting wave front gets the shape of a wave front generated by a single crystal transducer with the same outer dimensions. This wave front is parallel to the crystal. When the elements are fired in a sequence of pre-determined delays, the direction and focal point of the resulting wave front can be controlled, as explained by Wooh and Shi [1999] and Lee and Choi [2000]. In figure 1.6 two examples of beam forming using delay times are illustrated. For girth weld inspection, array probes have more elements then necessary for the gener- ation of a single beam. When a group of elements is used to generate a beam, this group can be shifted along the array( Portzgen et al. [2002], Moles et al. [2003] and Moles and Labbe [2005]). The position of the beam (or index point) can be varied while the position of the probe remains unchanged. The active group of elements may be different for the transmitting beam and the receiving beam. Tandem configurations can be constructed in this way. The beam generated by an array probe can be swept through a range of angles with a small increment. The result of each scan can be displayed in a polar plot, with amplitudes coded according to a color key. The resulting image is called a sectorial scan, it is well known from pre-natal examination of a foetus (Fenster [2001], Wells [2000], Hughes [2001]

18 14 Introduction Figure 1.6: Steering and focusing of an ultrasonic beam with a linear ultrasonic array. When the the active group of elements is displaced, the index point of the beam can be varied. Figure 1.7: Sectorial scan of an unborn baby in the womb. and Harvey et al. [2002], see figure 1.7). In the application field of industrial NDI, sectorial scans are used for detection and sizing of cracks. Sectorial scans are sometimes referred to as images. The geometry of investiga- tion can be plotted over the sectorial scan, so that the location of the defect easily can be identified. However, sectorial scans do not represent the entire reflectivity properties of the area under investigation because a single point in the image is observed by only one beam with a certain angle. Defects that are small compared to the wave length will scatter the wave energy in all directions. In that case, the defect will be detected and the position of the amplitude in the image will correspond to the real position. A larger defect behaves like a reflector and the reflected ultrasonic wave will propagate in a specific direction. If the reflected wave does not propagate back to the array, the defect will not be detected and

19 1.5 The use of arrays in seismic exploration 15 therefore not appear in the sectorial scan. Imaging by displaying multiple time-amplitude responses (or A-scans as they are called in the ultrasonic application field) with a color key that represents amplitude height might give the operator more insight. However, the information in the scans does not increase (Portzgen [2006]). Although ultrasonic arrays offer operational benefits and allow alternative inspection tech- niques like sectorial scans, the basic principles of ultrasonic inspection remains unchanged. In fact, the only difference with the use of phased arrays is the mechanism of transmitting and receiving the ultrasonic beams. Once the wave fronts have been formed, practically no difference can be observed between the wave front that was generated by a single crystal transducer and a phased array transducer. Consequently, the results will be similar and the same drawbacks and benefits concerning probability of detection, defect characterization, sizing and accuracy can be expected, see Armitt [2006]. Rather than using the elements of an ultrasonic array to form a wave front with certain characteristics, the individual elements can be used also as single sources and receivers. A-scans can be measured for each source receiver combination with the array in a fixed position. The data set created this way represents the most complete data set that can be gathered along the aperture of the array. All A-scans obtained from a beam created by a group of active elements can be reconstructed from this complete data set, as demonstrated by von Bernus et al. [2006]. This is possible because the A-scans from the data set can be phase shifted and added with phase shifts corresponding to any desired beam angle and focal spot. In the application field of seismic exploration, it is more common to make use of such data sets. In the next section, it is explained how images are constructed based on such data matrices in seismic exploration and how this application field can be linked with ultrasonic NDI. 1.5 The use of arrays in seismic exploration In seismic exploration, arrays have been used for many years to image the earths interior. Seismic data can be processed into a representative image, with minimal assumptions and without the use of reference reflectors. The algorithms are based on fundamental wave theory and are usually referred to as migration techniques, see e.g. Schnneider [1978], Berkhout [1982] and Claerbout [1985]. Most of the imaging techniques make use of inverse wave field extrapolation with the Rayleigh integral (see e.g. Berkhout [1982]). This ap- proach will be discussed in detail in chapter 2. In seismic exploration acoustic sound is used to image the earths interior to identify layers of different composition and complex structures like salt domes, such as shown in figure 1.8. The final objective is to localize and characterize hydro-carbon reservoirs. An acoustic sound source, like an air gun for marine applications or a vibrating truck or dynamite for land applications, is used and the reflected wave fields are recorded with hydrophones or geophones. For a survey along one spatial coordinate, the data can be presented in a matrix with in the rows the receivers and in the column the sources, see Berkhout [1982]. Ideally

20 16 Introduction Figure 1.8: 3D seismic image of a medium containing a salt dome (from the SEG/EAGE salt model presented by Burch and Burton [1984]). the matrix contains the information of all source-receiver combination so that it is com- pletely filled. In addition, the aperture where the sources and receivers are located must be long compared to the area of interest. Images can be obtained by applying mathematical operations on the data matrix. Different implementations for the imaging techniques can be used. The most important differences with standard ultrasonic imaging techniques as used in NDI are: The A-scans are processed to an image after the measurements. The algorithms to produce an image are based on fundamental wave theory. A single point in the image contains information acquired from multiple A-scans. The A-scans were taken from different positions so that the medium is insonified from many directions. The images represent the reflectivity properties of the medium at the corresponding positions. As a consequence, interpretation of the final image is transparent and relatively unambiguous. The data contains all the medium properties (reflectivity and position of layers, reflec- tors and diffractors, sound velocities and densities). In principle, all this information can be recovered without extensive a-priori knowledge. Ultrasonic techniques make use of reference block for system calibration. The re- sponse of a defect will be compared with the response of a known calibration reflector. In seismic exploration, calibration is not standard practice, since all the variables of interest can be derived from the images. The measurement set-up and the choice of ultrasonic probes in NDI depend on the type of defect that should be detected and characterized. Many design parameters

21 1.6 Outline and objectives of this thesis 17 for the probes must be optimized. In seismic exploration the diversity of parameters is much less and the measurement set-up is much more standardized. The most important similarities between seismic exploration and ultrasonic NDI are the use of sound and the use of array recorders. Although the scale is different, fundamental wave theory can be used in a similar way for both application fields. Hence, the appealing benefits of imaging that are common in seismic exploration (like unambiguous interpretation, no calibration procedure and standardized measurement set-up) can now also be explored in ultrasonic NDI. 1.6 Outline and objectives of this thesis The main objective of this thesis is to apply the imaging concepts as developed in seismic exploration to the application field of ultrasonic NDI in 2D and to give a proof of concept in 3D. The imaging concepts will be verified with ultrasonic data obtained from simple geometrical reflectors and with reflectors that are representative for defects in girth welds, with the exception of transverse cracks. As ultrasonic NDI is a broad application field, here we will concentrate on weld inspection of carbon steel girth welds that are common for newly constructed pipe lines. We will assume that carbon steel is a homogeneous and isotropic material. The geometry and the material constants (density and sound velocity) of the welds are assumed to be known and also typical for girth welds. However, the theory can be extended to more complex geometries and other materials like dissimilar welds. As a consequence of the geometry and the nature of the material, defects will be insonified multiple times via boundaries and by mode converted wave fronts. It will be demonstrated that these different wave fronts have different arrival properties and can be imaged indi- vidually. Images from different arrived wave fronts may contain more information on the defect because the defect may be insonified better. For example, defects that are located near the upper surface are better insonified via the back wall. Although the different wave fronts may lead to better images, they can also cause cer- tain artifacts in the images. It will be explained what causes these artifacts, what shape they have and where they are located. From that, a practical approach will be developed and demonstrated, to predict and suppress these artifacts. In the next chapter, a review of wave theory will given. Important results like the Kirchhoff integral and the Rayleigh II integral for forward and inverse wave field extrapolation will be revisited. The principles of imaging using inverse wave field extrapolation and the imaging condition will be discussed and illustrated with examples. The data used in the examples is obtained from acoustic and elastic finite difference wave field simulations, representative for the ultrasonic application. The 2D imaging approach will also be presented in matrix notation for efficient computer implementation. Furthermore, the 3D imaging approach, called the two pass method, will be presented as a 2D approach that is applied twice in two orthogonal directions. In one such a direction, the 2D zero-offset imaging approach

22 18 Introduction can be used. In chapter 3, the application of girth weld inspection and the defect types of interest will be discussed in more detail. The requirements of the imaging approach will be described in relation with girth weld inspection, based on existing codes and standards. Attention will be given to the design of the array transducer. This also involves an analysis of the reso- lution that can be achieved with the imaging approach. From this analysis, the expected performance will be compared with the requirements. In chapter 4, results of 2D images will be presented. The images were constructed from measurements on test blocks with machined defects. The machined defects are representa- tive for defects that are common to girth welds such as embedded and surface breaking lack of fusion defects, porosity, cold lap defects and lack of cross penetration defects. Images from different insonification paths and scatter path will be presented and discussed. In chapter 5, results of 3D images constructed with the two pass method will be presented. The images were constructed from measurements on blocks with machined reflectors and with an actual weld with an embedded tungsten fragment. The machined reflectors are not very representative for real defects. However, the purpose of these reflectors is to demon- strate the characteristics of the two pass method. The real weld with the tungsten fragment can be considered to be a real defect. In chapter 6, artifacts in images from the direct longitudinal insonification and the direct transversal scattering paths (the L-T path) caused by waves from the direct longitudinal insonification and longitudinal scatter path (the L-L path) will be discussed. An analytical example will be given to demonstrate the presence and shape of such an artifact correspond- ing to a point scatterer. The artifacts will be illustrated in images from real measurements. In addition, a procedure will be presented to suppress these artifacts. In chapter 7 the conclusions of the research will be presented and discussed. Finally, in chapter 8, some more elaborate discussions will be presented and suggestions for improvements and further research will be given.

23 2 Wave theory and imaging In this chapter, the principles of the wave equation based imaging approach are presented. The wave theory will be presented that is used for imaging based on inverse wave field extrapolation of acoustic waves. It also will be demonstrated that this theory can be applied to elastic waves. The imaging approach will be demonstrated with a numerical example. Finally, some practical implementation aspects for 2D and 3D imaging will be discussed with the aid of the matrix notation. 2.1 Introduction of the imaging philosophy In ultrasonic NDI, the words image and imaging are often used for different treatments of ultrasonic data. Confusing is the difference in names that are used to address the imaging methods. For example, names that are used for imaging in NDI are synthetic aperture fo- cusing technique (SAFT), such as described by Mayer et al. [1990], Thomson [1984], Lorenz [1993], Burch and Burton [1984], Johnson and Barna [1983], inverse wave field extrapolation (IWEX) (see Portzgen [2006] or Portzgen [2004]) sampling phased array (see von Bernus et al. [2006] orChiao and Thomas [1994]) or total focussing method TFM (see Wilcox et al. [2006] or Holmes et al. [2005]). Ultrasonic imaging techniques roughly can be divided into three categories: [1] Techniques that display data in a clever way. Examples are B-,C-,D-scans, and sec- torial scans, see e.g. Krautkramer [1977] and R/D-Tech [2004]. In this category, almost no post processing is applied to the data. Mainly some noise filtering, thresh- olding or rectification of the A-scans. The image is constructed by stacking A-scans

24 20 Wave theory and imaging whereby the amplitudes are represented with a color or gray scale. This was briefly discussed in sections 1.3 and 1.4. The mapping channels, as discussed in section 1.3, are referred to as B-scans. [2] Techniques that remove propagation effects from source to defect and from defect to receiver. The already mentioned examples above are of this category, whereby the process to remove the propagation effects are carried out in different ways (like in the time-space domain or the frequency-space domain or by only using data with coinciding source-receiver position). The techniques of this category are all based on linear wave theory (the Born approximation). By linear wave theory we mean that the wave field is linear in the deviations of the media properties from the steel properties, of a particular weld configuration. As a consequence, waves that were caused by scattering resulting from insonification via other scatterers are not taken into account. The imaging approach as described in this thesis belongs to this cate- gory. Because our approach is based on inverse wave field extrapolation, we refer to this approach as the IWEX approach (Inverse Wave field EXtrapolation). [3] Techniques based on non linear wave theory. These techniques aim to find the model that explains the data, see Marklein et al. [2006] and Gisolf and Verschuur [2005]. The imaging techniques of this category are usually performed with an iterative approach and are therefore calculation intensive and time consuming. We will now continue with a more detailed explanation of the imaging approach from cat- egory two. A single A-scan forms one measurement of an upward traveling wave field, caused by a secondary source such as a defect. According to fundamental wave theory, a source can be reconstructed from measurements of the entire wave field. Wave fields can be extrapolated forward in time and space. For example, the wave field caused by a stone thrown into the water can be predicted later in time by extrapolating measure- ments earlier in time. The result would be a weaker and bigger circular wave field further away from the position where the stone was thrown into the water (i.e. the source location). The opposite is also possible. The wave field can be extrapolated to positions where the wave field passed earlier in time then when the measurements were taken. This process is called backward or inverse wave field extrapolation. The result is a stronger wave field closer to the source. With this process, all propagation effects can be eliminated so that the wave field converges at the location of the source and at the time when the source was activated. If the source was a secondary source, the strength of the inversely extrapolated wave field equals the reflectivity of the secondary source multiplied by the incident wave field. Seismic images are produced based on the principles of forward and inverse wave field extrapolation. With the development of ultrasonic arrays, substantial parts of the reflected or scattered wave field can be measured. Ultrasonic arrays are the key to applying the imaging approach developed in seismic exploration. Here, a source like a vibrator truck in the land situation or an air gun in the marine situation is used to generate waves that propagate into the subsurface. The upward traveling wave field caused by scattering of the incident wave field is recorded by an array of geophones. An image is constructed by inversely extrapolating the recorded wave fields to all points in an image space that correspond to the area of interest. If a diffractor was present at a point in the image space, the inverse propagated wave field will converge at that position at the time when it became a secondary source.

25 2.2 The Rayleigh II integral 21 That time equals the travel time from the source to this point. Thus, a general imaging process for a single analysis point in the image space consists of three steps: [1] Removal of the propagation effects from an image point to the receivers. This step is performed in the space-frequency domain with the Rayleigh II integral for back propagation. After this step, for every source location the data consist of a single recording of the scattered field, by a virtual receiver located in the chosen image point. [2] Removal of the propagation effects from the sources to the image point. When a well sampled source geometry is available, it can be demonstrated, using the argument of reciprocity, that this step also involves back propagation with the Rayleigh II integral. After this step, the full data set has been reduced to a single signal generated by a virtual source in the image point and detected by a single virtual receiver located in the same position. [3] At the image point, the amplitude at t = 0 of the coinciding virtual source - virtual receiver recording is assigned to that point as image amplitude. In seismic explo- ration, this step is called applying the imaging condition. The three steps must be repeated for each point in the image space. The L-L and L-T imaging modes are selected by using L-wave propagation velocity in steps 1 and 2, or by using transversal wave (T-wave) velocity in step 1 and longitudinal wave (L-wave) velocity in step 2, respectively. In de following sections the theoretical principles involved in the imaging process as de- scribed above will be further examined. 2.2 The Rayleigh II integral The basis of the imaging process is the possibility to extrapolate a wave field from known values at a certain surface to any location in space. Starting point of the imaging theory is the general Rayleigh II integral derived from the Kirchhoff integral (see e.g. Berkhout [1987]), formulated as, Z G P (~rA , ) = P (~r, ) dS, (2.2.1) n S where P (~r, ) is the temporal Fourier transform of the measured pressure field p(~r, t), ~rA is the position vector of a point A not on the observation surface S, ~r is the position vector of an observation point on S and ~n is the direction normal to the surface (see figure 2.1). Furthermore, is the angular frequency and G is the Greens function. If we assume that we are dealing with a homogeneous medium, the Fourier transformed pressure P (~r, ) in equation (2.2.1) obeys the Helmholtz equation: 2 2 P (~r, ) + P (~r, ) = 0, (2.2.2) c2

26 22 Wave theory and imaging Figure 2.1: The Rayleigh II integral describes how the wave field at point A can be computed from the wave field at observation surface S. where c is the sound propagation velocity in the medium. The Greens function G describes the wave field due to a point source in A, which is defined in a homogeneous medium as, 1 G = ej c r , (2.2.3) 2r where r =| ~r ~rA | is the distance between an observation point on S and the point source in A. The Greens function can be causal (G+ ) or anti-causal (G ). The causal Greens function is the wave field of a causal point source, whereas the anti-causal Greens function is the wave field of an anti causal point sink. When the causal Greens function is used in equation (2.2.1), the Rayleigh II integral can be used to extrapolate a measured wave field away from the source. On the other hand, the anti-causal Greens function can be used to extrapolate the wave field towards the source. In our application the sources are the defects that act as reflectors and/or diffractors. If a defect is hit by an incoming wave front, it starts to act as a secondary source or distribution of sources, depending on the shape and size of the defect. By spatially back propagation the wave field due to such a source (distribution), we can find its location and produce an image of the defect. Hence, for the purpose of imaging, the measured wave field must be extrapolated in a direction closer to the source (distribution) and as a consequence we must use the anti-causal Greens function. Furthermore, we choose the recording plane S with a normal vector in the negative z-direction. Substituting the anti-causal Greens function, equation (2.2.3), in the general formulation of the Rayleigh II integral for inverse wave field extrapolation, equation (2.2.1), yields (Berkhout [1987]): Z Z zA z0 1 j c r j r P (~rA , ) = P (~r, ) e c dxdy, (2.2.4) 2 r3 p with r = (x xA )2 + (y yA )2 + (z0 zA )2 and where z0 indicates the location of the recording plane. If a secondary source is present in A, extrapolation to that point results in focussing the energy of the secondary source at the time is was activated, i.e. at the time the incident field reached A. If we assume that P is independent of the y coordinate, a one dimensional version of the Rayleigh II can be formulated (Berkhout [1982]):

27 2.3 Wave field extrapolation in elastic media 23 Z j c (zA z0 ) 1 (2) P (~rA , ) = P (~r, ) H ( r)dx, (2.2.5) 2 r 1 c (2) where H1 ( c r) denotes the first-order Hankel function of the second kind and with p r = (x xA )2 + (z0 zA )2 . Equation (2.2.5) represents a convolution integral over the spatial coordinate x. A far field expression can be formulated for c r >> 1 (Abramowitz and Stegun [1964]): r Z j 1 P (~rA , ) c (zA z0 ) P (~r, ) ej c r dx. (2.2.6) 2 rr In our application, we examine carbon steel girth welds. Carbon steel is an elastic medium, hence two wave modes, longitudinal and transversal, can exist. The different wave modes can convert to each other during transmission and reflection. In the next section, it is discussed that equations (2.2.4), (2.2.5) and (2.2.6)also can be used for imaging of wave fields in elastic media. 2.3 Wave field extrapolation in elastic media The derivation of the Rayleigh II integrals for forward and inverse extrapolation was ob- tained with the use of the Greens functions given by equation (2.2.3), describing the wave fields of an acoustic point source and a point sink. For girth weld inspection, we cannot assume acoustic wave fields, since the involved metals are elastic media. Shear waves as well as compressional waves will occur, which means that we need to consider the elastic wave equation. 2D elastic waves can be described in the Fourier domain by two scalar potential functions and (Aki and Richards [2002]) obeying the scalar Helmholtz equations: 2 2 + = 0, (2.3.7) cp 2 and: 2 2 + = 0. (2.3.8) cs 2 Equation (2.3.7) describes the wave field of compressional (longitudinal) waves with sound velocity cl and equation (2.3.8) describes the wave field of shear (transversal) waves with sound velocity ct . From the displacement vector U ~l of the compressional wave can be found through U ~l = 1 2 , whereas the displacement vector U~t of the shear vertical waves follows from U~t = 1 2 ( , ). The significance of these results is that compressional z x and shear waves are uncoupled during propagation in a homogeneous medium and can be treated in the same way as acoustic waves. On reflection and transmission, compression waves can be converted to shear waves and vice versa. With the factor 1 2 in the definition for U~l and U~t , the wave potentials and have the dimension of pressure. At the front wall, all scattered energy is converted back to pressure. As a consequence, the recorded pressure data contains both the and arrivals, albeit with different scaling factors be- cause of the conversion from shear to compressional wave mode at the front wall.

28 24 Wave theory and imaging From equations (2.3.7) and (2.3.8) corresponding Greens functions can be derived. Both compressional and shear waves can be extrapolated in space using the Rayleigh II integrals with appropriate velocities. 2.4 The imaging condition We now define an image domain below a recording plane and we use a source located in the recording plane. Once the source is fired, for example one element of an ultrasonic array, the wave propagates downwards into the medium. The receivers record all the reflected and diffracted waves traveling upwards. The recorded wave field is now back propagated to a point A in the image domain. The back propagation removes all propagation effects from point A to the receivers. If a discontinuity is present in A, the back propagated wave field will have a non-zero amplitude at the moment that A became a secondary source, i.e. at the moment the incident wave field reached A. This principle is the so called imaging condition. Using the position of the original source location and forward propagation techniques such as ray tracing Cerveny [2001], it is easy to find the moment when A became a secondary source if a scatterer was present. For homogeneous media, this travel time can be found analytically. For point A in the image domain, the amplitude of the inversely extrapolated recordings at the time that A became a secondary source is selected and used as image amplitude. This process is repeated for all grid points in the image domain. This process is called Kirchhoff migration and can be repeated for all source location, after which all sub-images can be summed. The image amplitude is related to the scattering coefficient in point A. If the down- ward propagating wave field from the real source to point A is denoted by P (~r; ) and if the scattered field propagating from the secondary source to the receivers is denoted by P (~r; ), the scattering coefficient R(~rA ; ) is defined by P (~rA ; ) = R(~rA ; )P (~rA ; ), (2.4.9) and the image amplitude I(~rA ) is defined by Z I(~rA ) P (~rA , )ejtSA d, (2.4.10) where tSA is the travel time from the source S located at the surface to point A. If in A no discontinuity was present, the scattering coefficient, and consequently the sec- ondary source strength, is zero, resulting in a zero image amplitude. In the next section, an example of the imaging process will be presented.

29 2.5 An example of imaging with simulated acoustic data 25 1 depth in (mm) 2 3 4 5 6 2 4 6 8 10 12 lenght in (mm) Figure 2.2: Model to demonstrate the imaging process. On the top of the model 128 receivers are placed. The black dot represents a circular diffractor in a homogeneous media. 2.5 An example of imaging with simulated acoustic data To demonstrate the imaging process, we use an acoustic material with a longitudinal sound velocity cl = 2475 m/s. The thickness of the material is assumed infinite, or all boundaries are absorbing. We place an array of 128 transducer elements at level z = 0. For this example, a 2D acoustic finite difference simulation code was used, such as described by Reynolds [1978] and Youzwischen and Margrave [1999]. The element width is 0.05 mm and the spacing between two adjacent elements is also 0.05 mm, hence the heart-to-heart distance between two adjacent elements is 0.1 mm and the total aperture is 12.8 mm. The wavelet used in the simulations has a center frequency of 4 MHz and a 50% bandwidth. The widths of the elements are small compared to the dominant wavelength so that the wave front due to one element will not have a strong directivity and can be assumed cylindrical. At level z = 3 mm a discontinuity is present below the center of the array aperture. The model is illustrated in figure 2.2. We use element number 20 as a source, and we follow the wave field while it propagates downwards, is scattered by the discontinuity and propagates upwards back to the receivers. The sequence in figure 2.3 shows the result of the finite difference simulation. At t = 2.4 s we can see that the wave front hits the discontinuity. The discontinuity becomes a secondary point source at this time. At t = 3.8 s, the scattered wave field has reached the receivers of the transducer array that are above the diffractor. In figure 2.4 the recordings are displayed as a function of time. The data recorded on all 128 receivers due to the scattering of the secondary source has got the characteristic shape of a hyperbola, the linear and stronger recordings above the hyperbola are due to the direct arrival. Using equation (2.2.6) the recorded data can now be back propagated in space. The result of back propagating the data to a point in the image space corresponds to a virtual recording of the wave field, taken at that position. Back propagation to all image points on a horizontal line in the image space can, therefore, also be regarded as virtually placing the receivers at that depth.

30 26 Wave theory and imaging (a) t = 1.0 s (b) t = 2.4 s, time of (c) t = 3.8 s imaging condition Figure 2.3: Results of finite difference simulation of a source located at position 20. The wave front propagates downwards and reflects at the diffractor at t = 2.401 s. 0 1 2 3 time in s 4 5 6 7 8 20 40 60 80 100 120 receiver number Figure 2.4: Recordings of the diffracted wave front in figure 2.3 on the 128 receivers. The diffraction response has the typical hyperbolic shape, with the apex located at the lateral location of the reflector (position 64). The two straight events are due to the direct field that is also recorded.

31 2.5 An example of imaging with simulated acoustic data 27 1 1 1 2 2 2 3 3 3 time in s time in s time in s 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 20 40 60 80 100 120 20 40 60 80 100 120 20 40 60 80 100 120 receiver number receiver number receiver number (a) Virtual receivers at (b) Virtual receivers at (c) Virtual receivers at depth = 1 mm depth = 2 mm depth = 3 mm Figure 2.5: Recordings of figure 2.4, inverse extrapolated to different depth levels. The sequence in figure 2.5 illustrates the back propagating process. The recorded data is back propagated to a number of virtual receiver levels with an increasing depth. At a depth of 3 mm, we see that the data is focussed at the position of the discontinuity at a virtual recording time of 2.4s. To find the contribution to the image in that point, we must apply the imaging condition, i.e. we calculate the time at which the secondary source was activated by the source wave field from source at location number 20. For the defect at 3 mm depth this time is t = 2.4 s. In figure 2.5c, we can see that the data focusses exactly at that time, thus giving a large image amplitude at that location. If we repeat the imaging process for each point in the image space, we obtain an im- age based on a single source (element number = 20) and all 128 receivers. The result is presented in figure 2.6. The maximum image amplitude is found at the position of the discontinuity. In the image of figure 2.6 we can see two weak curves crossing the maximum point. These curves are caused by the finite aperture of the receiver array. These effects can be reduced strongly when we combine the images obtained from several source positions, and by spatial tapering of the data records before inverse wave field extrapolation. As an example, we repeat the imaging process with elements 10, 20, 30,..., 120 as source elements and add the resulting images. The result is presented in figure 2.7. The amplitudes contributing to a point in the image space of each source should be cor- rected for the spherical spreading from that source to the image point. If the sources are small compared to the wavelength, the geometrical spreading is described by the Greens function in equation (2.2.3). For a point in the image domain, the contribution of all sources can be described again as the Rayleigh integral for inverse wave field extrapolation of common receiver records, using the argument of reciprocity and under the condition that the sources are closely spaced compared to the wavelength. Hence, the full imaging process can be represented by two inverse propagation steps. For all sources the recorded wave field is inversely propagated to a point in the image domain. Then, the virtual common

32 28 Wave theory and imaging 1 depth in (mm) 2 3 4 5 2 4 6 8 10 12 distance in (mm) Figure 2.6: Image obtained with a single source and all 128 receivers. The image shows highest energy at the location of the circular reflector from figure 2.2. Also two tails are visible because of a limited receiver aperture. The asymmetric shape of the artifacts is due to the oblique illumination from the single source at element number 20 (at distance 2 mm). 1 distance in (mm) 2 3 4 5 6 0 2 4 6 8 10 12 distance in (mm) Figure 2.7: Stacked image obtained with images from sources 10, 20, 30,..., 120 and all 128 receivers. The tails visible in figure 2.6 have largely disappeared. receiver record with sources still at the acquisition surface, is inversely propagated to the same point in the image domain. If we compare the image in figure 2.7 with the original model in figure 2.2, we can conclude that imaging by inverse wave field extrapolation is possible for this single point defect. A discontinuity with an irregular shape like a crack or lack of fusion defect, will behave as a distribution of point defects, all of which will be imaged in their correct positions. This allows a more accurate sizing and determination of the orientation of the defect. In the example presented in figure 2.2 no reflective boundaries were present. In practical situations responses caused by reflections from the back wall will also be recorded. In most metals, different wave modes are generated during transmission or reflection at boundaries. The waves generated by mode conversion will also appear in the measured data. In the next chapter the effect of boundary responses on the image calculated with the described procedure will be discussed. First, we will discuss some numerical implementation aspects, in the next section.

33 2.6 2D imaging implementation using the matrix notation 29 x (xn , 0) x n=1 n=N z rm,n zA (xm , zA ) m=1 A m=M Figure 2.8: The Rayleigh II integral for back propagation can be formulated in discrete matrix notation. 2.6 2D imaging implementation using the matrix notation According to the Rayleigh II integral for inverse propagation equation (2.2.4) zero spaced pressure measurements are required over an infinitely wide area. In addition, the source positions should be varied over the same area with the same spacing to acquire total insonification of the defects. In practice, recordings will be taken along a finite aperture on a limited number of locations and with a discrete set of source locations. For our ultrasonic measurements, linear arrays with typically 64 elements are used. The one-dimensional Rayleigh integral of equation 2.2.6 can be written as a sum over all the available receiver elements (figure 2.8). With z0 = 0 this yields: r N j c X zA P (xm , zA ; ) P (xn , 0; ) p ej c rm,n x, (2.6.11) 2 n=1 rm,n rm,n with P (xm , zA ; ) being the Fourier transformed pressure at an image point A located at (xm , zA ), P (xn , 0; ) the pressure recorded at element number n, N the total amount of recorder elements, x the heart-to-heart distance of the recorder elements and rm,n = p 2 (xn xm )2 + zA , with xn = (n1)x (figure 2.8). Note that in principle the summation in equation (2.6.11) should be infinite. Through the limited length of the receiver array, artifacts may arise as discussed earlier. We now write equation (2.6.11) as, N X P (xm , zA ; ) = Qm,n P (xn , 0; ), (2.6.12) n=1 where we have defined Qm,n as, r j c ej c rm,n Qm,n x p . (2.6.13) 2 rm,n rm,n

34 30 Wave theory and imaging Equation (2.6.12) can be formulated as a vector product: P (xm , zA ; ) = Q ~ (0; ), ~ Tm (zA ; 0; )P (2.6.14) or similarly, 0 1 P (x1 , 0; ) B B P (xn , 0; ) CC P (xm , zA ; ) = Qm,1 Qm,n . . . Qm,N B B .. C. C (2.6.15) . A P (xN , 0; ) Equation (2.6.14) formulates the discrete Rayleigh II integral for back propagation in vector notation for a single point that was insonified by a single source. The notation can be extended to a matrix vector operation so that it accounts for more points at depth level zA . The result yields, ~ (zA ; ) = Q(zA ; 0; )P P ~ (0; ), (2.6.16) or similarly, 0 1 0 10 1 P (x1 , zA ; ) Q1,1 Q1,n . . . Q1,N P (x1 , 0; ) B C B CB B P (xm , zA ; ) C B Qm,1 Qm,n ... CB P (xn , 0; ) C C B C =B CB C, (2.6.17) B .. C B .. .. .. CB .. C . A . . . A . A P (xM , zA ; ) QM,1 QM,N P (xN , 0; ) where m = 1, 2, ...M with M the total number of image points and with Q(zA ; 0; ) the so called inverse propagation operator. It can be demonstrated for homogeneous media that Q(zA ; 0; ) takes the form of a Toeplitz structure, meaning that elements along diagonal directions are identical. The matrix Q(zA ; 0; ) removes the propagation effects from each of the M points in the image space to all the N receivers. In fact, for a single point located in (xm , zA ), all the receiver positions are redatumed to a virtual point located in (xm , zA ). Later, this virtual point will be used together with the argument of reciprocity, to remove also the propagation effects from all the sources to this virtual receiver point. Equation (2.6.16) can be used for the back propagation of a wave field that was caused by scatterers that were insonified by a single source element. Like the extended formulation from one image point to several image points, we can extend equation (2.6.16) for more source elements, with a maximum of N elements. Then, the vectors P ~ (0; ) and P ~ (zA ; ) become matrices, which yields: P(zA ; 0; ) = Q(zA ; 0; )P(0; 0; ), (2.6.18) with 0 1 P (x1 , zA ; x1 , 0; ) P (x1 , zA ; xn , 0; ) . . . P (x1 , zA ; xN , 0; ) B B P (xm , zA ; x1 , 0; ) P (xm , zA ; xn , 0; ) . . . P (xm , zA ; xN , 0; ) CC P(zA ; 0; ) = B B .. .. .. C, C . . . A P (xM , zA ; x1 , 0; ) P (xM , zA ; xN , 0; ) (2.6.19)

35 2.6 2D imaging implementation using the matrix notation 31 and 0 1 P (x1 , 0; x1 , 0; ) P (x1 , 0; xn , 0; ) . . . P (x1 , 0; xN , 0; ) B B P (xn , 0; x1 , 0; ) P (xn , 0; xn , 0; ) . . . P (xn , 0; xN , 0; ) C C P(0; 0; ) = B B .. .. .. C. C (2.6.20) . . . A P (xN , 0; x1 , 0; ) P (xN , 0; xN , 0; ) Matrix P(0; 0; ) contains the Fourier transformed data of all source-receiver combinations for one temporal frequency. Each column refers to a source position and each row refers to a receiver position. Matrix P(zA ; 0; ) contains the pressure recordings of upward traveling waves at virtual receivers located in (xm , zA ) for one frequency , i.e. this is one complex number. When all the recorded wave fields are back propagated to all the M points, the imag- ing condition must be applied for all the N sources to find the imaging amplitudes. In fact, we must remove the propagation effects from the sources to the imaging points located on depth level zA . We can do this efficiently with the argument of reciprocity. This means that we may switch receiver locations with source locations. Hence, all the virtual receivers located in the points (xA , zm ) become sources and all the sources located at the surface be- come receivers. To remove the propagation effects from the new virtual source locations to the new receiver locations, we can use the back propagation matrix Q(zA ; 0; ) again. We must transpose this matrix since we have switched the sources and receivers. Multiplying both sides of equation (2.6.18) with QT (0; zA ; ) yields, P(zA ; 0; )QT (0; zA ; ) = Q(zA ; 0; )P(0; 0; )QT (0; zA ; ). (2.6.21) The result of equation (2.6.21) can be interpreted as pressure recordings of upward traveling waves by virtual receivers located at depth level zA , caused by virtual sources also located at depth level zA , hence P (zA ; zA ; ) = Q(zA ; 0; )P(0; 0; )QT (0; zA ; ). (2.6.22) Similar to equation (2.4.9), we can define the upward traveling wave field as the downward traveling wave field multiplied by a matrix that contains scattering coefficient, P (zA ; zA ; ) R(zA ; )P (zA ; zA ; ). (2.6.23) The physical interpretation R(zA ; ) is difficult. The diagonal elements are the scattering strengths of defect scatterers along depth zA . Interpretation of the diagonal elements is meaningful only for plane reflection interfaces. In seismic exploration, this is often a real- istic condition, but in weld inspection this condition is only met for planar defects that are large compared to the wavelength. Because the virtual sources and receivers are located at the same depth level zA in equation 2.6.23, we can find the imaging amplitudes for image points located at this level by apply- ing the imaging condition at t = 0. This yields a summation over all relevant frequency components. For the imaging amplitudes I(z ~ A ) we can define, K X ~ A) I(z diag[R(zA ; k )P (zA ; zA ; k )], (2.6.24) k=1

36 32 Wave theory and imaging where k are the discrete frequency components and K is the total number of frequency components. Note that we have selected the elements on the diagonal of the matrix. This diagonal represents the pressure recordings from virtual receivers caused by virtual sources located at coinciding locations. In case scatterers are present at depth level zA , the ele- ments on the diagonal of R(zA ; k ) will have a non-zero value. From equation (2.6.24) we can see that the image amplitude is also determined by the downward traveling wave field P (zA ; zA ; k ). Usually, this wave field is caused by a band limited source. The signature of this source is recognized in the image. For the implementation as described above, we assume that the data of all source-receiver combinations are available and the matrix P(0; 0; ) is completely filled. Due to practical limitations, it is possible that only the data can be obtained for the source-receiver combi- nations that have the same position. This is called zero offset data and in this case only the diagonal of matrix P(0; 0; ) is available. For 3D imaging, we will use linear arrays to measure the full data matrix in the direction parallel to the array, this is called the in-line direction. This can be done for many positions along the surface, so that zero offset data is obtained in the direction perpendicular the the array, the cross-line direction. In the next section, it will be discussed how zero-offset data can be processed efficiently. 2.7 2D Zero offset imaging Here, we will discuss the case when recordings are taken with coinciding transmitter and receiver positions. Such a data set is usually referred to as zero offset, meaning that only the diagonal of the data matrix P(0; 0; ) is filled with data. Note that for primary reflec- tions in zero offset data the path from source to scatterer is the same as the path from scatterer to receiver. The data matrix contains the recorded data of N experiments. If only the diagonal of this matrix is filled, we can interpret the diagonal as a vector that contains the recordings on all the N receiver positions as though they were recorded from a single experiment, whereby the scatterers in the subsurface are considered point sources that ignite at once, see figure 2.9. To account for the travel path from the surface to the scatters and back in reality, the waves caused by buried sources must travel with half the medium sound velocity. This interpretation is the well known exploding-reflector model, as used by Claerbout [1985], Loewenthal et al. [1976], Schnneider [1978] and Mland [1988]. Spherical spreading should be corrected before the exploding reflector model can be ap- plied. We can write the vector with zero offset recordings as, ~zo (0; ) = diag[P(0; 0; )], P (2.7.25) ~zo (0; ) the vector that contains the frequency components of the Fourier trans- with P formed pressures of the zero offset measurements compensated for spherical spreading. Note again that we consider this now as one physical experiment. In order to find the imaging amplitudes, we must back propagate the recordings with the Rayleigh II integral

37 2.7 2D Zero offset imaging 33 x (xn , 0) x n=1 n=N z rm,n zA m=1 (xm , zA ) m=M Figure 2.9: Zero offset imaging can be done with data of coinciding transmitter and receiver location. Zero offset imaging can be interpreted by back propagating the wave field of an exploding source located in A with half the medium velocity. for back propagation (equation (2.2.6)), using half the medium sound velocity, hence s Z j 2 zA 2 P (xm , zA ; ) = c Pzo (0; ) ej c r dx. (2.7.26) 2 rr Since it is assumed that the exploding reflectors are located in the subsurface, a second back propagation step to compensate for the propagation effects from the real sources (located at the surface) to the scatterers, can be omitted. Similar to equation (2.6.12), equation (2.7.26) can be written in a discrete notation for a limited number of sources and receivers, N X Pzo (xm , zA ; ) = Qm,n Pzo (xn , 0; ), (2.7.27) n=1 with Qm,n defined by equation (2.6.13) with half the medium sound velocity. Following the same steps of the previous section, we may write for more points on depth level zA in matrix-vector notation, ~zo (zA ; ) = Q(zA ; 0; )P~zo (0; ), P (2.7.28) where P~zo (zA ; ) contains the Fourier transformed pressures at depth level zA . The imaging condition must be applied to P ~zo (zA ; ), since the reflectors exploded at t = 0. We may write similarly to equation (2.6.24) of the previous section, for the image amplitudes, K X ~ A) = I(z ~zo (zA ; k ). P (2.7.29) k=1

38 34 Wave theory and imaging Equation (2.7.28) implies only a matrix vector multiplication. This operation is more efficient to evaluate with a computer then equation (2.6.24) for all source-receiver combi- nations, derived in the previous section. Therefore, it will require less computer operations and hence, less calculation time. Note, however, that zero offset measurements do not carry the same information as full offset measurements. In the next section, we will discuss 3D imaging by using both 2D imaging approaches in combination. Given the nature of the experiments, we will see that the first 2D imag- ing step will involve all source receiver combinations of equation (2.6.24), and the second 2D imaging step will involve zero offset imaging of equation (2.7.28) in the perpendicular direction. 2.8 3D imaging with linear arrays, the two pass method In theory, it is possible to construct a 3D image from ultrasonic data with the use of the 2D Rayleigh integral for back propagation given by equation (2.2.4). To evaluate the integral, recordings are necessary over a surface area S. For a good reconstruction of a defect, also sources are required over the same surface area for insonification in all direction. With a linear array, all combinations of transmitters and receivers can be measured over the line where the array is located. To obtain all the combinations of transmitters and receivers over a surface area, a 2D matrix array is required. Ultrasonic matrix arrays have already been studied, manufactured and used in the medical application field (Whittingham [1999], Fenster [2001]) and for NDI (Jesse and Smith [2002], Mahaut et al. [2004]). Although the technology is available, acquiring the data can be quite time consuming and requires a huge data storage capacity. In addition, processing the data into an image is also time consuming and, therefore, not yet practical in real time. The same issues can be found in seismic exploration, where a full areal source and receiver grid is not feasible in practice. In this application field, these issues have been studied and published. An efficient approach to 3D imaging was developed, that consists of two cascading 2D imaging processes in orthogonal lateral directions whereby a 3D scheme is obtained (Jakubowicz and Levin [1983] and Gibson et al. [1983]). This 3D scheme, called the two pass approach, is exact for homogeneous media as proved by Jakubowicz and Levin [1983]. In this section, we will describe the two pass approach that is used to obtain 3D images with ultrasonic linear array data. In a first pass, all lines in one direction (say the in-line direction of the linear array) are imaged by means of a 2D algorithm. In the in-line direction, all source-receiver com- binations can be obtained so that the implementation as described in section 2.6 can be applied. The images are then converted to a new data set that is sorted into lines in the or- thogonal direction and then 2D imaged in that direction, say the cross-line direction. With the use of linear arrays, only zero offset data is available in the cross-line direction. As a consequence, we may use zero offset imaging as described in section 2.7 for the second pass. In the space-frequency domain, the first pass of the process can be described as follows. The data must be Fourier transformed in the time direction. Then, 2D images in the

39 2.8 3D imaging with linear arrays, the two pass method 35 in-line direction (say parallel to the x-coordinate) must be constructed for each cross-line position (say parallel to the y-coordinate). With equation (2.2.6) we can back propagate the measured wave field of a single source S located at (xS , y, 0) to a depth level zA for each cross-line location y, this yields r Z j zA P (xS , y, 0; xA , y, zA ; ) = P (xS , y, 0; xR , y, 0; ) ej c rR dxR , 2c rR rR (2.8.30) where P (xS , y, 0; xR , y, 0; ) are the Fourier transformed pressure recordings at z = 0, P (xS , y,p0; xA , y, zA ; ) are pseudo-pressure recordings of virtual receivers located at zA , 2 2 rR = (xR xA ) + zA where xR is the x-coordinate of the receivers and where zA is the (generally incorrect) position to which the scatterers have been imaged. All source locations can be taken into account by applying equation (2.2.6) again. This yields, Z Z 2 j c (rR +rS ) j zA e P (xA , y, zA ; xA , y, zA ; ) = P (xS , y, 0; xR , y, 0; ) dxR dxS , 2c rR rR rS rS p (2.8.31) where rS = (xS xA )2 + zA 2 and where P (xS , y, zA ; xA , y, zA ; ) represents the Fourier transformed pseudo-pressure recordings of upward traveling waves measured by virtual re- ceivers located at zA , caused by scattered downward traveling waves generated by virtual sources also located at zA . In order to find the imaging amplitudes I(xA , y, zA ) of the 2D images for all cross-line positions, we must apply the imaging condition at t = 0. This yields integration of equation (2.8.31) over all frequencies: Z I(xA , y, zA ) p (xA , y, zA ; xA , y, zA ; 0) = P (xA , y, zA ; xR , y, zA ; )d. (2.8.32) In the second pass of the process, we convert the 2D images obtained in the first pass with equation (2.8.32), to pseudo-pressure recordings. Because only zero offset recordings are available, we will use the zero offset imaging approach as was described in section 2.7 for the second pass. We assume that the medium is homogeneous so that we can convert the space dimension of zA to time with the sound velocity, we define p (xA , y, 0; t) p (xA , y, zA ; xA , y, zA ; 0), (2.8.33) with 2zA . t (2.8.34) c We can consider p (xA , y, 0; t) as a zero offset data set. The factor 2 in equation (2.8.34) compensates for the double travel paths of the zero offset data. In order to obtain the imaging amplitudes, we apply equation (2.2.6) once to the Fourier transformed zero offset data, r Z j zA 2 P (xA , yA , zA ; ) = P (xA , y, 0; ) ej c r dy, (2.8.35) 2c rr

40 36 Wave theory and imaging in-line direction cross-line direction - y- x ? t (x0 , y0 , T0 ) si K s (x , y, t ) ? t 0 0 (x, y, t) s Figure 2.10: The amplitude at an arbitrary point (x, y, t) can be mapped to the apex (x0 , y0 , T0 ) either directly or in a two-step process. where P (xA , yA , zA ; ) is the Fourier transformed pressure in point p A = (xA , yA , zA ), P (xA , y, 0; ) is the Fourier transformed zero offset data, and r = (y yA )2 + zA . The image amplitudes for the final 3D image can be obtained by applying the imaging condition at t = 0 to equation (2.8.35), hence Z I(xA , yA , zA ) p (xA , yA , zA ; 0) = P (xA , yA , zA ; )d. (2.8.36) An intuitive proof of the two pass process for zero offset data was given by Gibson et al. [1983], where 3D imaging is regarded as a summation over trace (A-scan) amplitudes along the surface of hyperboloids in the space time domain, corresponding to diffraction paths and placing each sum at the apex or minimum-time position of the associated hy- perboloid. For a medium of constant velocity c, the surface of the hyperboloids are given by, 4(x x0 )2 4(y y0 )2 t2 = T02 + 2 + , (2.8.37) c c2 where x and y are orthogonal coordinates on the recording surface, and t is the two-way time at position (x, y) on the hyperboloid. The hyperboloids apex is at position (x0 , y0 ) and time T0 , as illustrated in figure 2.10. Summation to obtain the output amplitude at a fixed apex position (x0 , y0 , T0 ) can be viewed as a mapping of reflection amplitudes from the flank positions t(x, y) that satisfy equation (2.8.37). A property of the hyperboloids is that any vertical plane that intersects the hyperboloid contains a hyperbola characterized by the

41 2.8 3D imaging with linear arrays, the two pass method 37 same velocity c. The total summation can be done in two steps as illustrated in figure 2.10. First a temporary sum over a hyperbolic path in the x-direction is done for each value of y. The temporary sums will be placed at a local apex position at (x0 , y, t0 ). Then in the second step, these temporary sums are themselves summed along the hyperbola in the x-direction. The resultant amplitude at the apex point (x0 , y0 , T0 ) is the image amplitude at that point. In the next chapter, practical aspects to apply the theory described in this chapter will be discussed. Based on weld properties and acceptance criteria, array requirements like element size and frequency content of the signal, will be derived from resolution analysis.

42 38 Wave theory and imaging

43 3 Application of imaging techniques for weld inspection In this chapter, an overview of the most common weld properties is given, together with the practical consequences for imaging1 . It will be illustrated that most defects and their characteristics are related to the weld properties and to the welding process. Not all defects will cause a failure and, therefore, acceptance criteria have been developed. In this chapter, the requirements for the quality of images of defects will be derived based on these criteria. Finally, given the practical restrictions and requirements, some aspects of the resolution will be discussed. 3.1 Properties of girth welds in pipelines and defects Pipelines can be found all over the globe, both on-shore and off-shore, for the transportation of various products like oil and gas. The diameter of pipelines vary from 10 to 50 and the wall thickness from 5 mm to 35 mm. The pipeline and the weld properties depend on the product that is transported by the pipeline and of the location of the pipeline. The type of defects that can occur in newly constructed girth welds are, therefore, a result of the properties related to the pipe and the weld. Properties that influence the defect characteristics are, for example: 1 The application of imaging based on inverse wave field extrapolation to girth weld inspection was patented in July 2005, Int.Cl. G01N29/10 request number 1025267.

44 40 Application of imaging techniques for weld inspection The welding process, such as arc welding processes like gas metal arc welding (GMAW) or shield metal arc welding (SMAW). A good overview of most different welding pro- cesses can be found on www.Key-to-Steel.com. Depending on the welding process, defects like copper inclusions or hydrogen cracking (after the weld is finished) can occur. Also cold lap defects may be a result of the welding process, when two succes- sive welding layers were not fused properly. Furthermore, the welding can be done manually or automated. Both approaches can cause different defects. The weld bevel design, such as CRC weld preparation, narrow gap preparation or V-preparation. The weld bevel design determines the orientation of lack of fusion defects. Lack of fusion defects occur when the weld material does not fuse to the pipe, leaving a small air gap at the weld bevel. The pipe material and welding material (in this thesis, we will consider carbon steel pipelines and welds only). The welding material is usually related to the welding process. Different weld materials cause different types of defects. For example, the composition of the welding material can cause defects like slag inclusion or gas inclusions (porosity). In case the pipe is not perfectly cylindrical or wall thickness variations are present, hi-low defects can occur. These defects are caused by the miss alignment of the two pipes. The environmental conditions, like temperature, humidity, dirt, etc. Environmental conditions can cause lack of fusion defects or solidification cracks when the liquified welding material cools down too fast. Moist may be trapped into the welding bath and can cause hydrogen cracking or water vapor inclusions. The welder skills or, in case of automated welding, the equipment settings. Defects like incomplete penetration, burn through or undercut may be a result of poor welder skills. Welding is a sensitive process. When equipment settings for automated weld- ing are not optimized, all sorts of defects can occur. Figure 3.1 illustrates the location and nature of weld defects, according to Ginzel [2006]. Defects can be categorized as lack of fusion, incomplete penetration, lack of cross penetra- tion, volumetric defects and missed edge (surface breaking lack of side-wall fusion). Planar defects like cracks and lack of fusion have a relatively large surface area that can reflect the ultrasound. These type of defects can therefore be detected with low sensitivity. However, planar defects have a high directivity preference. This can even result in a reflection of the insonifying ultrasound to a direction where no receiver is located and hence, the defect will not be detected. The orientation of lack of fusion defects is usually assumed to be parallel to the weld preparation. The angle of the weld preparation and hence the assumed orientation of the lack of side wall fusion defects can vary from 0 to 45 with the normal direction to the surface. The high angles (30 to 45 ) are common in the root and in the first fill zone (indicated by zone 6 in figure 3.1) for CRC and narrow gap weld preparations. These type of weld preparations are mainly used when the welding process is automated. Also, the high angles are common for V- and X-weld preparations. These type of weld preparations are mainly used for manual welding. Lack of fusion defects with small angles (0 to 10 ) are common in subsequent fill zones like zones 1 to 4 in figure 3.1. Other defects with a small angle can also occur in the so called LCP zone (zone 5 in figure 3.1) or in the center of the weld (solidifying cracks). Defects with an orientation close to 90 for example cold lap defects when two fill layers do not fuse sufficiently, can also occur. In

45 3.1 Properties of girth welds in pipelines and defects 41 lack of fusion cap zones 1 undercut copper / slag inclusion 2 solidification crack cold lap 3 lack of fusion typical porosity 4 lack of cross penetration 5 root bead porosity 6 hi-low Figure 3.1: Overview of defects that are common in girth welds. The weld in this example has got a CRC weld preparation. The zones defined here refer to the welding layers. summary, the orientation of planar defects that can occur in girth welds ranges from 0 to 90 . However, as a rule of thumb, the majority of the defects will be orientated in the range from 0 to 10 and from 30 to 45 . Volumetric defects like porosity and slag or copper inclusions will cause the ultrasound to scatter in all directions. Therefore, the detection is less dependent on the directivity properties and position of the transmitter and or receiver. However, to find these type of defects, a higher sensitivity is necessary because the ultrasonic energy will decrease as a result of spreading of the wave fronts. Volumetric defects are usually expected in the volume of the weld and in the root. Porosity occurs as clusters of pores in a nest. Al- though these nests can be detected, with standard ultrasonic techniques it is difficult, to identify the individual pores in a porosity nest. In section 3.4, the resolution that theo- retically can be achieved with imaging by inverse wave field extrapolation will be discussed. Welds will typically have a reinforcement at the cap and the root. The geometry of the reinforcement are the weld beads as is illustrated in figure 3.1. Although the cap and root are irregular, the ultrasound will reflect at the same area causing a particular pattern when scans are recorded, around the circumference. Defects like under-cut or hi-low will cause discontinuities in the geometry, this is visible as a change in the pattern in standard auto- mated ultrasonic testing. The consequence of the cap reinforcement for imaging by inverse wave field extrapolations is the limited accessability. Because of the irregular geometry, no transmitters and/or receivers can be placed on top of the cap. Hence, the accessible aperture will have a gap. In this thesis, we will discuss the case when the weld cap is removed so that the full aperture is accessible.

46 42 Application of imaging techniques for weld inspection Inhomogeneities in girth welds detected with ultrasonic inspection are not always defects that will cause rejection of the weld. In the next section, an overview will be given of the different acceptance criteria for inhomogeneities that are prescribed by codes and stan- dards. From the acceptance criteria, the requirements for the resolution of the images can be determined. 3.2 Rejection criteria Once an inhomogeneity is detected or identified in an image, it must be assessed according to acceptance criteria to determine if the inhomogeneity is considered a defect. In that case, the weld is rejected and requires repair or replacement. For automated ultrasonic girth weld inspection, two types of acceptance criteria exist: [1] acceptance criteria based on good workmanship, and [2] acceptance criteria based on fracture mechanics or engineering critical assessment (ECA) A good overview and detailed discussion on these two types is given by Ginzel [2006], the following will be a summary of this work. Traditionally, workmanship criteria were developed for manual welding. These were based on what a good welder could do consistently and the assessment has been based on what was seen visually and by radiography. Acceptance criteria based on good workmanship have proved to be safe. However they have no basis in terms of pipeline design, or the materials used in the construction. These criteria do not consider any physical failure mechanism that would lead to probability of failure distributions. Consequently, good workmanship criteria are very conservative and aim to monitor welders performance rather than evaluate weld integrity. Examples of codes for automated girth weld inspection based on workmanship are (after Ginzel [2006]): API 1104 API [1999] The Australian Standard (AS) 2885.2 -2002 Pipelines-Gas and liquid petroleum Part 2: Welding clause 22 The Canadian Standard (CSA) Z662 for Oil and Gas Pipeline systems The International Standard Organization ISO 13847 Petroleum and natural gas in- dustries - Pipeline transportation systems - Welding of pipelines (published in 2000) Det Norske Veritas (DNV) OS F101 Submarine Pipeline Systems As parameters in materials involved in the pipeline construction (pipe and welding) became better understood and new welding processes were developed that put less emphasis on the welders skill, fracture mechanics principles became more suitable as acceptance criteria. The acceptance criteria are based on the actual applied stress and measured material prop- erties and use calculations to determine actual flaw size that would cause a failure. Before an assessment of allowable flaw size can be made, the material used for the pipe-line con- struction must be assessed for its toughness. This is in fact the ECA and it will determine

47 3.2 Rejection criteria 43 250 NEN 3650 DNV EPRG Tier 2 200 API 1104 BS 4515 (PD 6493) defect length mm 150 100 50 0 0 2 4 6 8 10 defect height mm Figure 3.2: Comparison of acceptance criteria for different techniques and codes for a 15.3 mm thick, 24 diameter pipeline (after Krom et al. [2000]). the most likely mechanism of metal failure. The assessment can be made by empirical ex- amination of the material or by the use of numerical computer models or a combination of those two. The standards listed above also provide guidelines to use ECA rejection criteria. They make use of different computational models or use other standards as reference. For example, API 1104 in its Appendix A has one set of calculations for fractures based solely on brittle fracture. The AS 2885.2 references BS 7910 (1999) Guide on the methods for assessing the acceptability of flaws in metallic structures. The ISO 13847 and CSA Z662 use guidelines from the British Standard (BS) PD6493 Guidance on methods for assessing the acceptability of flaws in fusion welded structures (London UK 1991). The fact that there are many different codes and standards with different acceptance crite- ria for defects in girth welds illustrates that it is difficult to define an unambiguous defect height and length that can be used for resolution analysis of the inverse wave field imaging approach. In addition, the acceptable defect length and height can be dependent on each other, on the nature (planar of volumetric) and location (sub- surface or surface breaking) of the defect and on the wall thickness. A comparison of different NDT techniques and ac- ceptance criteria for different codes was performed by Krom et al. [2000] for a 24 diameter pipeline with a wall thickness of 15.3 mm. Figure 3.2 compares the allowable defect length related to the defect height for this case. A similar plot can be found in Ginzel [2006] for a 42 diameter pipeline with a wall thickness of 17 mm. Plots like figure 3.2 can be used to give a rough estimate of the defect lengths and heights of interest. Depending on the wall thickness, the maximum allowable defect length will be in the order of 10 mm and the maximum allowable defect height will be in the order of 3 mm. These numbers can be used as guidlines to determine the requirements for the imaging equipment. Although the codes and standards give clear guidelines for the maxi- mum allowable defect length and height, no requirements are given for the tolerance of the

48 44 Application of imaging techniques for weld inspection determined defect sizes and reproducibility of the measurement. For this thesis, we will assume that the maximum variance on the determined defect size should not exceed 1 mm for the defect height and 2 mm for the defect length. Volumetric defects are also considered in most codes and standards listed above, although in a different way and not in such a straightforward way as cracks or planar defects. For example, API 1104 states that volumetric clusters may not exceed 13 mm as maximum dimension and an individual volumetric defect may not exceed 6 mm in both width and length. AS 2885.2 states that slag inclusions require assessment of flaw width, which is not to exceed 2 mm, individual pores may not exceed 3 mm in diameter or it may not exceed 25% of the thinner of the nominal wall thicknesses joined. For the inverse wave field extrapolation imaging approach, we will aim to resolve two 2 mm diameter pores or less. With the roughly estimated defects sizes of interest as presented in this chapter, based on the codes and standards, the frequency of ultrasound and array element requirements can be determined. The ultrasonic waves must be well digitized in time and space in order not to loose any vital information. This will be treated in the next section. 3.3 Spatial and temporal sampling In the previous section, the type and size of critical defects were discussed. Based on this information, the design and properties of the measurement system can be determined. For the imaging of defects with ultrasound, the frequency range or temporal bandwidth must be chosen such that the defects can be detected and characterized with sufficient resolution. If the frequency of the ultrasound is too low, defects may be missed or not sized with suf- ficient resolution. If the frequency is too high, the waves may attenuate due to scattering at grain boundaries. The surface area required to transmit and receive all the signals of interest will usually not exceed 20 cm. The girth weld is located in the center of this surface area. The upward traveling waves must be measured over this aperture. Analogue signals generated by the piezoelectric elements of the arrays must be digitized. To avoid temporal aliasing, the sample frequency fsamp must be higher then twice the highest frequency in the temporal bandwidth: fsamp = 2fN yquist > 2fmax , (3.3.1) where fmax is the highest frequency in the bandwidth generated by the source elements that will be used for imaging and fN yquist is the Nyquist frequency, which is defined as half the sampling frequency. In practice, array transducers with a center frequency between 1 MHz and 10 MHz are common with a bandwidth varying from 50% to 95%. The cor- responding wavelengths for transversal and/or longitudinal waves vary from 0.5 mm to 6 mm. Before the signals are digitized, an analogue low pass filter will be used to ensure that the temporal bandwidth is limited and will not cause aliasing. The sampling frequency is usual well above 50MHz for most ultrasonic array systems.

49 3.3 Spatial and temporal sampling 45 r a p P (, r; ) Figure 3.3: Configuration of the elements of an ultrasonic array, with element size a, pitch p and arrival angle of the wave field . The upward traveling wave fields are digitized in space by the array, whereby the spa- tial sampling frequency depends on the element heart-to-heart separation. This distance is usually called the pitch. To avoid spatial aliasing, an equation similar to expression (3.3.1) can be used for the pitch p: cmin p< , (3.3.2) 2sinmax fmax where cmin is the minimum sound velocity in the material and max the maximum angle between the arrival angle of the reflected wave field and the normal vector of the surface where the elements are located, see figure 3.3. The pitch is usually a compromise. Ultrasonic systems have a fixed number of channels that can address array elements, typically 128 or 256. If the pitch is small, than the aperture will not be large enough. If the pitch is too large, expression 3.3.2 will be violated unless max approaches zero. In that case, only wave fronts parallel to the surface can be measured without spatial aliasing. The pitch of arrays for girth weld inspection typically varies from 0.5 mm to 2 mm. In practice, the elements of the array will have a certain width, denoted by a in figure 3.3. Large elements will generate a high acoustic pressure which is beneficial for the signal to noise ratio. However, the transmitter and receiver directivity is also dependent on the element width. According to Berkhout [1987], Wooh and Shi [1999] and Azar et al. [2000]: P (, r; ) S()asinc(a sin), (3.3.3) c

50 46 Application of imaging techniques for weld inspection 1 a = 0.5 mm 0.9 a = 0.8 mm a = 1 mm 0.8 a = 2 mm normalised directivity pressure 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 80 60 40 20 0 20 40 60 80 in Figure 3.4: Transmitter and/or receiver directivity behavior of a 4 MHz 50% bandwidth array element with a 0.5 mm, 0.8 mm, 1 mm and 2 mm width. where P (, r; ) is the Fourier transformed pressure in a point located in (r, ) (see figure 3.3), S() the source signature and is the direction of the normal to the wave front. Ideally, the transmitter and receiver characteristics are equal for all directions, i.e. for 90 < < 90 . These directivity properties approach a point source and/or receiver. Figure 3.4 illustrates the directivity behavior of equation (3.3.3) for an element with vary- ing width that generates a longitudinal Gaussian pulse with a 50% bandwidth and a 4 MHz center frequency. The element width results in a spatial filter for high angles. Most of the results in this thesis were obtained from measurements performed with a 4MHz array transducer that with a 0.8 mm element width. The line corresponding to an element width of 0.8 mm in figure 3.4 is representative for the directivity properties of the array transducer in the in-line direction, and as can be seen in this figure, the directivity behavior will not cause any major limitations. It is assumed in this thesis that all elements behave as point sources and point receivers in the in-line direction. The elements of the array used for the 3D measurements have a length of 1.9 mm. The line corresponding with a 2 mm element width in figure 3.4 is representative for the cross line directivity. In the cross-line direction, we cannot assume that the elements behave as point sources and point receivers. Hence, we can expect some limitations in our images related to the directivity. In the next section, some aspects on the resolution that can be achieved with the same 4 MHz array probe will be discussed. The influence of the directivity in the cross-line direction will also be discussed. 3.4 Resolution analysis A common approach to analyzing the resolution that can be achieved with imaging systems is to derive the point spread function (PSF). In the ideal situation, this function will be

51 3.4 Resolution analysis 47 L x np n p a z rD rA n A = (xA , zA ) D = (0, zD ) Figure 3.5: At the surface z = 0, the pressure is recorded of a point source S. The recorded wave field will be back propagated to a point A to determine the point spread function. a Dirac pulse, hence with a zero spatial extent and an infinitely high image amplitude. The PSF can be obtained by evaluating the Rayleigh II integral of equation (2.2.6) for the pressure field of a point source located in (xD , zD ). Here, we will derive the PSF in the 2D case starting with equation (2.2.4). The resolution in the 3D situation can be derived from the 2D case since our 3D imaging approach consist of two 2D imaging steps (see section 2.8). In practice, the aperture will be limited and the integral from minus infinity to plus infinity will be truncated. The far field approximation for the 2D Rayleigh II integral for back propagation then becomes, r L/2 Z j c 1 P (xA , zA ; ) zA P (x, 0; ) ej c rA dx, (3.4.4) 2 rA rA L/2 with L the length of the array, (xA , zA ) andp (0, zD ) the coordinates p of point A and the 2 2 diffractor D respectively, and with rD = x2 + zD and rA = (x xA )2 + zA . Fur- thermore, P (x, 0, ) is the Fourier transformed pressure at z = 0 caused by the point source D. Since we have a limited number of array elements, we can replace the integral in equa- tion (3.4.4) with a sum over the total number of elements, r (N 1)/2 j c X 1 P (xA , zA ; ) = zA Pn (np, 0; ) ej c rnA p, (3.4.5) 2 rnA rnA n=(N 1)/2

52 48 Application of imaging techniques for weld inspection where the total number of elements is p N , Pn (np, 0, ) is the Fourier transformed pressure 2 on the n-th element and with rnA = (xA np)2 + zA . The recorded pressure on the n-th element caused by D can be formulated as, s 2 ej c rnD Pn (np, 0; ) = S()An , (3.4.6) j c rnD with S() is the source signature, An is an amplitude factor that accounts for the di- rectivity properties of the receiver elements given by equation (3.3.3), and with rnD = p 2 (np)2 + zD . The Fourier transformed pressure in A becomes, using equations (3.4.5) and (3.4.6), (N 1)/2 X ej c (rnA rnD ) P (xA , zA ; ) = S()zA An p. (3.4.7) n=(N 1)/2 rnA rnD rnA For points A in the far2 field and close to D, we may approximate equation (3.4.7) with rnA rnD rnA zA and with (rnA rnD ) (zA zD ) nptan, where tan = xzA A (see figure 3.5). For now, we will assume that the receiver elements have the properties of point receivers, hence An =1. With these approximations, equation (3.4.7) yields, (N 1)/2 ej c (zA zD ) X P (xA , zA ; ) S() ej c nptan p. (3.4.8) zA n=(N 1)/2 Equation (3.4.8) can be further evaluated. The summation over n can be recognized as a geometric sequence which can be written in a closed form, p ej c (zA zD ) sin(N c 2 tan) P (xA , zA ; ) = S() p p. (3.4.9) zA sin( c 2 tan) The PSF follows from equation (3.4.9) by evaluating the amplitude of the back propagated pressure at t = 0 (imaging condition). Rather then transforming equation (3.4.9) to the time domain, the expression can be summed for all frequency components in the spectrum, hence Z P SF (xA , zA ) = P (xA , zA , )d. (3.4.10) In figure 3.6, the PSF in the z- and x-direction is plotted based on equation (3.4.10). For the PSFs in figure 3.6 and for the PSF plots that will follow in this section, the temporal bandwidth of the input signal and the other array properties (element length and width and maximum number of elements N =64) correspond with the array that will later be used for the measurements. The bandwidth is from a gaussian pulse with a 50% bandwidth and a 4 MHz center frequency. The pitch used for the plots was p=0.85 mm. The source diffractor is located at zD = 10 mm. For the z-direction, the PSF given by equation (3.4.10)

53 3.4 Resolution analysis 49 was evaluated with xA = 0. The result is presented in figure 3.6a. If equation (3.4.9) is evaluated for xA = 0, then we can derive for the PSF, Z ej c (zA zD ) P SF (0, zA ) S() d. (3.4.11) zA From this result, it can be seen that the resolution in the z-direction is not dependent on the number of elements and the pitch of the receiver elements. The resolution in the z-direction is determined by the temporal bandwidth of the input signal, the sound velocity and the diffractor depth zD Diffractor depth z = 10 mm Diffractor depth zD = 10 mm D 1 N = 10 N = 30 0.8 N = 60 0.75 normalised point spread function normalised point spread function N = 200 0.6 0.5 0.4 0.25 0.2 0 0 0.25 0.2 0.5 2 1.5 1 0.5 0 0.5 1 1.5 2 3 2 1 0 1 2 3 z z in mm x in mm A D A (a) Resolution in the depth direction. (b) Resolution in the horizontal direc- The resolution in this direction is only tion for a different number of receiver el- dependent on the wavelet signature. ements. Figure 3.6: Resolution plots for the x- and z-direction for a gaussian pulse with a 50% bandwidth and a 4 MHz center frequency. The pitch of the array p is 0.85 mm and the directivity properties of the elements are neglected. For the resolution in the x-direction, the PSF of equation (3.4.10) was evaluated with zA = zD and the result is presented in figure 3.6b. In the x-direction, the resolution is dependent on the number of elements and on the depth. From figure 3.6b, it can be seen that the resolution improves when more receiver elements are used. The illustrated PSF in figure 3.6 was obtained using a far field approximation. A bet- ter approximation of the PSF was derived by Volker [2002]. It is also possible to obtain a more accurate PSF when equation (3.4.4) is evaluated numerically. In figure 3.7 the vertical and the horizonal PSFs are presented for a diffractor located at a depth of 5 mm,

54 50 Application of imaging techniques for weld inspection Diffractor depth z = 5 mm Diffractor depth z = 5 mm D D 1 N = 10 N = 10 N = 30 N = 30 N = 60 0.8 N = 60 normalised point spread function normalised point spread function N = 200 N = 200 0.5 0.6 0.4 0.2 0 0 0.2 0.5 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z z in mm x in mm A D A (a) (b) Diffractor depth z = 10 mm Diffractor depth z = 10 mm D D 1 N = 10 N = 10 N = 30 N = 30 N = 60 0.8 N = 60 normalised point spread function normalised point spread function N = 200 N = 200 0.5 0.6 0.4 0.2 0 0 0.2 0.5 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z z in mm x in mm A D A (c) (d) Diffractor depth z = 30 mm Diffractor depth z = 30 mm D D 1 N = 10 N = 10 N = 30 N = 30 N = 60 0.8 N = 60 normalised point spread function normalised point spread function N = 200 N = 200 0.5 0.6 0.4 0.2 0 0 0.2 0.5 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z z in mm x in mm A D A (e) (f) Figure 3.7: The PSFs for a diffractor at depths, 5 mm, 10 mm and 30 mm derived for different numbers of receiver elements N . The pitch of the elements on the array is 0.85 mm, the directivity properties were not taken into account. The left plots illustrate the vertical PSF, and the right plots illustrate the horizontal PSF.

55 3.4 Resolution analysis 51 10 mm and 30 mm respectively. The PSFs were calculated with a pitch of 0.85 mm and for different numbers of elements: 10, 30, 60 and 200. The directivity properties of the elements were not taken into account. From the results of figures 3.7a ,c and e we can see that the vertical PSF does not change significantly for different depths of the diffractor zD . The number of elements does not change the main lobe of the vertical PSF significantly. However it can be noted that the side lobes are reduced by a larger number of elements. Furthermore, it can be seen that for the far field, the vertical PSF indeed approaches the approximated PSF of figure 3.6a). To determine the vertical resolution, we must define the criterium when two adjacent point scatterers can be resolved. A common criterium is the Rayleigh criterium that states that two point diffractors D and D can be resolved when the main lobe of D coincides with the first minimum of D . Hence, the resolution is the distance from the main lobe to the first minimum. According to this definition, the vertical resolution in the example is approxi- mately 0.5 mm. From the results of figures 3.7b ,d and f we can see that the horizontal PSF changes with the number of elements and with the depth. In the near field, the number of elements is less critical then in the far field. Hence, if high resolution is required far away from the array, the number of elements must be increased. It can be noted that the amplitude of the side lobes in the horizontal direction is less then in the vertical direction. The far field approximation illustrated in figure 3.6b is less accurate and may be used to give a rough estimate of the resolution in the far field. With the Rayleigh criterion, it can be seen that the resolution for imaging depths less then 30 mm is less then 1 mm with 60 elements. The back propagated pressure field given by equation (3.4.7) gives the pressure distribution of a point source located at (0, zD ). In our imaging approach, we insonify a scatterer that will become a secondary source at the moment when the wave fronts hits the scatterer, say at tS . If we would use only one source to insonify the scatterer and receive with all the available receivers along the array (the common-source approach), equation (3.4.7) can be used to determine the resolution when the imaging condition t = tS is applied. The results presented in figure 3.6 and figure 3.7 apply to one common-source insonifi- cation, where only one column of the data matrix is filled with data. It is demonstrated by Chiao and Thomas [1994] and Davies et al. [2006], that when all the elements are also used as sources (the full-array approach), the resolution in the image can be determined with P SF 2 (xA , zA ), where P SF (xA , zA ) can be obtained with equation (3.4.10). In this case, the entire data matrix is filled. In addition, it was demonstrated by the same authors that in case measurements were taken whereby the source and receiver elements always coin- cides (the zero offset or backscatter approach), the horizontal resolution can be determined by evaluating equation (3.4.10) with P (xA , zA ; 2). If we also account for the directivity properties of the transmitters and receivers, we must evaluate equation (3.4.7) with, An = S()asinc(a sinn ), (3.4.12) c np where tann = zD (see figure 3.5). Figures 3.8a and b present the PSF in the horizontal and vertical direction for the common

56 52 Application of imaging techniques for weld inspection source, the zero offset and the full array approach. The diffractor depth zD is 30 mm, the number of elements is 60 and the pitch p = 0.85 mm. In these examples, the PSFs were evaluated including the directivity function An , with element width a = 0.8 mm, which is representative for the transducer that was used for the measurements in the in-line direc- tion. From figures 3.8a and b, it can be observed that the zero offset approach produces the smallest main lobe and the full array approach produces the smallest side lobes. The directivity caused by the element width increases the amplitude of the side lobes in the vertical direction. If we apply the Rayleigh criterium, we can state that the resolution in the horizonal and vertical direction is less then 1 mm, with the characteristics of the array that was used for the measurements in the in-line direction. It should be noted, that al- though the resolution of the common-source approach is good, the signal to noise ratio will be poor compared to the zero-offset and the full-array approach, because only one source is used. Figures 3.8c and d present the PSF in the horizontal and vertical direction for the common source, the zero offset and the full array approach for another scenario. The diffractor depth zD is 30 mm, the number of elements is 60 and the pitch p = 1 mm. In these examples, the PSFs were also evaluated including the directivity function An , with element width a = 2 mm. This is representative for the transducer that was used for the measurements in the cross-line direction. Although the directivity causes a broader PSF, it can be stated that the resolution in the cross-line direction is less then 2 mm. Note that the element width is larger then the pitch, hence the aperture is scanned with overlapping elements. This is possible with the zero offset approach in the cross-line direction, whereby the position of the array is moved each 1 mm. As conclusion of the foregoing resolution analysis, we can summarize the following for an array transducer with 64 elements of which the width is 0.8 mm, the length is 1.9 mm, the pitch is 0.85 mm and that has a center frequency of 4 MHz with a 50% bandwidth: The resolution that can be achieved with full array measurements in the in-line direction is for the vertical and horizontal direction less then 1 mm. Compared to the required resolution based on acceptance criteria as described in section 3.2, we can conclude that the images that are produced from the data measured with the specified array contain sufficient resolution to size the defect height within a range of at least 30 mm. The resolution that can be achieved with zero offset measurements in the cross-line direction is less then 2 mm, for both the vertical and horizontal direction. Compared to the required resolution based on acceptance criteria as described in section 3.2, we can conclude that the images that are produced from the data measured with the specified array contain sufficient resolution to size the defect length within a depth range of at least 30 mm. In the next chapter, results of 2D images from measurements on carbon steel test pieces with defect like reflectors will be presented.

57 3.4 Resolution analysis 53 Diffractor depth zD = 30 mm, N = 60 Diffractor depth zD = 30 mm, N = 60 1 common source common source 0.8 zero offset zero offset full array 0.8 full array normalised point spread function normalised point spread function 0.6 0.4 0.6 0.2 0.4 0 0.2 0.2 0.4 0 0.6 0.2 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z z in mm x in mm A D A (a) Pitch p = 0.85 mm and element width (b) Pitch p = 0.85 mm and element width a = 0.8 mm. a = 0.8 mm . Diffractor depth zD = 30 mm, N = 60 Diffractor depth zD = 30 mm, N = 60 1 common source common source 0.8 zero offset zero offset full array 0.8 full array normalised point spread function normalised point spread function 0.6 0.4 0.6 0.2 0.4 0 0.2 0.2 0.4 0 0.6 0.2 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z z in mm x in mm A D A (c) Pitch p = 1 mm and element width a (d) Pitch p = 1 mm and element width a = 2 mm. = 2 mm. Figure 3.8: PSF calculated for a diffractor at 30 mm depth for the common source, the zero offset and the full array approach. The directivity properties of the elements are taken into account. Figures a) and b) are representative for the in-line direction, figures c) and d) are representative for the cross line direction.

58 54 Application of imaging techniques for weld inspection

59 4 2D imaging results from measured data In this chapter, the results of 2D and 3D images from carbon steel test pieces with reflectors will be presented. The 2D images were obtained from defect-like reflectors 1 . In the following sections results of images from array measurements of a bore hole and more defect-like reflectors in carbon steel test pieces, will be presented. All reflectors are long in the direction perpendicular to the array, such that a 2D situation can be assumed. Images from an isolated bore hole are used to analyze the characteristics of the imag- ing approach, since the bore hole approaches the characteristics of a point scatterer. The defect-like reflectors are representative for (see section 3.1): lack of fusion defects (a 1 and 2 mm slit with a 45 orientation), surface breaking crack (a 2 mm notch with a 45 orientation), porosity (three bore holes with a 0.5 mm diameter, with the centers separated 1 mm and 1.5 mm respectively), lack of cross penetration (a 2 mm slit with a 0 orientation), cold lap defects (a 2 mm slit with a 90 orientation). For the experiments an ultrasonic phased array system with 128 channels, split over two connectors of 64 was used (see figure 1.3). The measurements for the 2D images were per- 1 Some of the results presented here have been published (Portzgen et al. [2007])

60 56 2D imaging results from measured data formed with an array probe that consists of 64 elements with a pitch of 0.85 mm, gaps of 0.15 mm separating the elements, and 15 mm length. The length of the elements is much larger than the width. As a consequence, the directivity behavior of the elements can be compared with a line source (see section 3.3). This supports our assumption that the we are dealing with a 2D set-up. The center frequency of the probe is 4 MHz with a 50% bandwidth. For the calculation of images in the following sections of this chapter, the IWEX imag- ing procedure was implemented in matrix notation as presented in section 2.6. The im- plementation was done in the computer program language Matlab. Images of different insonification and scatter paths (the L-L, L-T and the LL-LL paths) will be presented and discussed in more detail. 4.1 Imaging a bore hole Although a single isolated bore hole is not really representative for weld defects, it is useful to study the properties of imaging based on inverse wave field extrapolation with a bore hole. When the bore hole is small compared to the wave length, the scatter behavior will be representative for a point scatterer. Identifying the arrivals of the different modes will be straight forward. The measurements for this example were taken from a 20 mm thick carbon steel plate (ct = 3250 m/s and cl = 5900 m/s) with a 1.5 mm diameter bore hole drilled in the center. The A-scans of all possible source / receiver combinations were recorded. The measurement setup is illustrated in figure 4.1. The data from source 15, 25 and 35 are shown in figure 4.2. In this figure, we can see several events: [1] A weak diffraction caused by the hole. The wave incident on the defect was the wave traveling from the source to the defect directly. Note that the travel times are different depending on the source position. [2] A fast surface wave known as the creep wave. [3] A slow surface wave known as the Rayleigh wave. [4] A strong reflection of the longitudinal wave from the back wall. [5] A strong shear wave, converted from longitudinal at the back wall. Note that at zero degree reflection (in the center of the apex), no mode conversion is present. [6] Second longitudinal wave reflection from the back wall, that also reflected from the inside of the front wall. In the data, also strong signals caused by cross coupling between adjacent elements and consistent signals caused by the ultrasonic electronics are visible. These signals appear early in the recording and they will effect the contribution to image points just below the surface only. However, this area is very well insonified by the back wall reflection, as we will show. When the incident wave field reflects at the back wall, the reflected wave field will also be scattered by the bore hole. All multiple back wall - front wall reflections will insonify

61 4.1 Imaging a bore hole 57 Figure 4.1: Measurement set-up with a 64 element 4 MHz array probe. The probe is placed on a 20 mm thick steel block with a 1.5 mm bore hole. the bore hole at different times. This is also true for multiple mode converted waves. The presented IWEX algorithm can be applied to all individual insonification events. Since our data contains multiple insonifications of the bore hole, we can make separate images from different arrivals, including those caused by mode converted waves. In figure 4.3a the resulting image is presented for the first arrival signals (longitudinal- bore hole-longitudinal or L-L paths). From figure 4.2 and 4.3a we can see that, although the signal appears very weak in our data and seems obscured by noise, by imaging we still get an excellent result with a good signal to noise ratio at the position of the bore hole. The good signal to noise ratio is caused by the combination of images from all sources, canceling the random noise and source position dependent aperture effects. The position of the amplitude in the image corresponds with the top side of the bore hole. At the top of the image, where the surface of the steel plate is located, we can see contributions to the image caused by the energy of the creep waves, the Rayleigh waves and the cross talk of the adjacent elements. The surface waves form a dead zone in the first 2 mm. The noise in the shallow part of the image can be suppressed in a data processing step by blanking the linear events caused by the surface waves (figure 4.2). If a defect is located in this zone, an image can be produced from other arrivals. We can see that also the back wall is imaged at the correct position. When the wall thickness would vary, this variation would also be visible in the image. Hence, it is not necessary to know the wall thickness before the experiment. However, for images of subsequent arrivals, the wall thickness must be known, either as an a-priori parameter or determined by the image of the L-L arrivals. Figure 4.3b illustrates the image of the bore hole computed from at the bore hole mode converted longitudinal waves (longitudinal-bore hole-transversal or L-T paths). Two strong

62 58 2D imaging results from measured data Figure 4.2: Data recorded on all 64 elements for source elements 15, 25 and 35. Note that waves caused by mode conversion are also measured. The numbers refer to the various events, as explained in the main text. artifacts can be identified in figure 4.3b: [1] A second back wall, caused by the L-L back wall event. Due to the higher sound velocity for longitudinal waves, the L-L back wall event is imaged at a shallower depth 14.5 mm in the L-T image. [2] A curved event above the bore hole. This is also caused by the faster traveling longitudinal waves. The L-L reflection energy of the bore hole is not focussed by the L-T imaging procedure. The position of imaged energy caused by the L-T path of the bore hole corresponds with the actual location. The artifacts are fully determined by the previous correctly imaged waves. In figure 4.3a, no artifacts are visible, however, it may be possible that artifacts also occur in this image. This will be discussed in more detail in chapter 6. The correctly imaged energy in the L-L image will cause the artifacts in images from later arrivals. The L-L energy leaks into those images. This leaking energy can be isolated in the original data by a forward modeling procedure. Then a masking filter or an adaptive filter can be constructed to suppress the already imaged energy in the original data so that a new data set is obtained without the events causing the leakage artifacts. This will also be discussed in detail in chapter 6.

63 4.2 Imaging of embedded lack of fusion defects 59 1 0.5 0 0.5 1 1 0.5 0 0.5 1 1 0.5 0 0.5 1 0 0 0 2 2 2 4 4 4 6 6 6 distance in (mm) distance in (mm) distance in (mm) 8 8 8 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 distance in (mm) distance in (mm) distance in (mm) (a) Image of the bore hole (b) Image of the bore hole (c) Image of the bore hole obtained by using the L-L obtained by using the L- obtained by using the LL- paths T paths LL paths Figure 4.3: Recordings of figure 2.4, imaged for different propagation scenarios. Figure 4.3c illustrates the image computed from the longitudinal back wall reflection. The wave is scattered by the bore hole, travels back to the back wall and is reflected to the receivers, this is the LL-LL path. The image shows the bore hole at a slightly deeper position. We are actually imaging the bottom of the bore hole now. Furthermore, some artifacts are visible. Again, these are due to mode converted energy that fulfills the imaging condition for a different mode of the incident field giving rise to image energy where it does not belong. At 12 mm the mode converted wave field from the back wall is imaged as if it were an LL-LL event, and at 15 mm we can see energy due to mode conversion by the bore hole itself. In the next sections, results will be presented from defect-like reflectors. 4.2 Imaging of embedded lack of fusion defects Probably the most common weld defects are lack of fusion defects. The orientation of lack of fusion defects can vary from 0 to 45 with the normal direction to the surface. Here, we will present two examples of a 1 mm and a 2 mm slit with a 45 orientation, see figures 4.4a and 4.4b. In principle, images can be generated from many different arrivals. Here, we will only present the best images in order to avoid artifacts as were identified in the previous section.

64 60 2D imaging results from measured data Figure 4.5a and 4.5b shows the result of the IWEX image obtained with the L-L arrivals of the 1 mm slit and the 2 mm slit respectively. The locations of the slits are imaged, together with the back wall and surface of the block. The orientation of the 1 mm slit effectively cannot be resolved, as can be seen in 4.5a. This effect is caused by the poor ratio between the (longitudinal) wavelength (= 1.6 mm) and the defect. The defect is so small that it will get the properties of a point scatterer. Theoretically, a better result will be obtained when higher frequencies are used (see section 3.4 for more detail). However, the use of higher frequencies will have practical disadvantages. Waves with wave lengths in the order of the grain size will scatter at the grain boundaries. In addition, the array must have more and smaller elements in order to avoid spatial aliasing and to maintain a sufficiently large aperture (see sections 3.3 and 3.4). The parameters of the array and the measurement system must be a good trade off to obtain sufficient resolution and avoid critical side effects. The orientation and length of the 2 mm slit can be recognized better in the resulting image of the L-L arrivals as presented in figure 4.5b. Compared to standard ultrasonic in- spection techniques like ToFD and pulse-echo, this result is quite remarkable. As opposed to these techniques, the image can directly be compared with the original cross section that is presented in figure 4.4b. The interpretation is straight forward because the size, orientation and position are imaged relative to the surface and back wall. Small defects like the 1 mm slit will behave as point scatterers. It is interesting to an- alyze the distance between two adjacent point scatterers that can just be resolved. In the next section, the resulting image of 3 bore holes close to each other will be presented. The bore holes represent a porosity cluster. The position of the 1 mm and 2 mm 45 slits was well outside the surface area where the dead zone is located. In the next section, we will also present images of a inclined slit that is located in this area. (a) Picture of a 1 mm slit at 45 , rep- (b) Picture of a 2 mm slit at 45 , represen- resentative for a lack of fusion defect tative for a lack of fusion defect Figure 4.4: A 1 mm and a 2 mm slit orientated at 45 in a 10 mm thick carbon steel plate. The slits are representative for a lack of fusion defects in a weld.

65 4.2 Imaging of embedded lack of fusion defects 61 1 0.5 0 0.5 1 1 0.5 0 0.5 1 0 0 2 2 distance in (mm) 4 distance in (mm) 4 6 6 8 8 10 10 12 12 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 distance in (mm) distance in (mm) (a) Image of a 1 mm slit at 45 , imaged (b) Image of a 2 mm slit at 45 , imaged with the L-L path with the L-L path Figure 4.5: Images of the slits from figure 4.4. The 1 mm slit is too small compared to the wave length to recognize the orientation of the defect. The orientation of the 2 mm slit can be recognized.

66 62 2D imaging results from measured data 4.3 Imaging surface breaking defects and porosity Surface breaking defects are considered very critical. From a fracture mechanics point of view, surface breaking defects are more likely to grow and cause failure, than embedded defects, especially when the pipeline is subject to fatigue. For this reason, acceptance cri- teria for surface breaking defects are usually more strict then for other types of defects. Surface breaking defects located at the inner diameter of the pipe are relatively easy to find using ToFD or the pulse-echo corner trap technique. In order to receive a good signal and to give a good size estimate of the defect with the corner trap technique, the defect must be perpendicular to the surface. When the defect is not perpendicular to the surface, the size estimate will be poor and in severe cases, the defect can even be missed. This happens when the corner trap effect fails and the sound reflects in a direction that is unsuitable for the receiver. ToFD is less dependent on the orientation because the detected signal was generated at the defects tip and not as a result of a corner effect. Surface breaking defects located at the outer diameter of the pipe can be detected and sized similarly to those at the inner diameter. With the ToFD technique detecting and sizing of defects located at the outer diameter is troublesome. The lateral wave that travels directly under the surface obscures the defect. Hence, both conventional techniques are not optimal for detecting and sizing of defects at the outer surface. The properties of a surface breaking defect are most critical when the crack is located at the upper surface and when the crack is not perpendicular to the surface. Therefore, a test block was manufactured that contains a 2 mm deep slit with a 45 inclination (see fig- ure 4.6a). Measurements were done with the 4 MHz probe, whereby the probe was placed directly on top of the slit. In section 4.1, we noticed that defects at the outer surface may be obscured due to the dead-zone in the L-L images. In figure 4.7a, the image constructed with the L-L arrivals from the inclined slit at the upper surface is presented. Indeed, the slit cannot be identified in this image, because the 2 mm slit is entirely obscured by the dead zone. In addition, in order to insonify the slit with the L-L mode, the directivity of the elements should support very high angles. This is a practical limitation of the elements. Insonification via the back wall requires less steep angles for the insonification and there will be no dead zone. In figure 4.7b, the resulting image constructed with the LL-LL mode is presented. It is clear that as a result of insonification via the back wall, the slit is imaged. The orien- tation of the slit cannot be resolved. This, again, is caused by the poor ratio between the wavelength and the defect length. In addition, the resolution is dependent on the defect depth. The depth will now be twice the wall thickness since the defect was insonified via the back wall. In conventional inspection, detecting of porosity or inclusions is performed with the stan- dard pulse-echo method. The reflectivity of individual pores is very low compared to lack of fusion defects. Therefore, the sensitivity must be increased significantly. Sizing of porosity is almost impossible with the pulse-echo technique. It is difficult to resolve individual pores and the amplitude does not simply relate to the defect size.

67 4.3 Imaging surface breaking defects and porosity 63 To study the performance of the imaging approach for porosity, a test block was man- ufactured with three small bore holes, see figure 4.6b. The holes have a 0.5 mm diameter (much smaller than the wave length) and are separated 1 mm and 1.5 mm center-center. The resolving power needed to resolve two adjacent defects can be determined with the three holes. Some codes have special requirements for neighboring defects (Ginzel [2006]). When defects are too close to each other, they will interact. The acceptance criteria will then be applied to the sum of both defect lengths and the separation distance. In figure 4.8a, the L-L image of the three bore holes is presented. It can be seen that the outer right bore hole can be identified separately from the other two. To study the resolving performance in more detail, the envelope of the L-L image was taken, so that the phase information is ignored. The defects appear as three round blobs in the result- ing image that is presented in figure 4.8b. In this image, the maximum of the blob can easily be identified. The three blobs from figure 4.8b can also be displayed as a surface, see figure 4.8c. This result shows that for this case, the horizontal resolution is slightly better than the vertical resolution. In figure 4.8b a white dotted line is plotted that crosses the maximum values of the three blobs. Figure 4.8d shows the amplitudes as a function of the distance on this line. From figure 4.8d, it is clear the two bore holes at the right can be resolved completely. The distance corresponds with the true value of 1.5 mm. The two left bore holes can just be resolved, the two lobes intersect at approximately half the maximum amplitude (-6dB). From this result, it can be stated that at this depth, two point like scatterers can be resolved when they are separated no less then 1 mm. Note that this result complies with the resolution analysis as presented in section 3.4, and that this result meets the requirements that were determined in section 3.2. In the next section, the results of images from two slits will be presented, representative for a cold lap defect and a lack of cross penetration defect. (a) Picture of a 2 mm notch at 45 (b) Picture of three bore holes with a 0.5 mm diameter. The center of the holes are separated 1 mm and 1.5 mm respectively Figure 4.6: Artificial defects representative for a for a surface breaking defect (left) and for a porosity cluster (right).

68 64 2D imaging results from measured data 1 0.5 0 0.5 1 1 0.5 0 0.5 1 0 0 2 2 distance in (mm) 4 distance in (mm) 4 6 6 8 8 10 10 12 12 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 distance in (mm) distance in (mm) (a) Image of a 2 mm surface slit at 45 , (b) Image of a 2 mm surface slit at 45 , imaged with the L-L path imaged with the LL-LL path Figure 4.7: The L-L and the LL-LL image corresponding with de notch of figure 4.6a. The notch can not be identified in the L-L image because it is obscured by the dead zone. The LL-LL image reveals the defect.

69 4.3 Imaging surface breaking defects and porosity 65 1 0.5 0 0.5 1 0 0.2 0.4 0.6 0.8 1 0 0 2 2 distance in (mm) 4 distance in (mm) 4 6 6 8 8 10 10 12 12 20 22 24 26 28 30 32 34 36 20 25 30 35 distance in (mm) distance in (mm) (a) The L-L image of the three bore holes (b) The envelope of the L-L image from figure a 1 0.9 0.8 normalised image amplitude 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30 distance in mm (c) Surface plot of the envelope of figure (d) Distance-amplitude plot at the loca- b tion of the white dotted line of figure b Figure 4.8: Different results of the L-L image of the three bore holes corresponding with figure 4.6b. The resolution obtained from the experiments complies with the resolution analysis of section 3.4.

70 66 2D imaging results from measured data 4.4 Imaging cold lap and lack of cross penetration defects Cold lap defects and a lack of cross penetration (LCF) defects are actually variations of the lack of fusion defects that were presented in section 4.2. The orientation of the cold lap defect is 90 and the orientation of the LCF is 0 . From the analysis of these two ori- entations together with the 45 orientation, a good impression is obtained of the behavior of the imaging approach for intermediate angles. Figure 4.10 presents the result of the L-L image from the 2 mm slit with a 90 inclination. This orientation is optimal for direct and almost perpendicular insonification. Both the reflected and the diffracted waves will be measured and sampled by the array. The phase signature of the defect caused by the bandwidth of the source is not interrupted (see figure 4.10a) as is the case with the 2 mm 45 slit of figure 4.5b. The area directly underneath the slit is located in a shadow area. This area will not be insonified well by the L-L mode. This can be seen from the location of the back wall underneath the slit. In figure 4.10a, the amplitude of the image is more faint on this location, between 26 mm and 29 mm. The shadow effect can be observed better in the envelope of the L-L image, presented in figure 4.10b. The results of the L-L and the LL-LL images of the 0 are presented in figure 4.11. The upper tip of the defect is clearly visible in the L-L image of 4.11a. However the length of the slit can not be observed from this image. In the LL-LL image presented in 4.11b, the upper tip can be observed vaguely and the lower tip is more prominent. This makes sense, since the lower tip is better insonified via the back wall. The L-L and the LL-LL images have been scaled and added and the resulting image is presented in 4.11c. The envelop of this image is presented in 4.11d. In these images, the upper and lower tip are both visible. How- ever it is not evident that the images show a single defect rather than two point scatterers. The same phenomenon can be observed when almost vertical defects are inspected with the ToFD technique. Here, the phase information is used to determine if the defect is a single one or two point scatterers. Two point scatterers will have the same phase but the phase of the upper and lower tip of a vertical defect will be opposite. This also can be observed in figures 4.11b and 4.11c, where the phase of the upper tip is opposite to the phase of the lower tip. An alternative approach to distinguish a vertical defect from two point scatterers is by comparing the L-L image with the LL-LL image. It is likely that two individual point scatterers appear both in the L-L image, because the scatterers can be insonified almost equally well. The lower tip diffraction will be much weaker because the wave front has to bend around the defect. The same applies to the upper tip diffraction insonified with the LL-LL mode. In conclusion, two individual point scatterers will appear in both the L-L and the LL-LL image with comparable amplitudes. In case of a vertical defect, the upper tip will show better in the L-L image and the lower tip will show better in the LL-LL image. In the next chapter, results will be presented from 3D images that were generated from measurements with a 5MHz linear array.

71 4.4 Imaging cold lap and lack of cross penetration defects 67 (a) Picture of a 2 mm slit at 90 (b) Picture of a 2 mm slit at 0 Figure 4.9: A 1 mm and a 2 mm slit orientated at 45 in a 10 mm thick carbon steel plate. The slits are representative for a lack of fusion defects in a weld. The corresponding IWEX images are presented in figure 4.5. 1 0.5 0 0.5 1 0 0.2 0.4 0.6 0.8 1 0 0 2 2 distance in (mm) distance in (mm) 4 4 6 6 8 8 10 10 12 12 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 distance in (mm) distance in (mm) (a) The L-L image of the 2 mm slit at (b) The envelope of the L-L image from 90 figure a Figure 4.10: Different presentations of the result of the L-L image from the 2 mm slit representative for a cold lap defect.

72 68 2D imaging results from measured data 1 0.5 0 0.5 1 1 0.5 0 0.5 1 0 0 2 2 distance in (mm) distance in (mm) 4 4 6 6 8 8 10 10 12 12 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 distance in (mm) distance in (mm) (a) The L-L image of the 2 mm 0 slit (b) The LL-LL image of the 2 mm 0 slit. 1 0.5 0 0.5 1 0 0.2 0.4 0.6 0.8 1 0 0 2 2 distance in (mm) distance in (mm) 4 4 6 6 8 8 10 10 12 12 20 22 24 26 28 30 32 34 36 20 22 24 26 28 30 32 34 36 distance in (mm) distance in (mm) (c) Sum of the L-L and the LL-LL images (d) The envelope image of the summed of figure a and b L-L and LL-LL images from figure c Figure 4.11: Results of the L-L and the LL-LL images from the 2 mm 0 slit. The upper tip of the slit can be clearly observed in the L-L image and the lower tip can be observed in the LL-LL image. The images can be scaled and combined for a complete picture.

73 5 3D imaging results from measured data In this chapter, the results will be presented of 3D images that are produced with the two pass method as was described in section 2.8. For the measurements a 5 MHz with a 50% bandwidth linear array was used. For proper 3D imaging it is required that the directivity of the elements is similar to that of a point source. The pitch of this array is 0.85 mm, similar to the array that was used for the 2D measurements, and the length of the elements is 1.9 mm. The ratio between the pitch and the length of the elements should be close to 1, for the elements to behave as point sources. Since the element dimensions are close to the dominant wavelength, we will assume for our calculations, that the elements behave as point sources, but we will see that the effects of the beam directivity can be identified in the actual results. The test objects used for 3D imaging contained geometrically interesting reflectors, to demonstrate the improvements of 3D imaging over 2D imaging. In the next sections, results of the following test pieces will be presented: A single bore hole perpendicular to the surface with a round bottom hole. Three bore holes with an inclination, two of which are deep and with an opposite inclination and the third less deep and close to one of the other bore holes. All bore holes have round bottom tips. An inclined slit whereby the end of the slit is also inclined. A weld with a small tungsten plate embedded to represent a lack of fusion defect.

74 70 3D imaging results from measured data Figure 5.1: Measurement set-up with the 5 MHz array probe used for 3D imaging. The probe is mounted in a spring loaded frame and it is submerged into a water tank. The 3D images that will be shown in the following sections are produced by imaging with the two pass method as presented in section 2.8. The first imaging step was applied to the data obtained from a single position of the array. At such a position, all combinations of source-receiver elements were obtained. At this fixed position, the imaging is performed in the in-line direction using the IWEX approach as presented in section 2.6. This direction is per definition parallel to the array. Usually, the x-axis is chosen to coincide with the in-line direction. Similar, the cross-line direction is per definition the direction perpendicular the the array. Usually, the y-axis is chosen to coincide with the cross-line direction. In this direction, the zero-offset imaging approach was performed, as described in section 2.7. The depth of a defect is measured from the upper surface and usually, this direction coincides with the z-direction. During the measurements the probe was mounted into a spring loaded frame that was submerged into a water tank to assure constant coupling. The spring loaded frame was fixed to an arm of a x-y table, such that the position of the probe could be determined with an accuracy of 0.1 mm. The measurement set-up is illustrated in figure 5.1.

75 5.1 3D imaging of a round bottom hole 71 5.1 3D imaging of a round bottom hole Similar to the cylinder in the 2D imaging, a single round bottom hole forms the most basic reflector that will be used to study the properties of our 3D imaging approach. A 40 mm thick test block was manufactured with a 3 mm diameter bore hole. The bore hole consist of a round tip and it was drilled 20 mm deep from the bottom in the vertical direction. For this test block, the scan direction is not relevant because the geometry of the reflec- tor is symmetric in all directions. In the cross-line direction (y-axis) measurements were recorded each 1 mm over a 30 mm aperture. At a single position in the cross-line direction, all transmitter and receiver combinations were recorded with the 64 elements, resulting in 4096 A-scans. With all the positions in the cross-line direction, the total data set consists out of 122880 A-scans. Following the two-pass method, 2D images were produced for each position in the cross- line direction, resulting in 30 images. In figure 5.2a, three slices are presented through the 30 2D images that are cascaded in the cross-line direction. It consists of the top view (xy-plane), the side view (yz-plane) and the front view (xz-view). All slices intersect with the bore hole. The individual slices are presented in 5.2b, c and d respectively. In the top view slice (at depth = 20 mm) presented in figure 5.2b, the bore hole is clearly visible. It can be observed directly that the resolution in the in the in-line direction is better then in the cross-line direction. The slice was taken trough the maximum value at depth = 20 mm and the response of the bore hole forms an oval. The oval will be different depending on the depth of the slice. Therefore, other slices must be observed for a conclu- sive statement on the resolution can be made. In the slice presented in 5.2c, it can be observed that the resolution in the cross-line direction is very poor. This is a result of the large beam spread in this direction caused by the fact that the element has got a length of 1.9 mm only. In fact, this image shows the hyperbolic shape of a point scatterer. With conventional inspection techniques like the pulse-echo method, such a large beam spread is very undesirable. Due to the large beam spread, the defect length will be over sized with the -6dB amplitude drop approach. For the pulse-echo technique, it is therefore desirable to use elements with a larger length, so that the beam spread in the cross-line direction is reduced. However, although the beam spread may be smaller, the sizing capability with the -6dB drop method can never be better then the length of the element itself. The hyperbola shape will then change to a hyperbolic with a flattened apex over the length of the element, whereby the diffraction tails fades. For our imaging approach, it is very desirable to have a large beam spread, since the defect will then be insonified from more directions. The slice of figure 5.2c can be considered as a zero-offset record, when the vertical depth axis is transformed into a time axis with the appropriate sound velocity (exploding reflector model). The hyperbola will contribute to the image amplitude when the cascaded 2D im- ages are imaged in the cross-line direction. Looking closely at the event, it can be seen that the hyperbola is not perfect at the tails (from 0 mm to 5 mm and from 20 mm to 30 mm in figure 5.2c). The amplitude of these parts of the hyperbola is weaker then the amplitude in the apex. This effect is caused by the directivity of the elements. The elements have a

76 72 3D imaging results from measured data (a) Three different slices through the cascaded 2D cross-line images 0 0 0 5 5 5 10 10 10 15 15 crossline (mm) depth (mm) depth (mm) 15 20 20 25 25 20 30 30 25 35 35 40 40 30 0 2 4 6 8 0 5 10 15 20 25 30 0 2 4 6 8 inline (mm) crossline (mm) inline (mm) (b) Slice through (c) Slice through the yz-plane (d) Slice the xy-plane through the xz-plane Figure 5.2: Result of images produced with the data from a test block with a 3 mm round bottom hole. The data was imaged in the in-line direction only. Here, the cross-line direc- tion corresponds with the y-axis and the in-line direction with the x-axis.

77 5.1 3D imaging of a round bottom hole 73 length of 1.9 mm and as can be seen in figure 3.4, wave fronts with high angles (> 40 ) have been attenuated. Furthermore, the phase of the signal at the tails of the hyperbola, appears to be cross- hatched. This is caused by spatial aliasing. The sample distance in the cross-line direction was 1 mm, note that this distance is almost half the element length. Even if the sample distance is decreased, the hyperbola would not be smooth as a result of the directivity of the elements. However, it should also be noted that, although the waves with high angles are aliased, the directivity of the elements attenuates those waves. Hence, element size can be considered a spatial filter. The slice along the in-line direction presented in 5.2d gives the result of the 2D image at the position of the bore hole. The resolution in this image is similar to the results that were obtained and presented in the previous chapter, as expected. Also, it can be observed that only the tip of the bore hole is imaged. The sides of the bore hole do not appear because reflections from the smooth side were not detected over the limited aperture of the array. If the bore hole had an irregular rough surface, the waves would scatter and responses from the sides would be recorded over the receiver aperture. In practice, defects always will have an irregularly facetted surface. This will be an advantage for our imaging approach. Diffracted waves will be detected over a larger part of the array then reflected waves. Figure 5.3 presents the results of the images that are obtained when the data is imaged in both directions. The second direction, the cross-line direction, is imaged with the zero off- set approach as described in section 2.7. Figure 5.3a illustrates three slice through the bore hole. The slices in the xy-plane, the yz-plane and the xz-plane are presented separately in figures 5.3b, c and d respectively. In the top view presented in 5.3b, the improvement in the resolution can be observed. The black oval shaped image of figure 5.2b has become more circular. Some differences can be observed between in-line and cross-line directions. The second step was imaged width the zero-offset technique and, as was discussed in section 3.4 the resolution determined by the point spread function is given by equation (3.4.11) with P (xA , zA ; 2). However, in practice the element size (1.9 mm) dictates the resolution. Therefore, in the cross-line direction side lobes can be observed. The improvement of the resolution can be observed best in the side view slice presented in figure 5.3c. The strong hyperbolically shaped event that could be observed in figure 5.2c has now collapsed into the location of the bore hole. Although some side lobes can be observed, it is clearly demonstrated that the image represents a point scatterer. Also, some side effects can be observed in figure 5.3c as tails that originate from the back wall. These events are caused by the limited aperture that was used in the cross-line direction. The events can be suppressed by using a larger aperture in the cross-line direction. Other techniques to suppress these events, such as developed in seismic exploration, are based on smoothing the contribution of high insonification angles (aperture tapering).

78 74 3D imaging results from measured data (a) Three different slices through the two pass imaged data 0 0 0 5 5 5 10 10 10 15 15 crossline (mm) depth (mm) depth (mm) 20 20 15 25 25 20 30 30 25 35 35 40 40 30 0 2 4 6 8 0 5 10 15 20 25 30 0 2 4 6 8 inline (mm) crossline (mm) inline (mm) (b) Slice through (c) Slice through the yz-plane (d) Slice the xy-plane through the xz-plane Figure 5.3: Result of images produced with the data from a test block with a 3 mm round bottom hole. The data was imaged in both direction with the two-pass method. The im- provement in the resolution in the cross-line direction, compared with figure 5.2c, is clearly visible.

79 5.2 3D imaging of three inclined cylinders with round bottom holes 75 5.2 3D imaging of three inclined cylinders with round bottom holes In this section, the results of 3D images from a test block with three bore holes will be presented. The three bore holes were drilled in a 25 mm thick carbon steel test plate. Two of the bore holes have a 1 mm diameter and are drilled 20 mm deep with an angles of 45 and -45 . The third hole was drilled adjacent to one of the other bore holes with a center to center separation of 2.25 mm. The third hole has a 0.5 mm diameter and it was drilled 10 mm deep with a 45 angle, hence parallel to one of the other holes. All of the three bore holes have spherical tips. The three bore holes are visualized in figure 5.4, a technical drawing is found in appendix C, figure C.1. The data was acquired similarly to the data of single round bottom hole of the previ- ous section, with recordings over an aperture of 30 mm with an in-line scan every 1 mm. The previous example of the single bore hole can be considered a special case, since the scan direction is not important because of the symmetry of the reflector. In this exam- ple, the scan direction is important. In the in-line direction, all combinations of sources and receivers are recorded (hence the full data matrix). In the cross-line direction, only zero-offset measurements are obtained (hence the diagonal of the data matrix). When the defects are very small and behave as point scatterers, the spherical wave front will be evenly distributed along the surface. However, if the defect becomes larger, it will reflect energy in certain directions. In that case, the wave front will have a certain directivity and the distribution of the reflected wave front along the surface will have a high energy at some locations. The location of this optimum is dependent on the orientation of the defect and it can be determined by following ray paths. When the full data matrix is recorded, there will be multiple combinations of ray paths that contribute to the data matrix. In case of zero-offset measurements, only the ray path that leads back to the source (perpendicu- Figure 5.4: Three bore holes with an inclination and with different depths and diameters, used to produce a 3D image.

80 76 3D imaging results from measured data Figure 5.5: Zero-offset measurements (left) are more sensitive for the orientation of planar defects then full-array measurements (right). In case of zero-offset, only the perpendicular rays and the weak tip diffractions will contribute. In case of full-array, the ray paths from different source and receiver elements and the weak tip diffractions will contribute. lar insonification) and the weak tip diffractions will contribute to the data matrix (figure 5.5). As a consequence, the scan direction is important when the measurement aperture is limited. Ideally, the scan direction should be such that the measurement aperture covers the area where the highest energy caused by perpendicular insonification and reflection for optimal zero-offset measurements, can be expected. For the measurements of the three bore holes, the in-line direction coincided with the direction of the inclination of the holes. Hence, the flanks of the bore holes should be detected with the full-array approach. Figure 5.6 presents the result after the data was imaged in both directions. In this figure, three slices are presented: A vertical slice at 15 mm cross-line position. This slice shows the two flanks of the opposite inclined deep bore holes. The amplitude of the tips is higher than the amplitude at the flanks. Because the tips scatter the waves in all directions, both the zero-offset and the full-array measurements have received the wave fields. However, the flanks are detected only by the full-array measurements, and the zero- offset measurements will not contribute significantly. A vertical slice at 42 mm in-line position. This slice illustrates that the resolution in the cross-line direction is better then in the in-line direction. This was also noted in section 5.1. A horizontal slice at 17 mm depth. This slice was taken through the tip of the small bore hole. Indeed the small tip is imaged and it can be resolved from the larger adjacent bore hole. The results of figure 5.6 can be observed in more detail when the individual slice are pre- sented. Figure 5.7a presents the vertical slice at 15 mm cross-line position. In this figure,

81 5.2 3D imaging of three inclined cylinders with round bottom holes 77 Figure 5.6: Three different slices through the data from a test block with three bore holes with an inclination and with spherical tips, that was imaged in both directions. 0 0 5 5 depth (mm) depth (mm) 10 10 15 15 20 20 25 25 0 10 20 30 40 50 0 10 20 30 40 50 inline (mm) inline (mm) (a) Cross-line position: 15 mm (b) Cross-line position: 13 mm Figure 5.7: Two xz-slices through the 3D image space of a test block with three bore holes from figure 5.4. The slice of figure a represents a cross section of the two large inclined bore holes. The slice of figure b represents a cross section of the small inclined bore hole.

82 78 3D imaging results from measured data 0 0 0 0 5 5 10 10 5 5 15 15 20 20 10 10 inline (mm) inline (mm) depth (mm) depth (mm) 25 25 30 30 15 15 35 35 40 40 20 20 45 45 50 50 25 25 5 10 15 20 25 30 5 10 15 20 25 30 8 10 12 14 16 18 8 10 12 14 16 18 crossline (mm) crossline (mm) crossline (mm) crossline (mm) (a) Depth: 10 mm (b) Depth: 17 mm (c) In-line po- (d) In-line po- sition: 12 mm sition: 35 mm Figure 5.8: Figures a and b represent two xy-slices through the 3D image volume of the 3D image data from a test block with three bore holes from figure 5.4 and figures c and d represent two yz-slices through this volume. The slice presented in figures a and c, intersects the ends of the large bore holes, figure b and d intersects with the end of the small bore hole. the amplitude differences between the tips and the flanks is better observable. Further- more, the orientation of the two deep bore holes can be identified clearly. The orientation is 45 , corresponding to the actual bore holes. Figure 5.7a also illustrates a small defect at position (30 mm,22 mm). This was not an intended defect, but must have been created during the manufacturing of the block. Figure 5.7b present the vertical slice at 13 mm cross-line position. At this position, the small bore hole is located. The flank of the bore hole is not evident, because the diameter of the bore hole is smaller and causes less diffraction. However, the tip of the defect, located at position (35 mm, 17 mm), is clearly visible. The two flanks of the adjacent deeper bore holes also can be identified vaguely as a result of the resolution limitations in the cross-line direction. Figures 5.8a and b presents two horizontal slices at depth 10 mm and 17 mm respec- tively. The horizontal slice of figure 5.8a was taken through the tips of the two 1 mm diameter bore holes. The position of the two holes can be identified clearly. Again it can be seen that the resolution in the in-line direction is better than in the cross-line direction. Figure 5.8b reveals the tip of the 0.5 mm diameter bore hole. Figures 5.8c and d present two vertical slices at in-line positions 12 mm and 35 mm re- spectively. The presence and positions of the two bore hole tips can be identified in the

83 5.2 3D imaging of three inclined cylinders with round bottom holes 79 images. Furthermore, some weak events are visible in both images, as a result of aperture limitations. In the next section, the results will be presented of an inclined planar reflector. The planar reflector was scanned in two directions, so that the limitations of zero-offset measurements in combination with limited measurement aperture become more evident. Furthermore, we will present an additional approach to visualize the results, using scatter plots.

84 80 3D imaging results from measured data 5.3 3D imaging of a planar inclined slit In the previous section the results were presented and analyzed of 3D images from a test block with three bore holes with spherical tips. We have seen that the direction in which the cross-line measurements are obtained, is relevant for the resulting image. Here we will illustrate this in more detail with the use of a planar inclined slit (5.9). So far, we have presented the results as orthogonal slices through the image volume. When the geometry of the defect is not in one of the orthogonal planes, it is difficult to recognize the defects shape. Therefore, we will also visualize the results with 3D scatter plots. The test piece of which the results will be illustrated here, contains a 10 mm wide slit, under a 45 angle with the surface in a 25 mm thick carbon steel block. The end of the slit is not straight, one side is 20 mm and the other side is 23.5 mm long. Furthermore, the slit is orientated 35 relative to the normal of the length of the block (see the technical drawing in appendix C, figure C.3). The first set of measurements performed on this test piece, were carried out with the cross-line direction parallel to the length of the test piece. Hence, the angle between the in-line direction and the slit was 35 . The cross-line steps were 1 mm and the cross-line aperture was 40 mm. The measurements were 3D imaged with the two-pass method. We have applied a thresh- old to the resulting imaged data, and displayed this data with amplitudes higher then the threshold in a 3D scatter plot. The result of the first series of imaged measurements is presented in 5.10. Figures 5.10a, b and c present three different views of the imaged volume. From these results, we can observe the following: The top end of the slit was detected and imaged. It can be seen that the top end is Figure 5.9: Test piece with an inclined slit and and skewed end.

85 5.3 3D imaging of a planar inclined slit 81 (a) (b) (c) Figure 5.10: Three different views of the volumetric scatter plot that was obtained by applying a threshold to the image volume. The end of the slit is clearly visible, however the flanks of the slit was not detected. The shadow that is caused by the flank is visible as a gap in the imaged back wall. not orientated such that it can be clearly visualized in one of the orthogonal planes. Those planes would intersect the imaged top end. The flank of the slit is absent. This is caused by the unfavorable orientation of the zero-offset measurements in the cross-line direction. The imaged back wall shows a large gap. This area is caused by the shadow effect of the slit. This area of the back wall was not insonified because the slit obscured the sound path. However, it should be noted that such a shadow area indicates the presence of a defect. The shape of the shadow area may be analyzed to obtain more information on the defects characteristics. If the orientation of the reflector is not known, all one can do is to scan the test piece parallel to one of the sides of the test block. However, in our case a second series of measurements was done with a more suitable orientation for the defect under consideration. The cross-line direction in this case, was parallel to the defect, such that zero-offset insonifications would receive reflections from the flank of the slit. Figure 5.11 presents three different views of the scatter plot that was obtained from the result of the second series of measurements. From the results, we can observe the following: The flank of the slit is now clearly visible. It can be seen that the slit is inclined with respect to the back wall. The exact angle of the inclination is difficult to obtain from the scatter plots. It can be seen that the end of the slit is skewed. However, it remains difficult to obtain the exact angle of the skewed slit end.

86 82 3D imaging results from measured data (a) (b) (c) Figure 5.11: Three different views of the volumetric scatter plot that was obtained from a second series of measurements of the test block with the inclined slit. The orientation of the slit was now chosen favorable with respect to the the cross-line direction. The flank of the slit is now also imaged and clearly visible. The shadow area is still present. However, the area under the slit was now better insonified and the area is smaller. From figure 5.11, we can determine the orientation of the flank from the appropriate view angle of the scatter plot. With that information, we can draw an inclined slice through the image volume, that coincides with the flank. The result is presented in figure 5.12. From this result, we can observe the following: From the inclined slice, the angle of the slit end can be determined. The amplitude of the imaged flank becomes weaker for deeper positions. This is a result of the fact that less elements can detect the deeper areas in the zero-offset configuration. We obtained already valuable information from the image volume, with the scatter plots and the inclined slice. In figure 5.13 also illustrates some orthogonal slices through the image volume. Figures 5.13a, b and c are vertical slices at three different cross-line position, 14.7 mm, 17.1 mm and 19.6 mm respectively. From these figures, the angle of the slit can easily be determined. The orientation found is 45 , corresponding with the actual slit orientation. Figures 5.13d, e and f are vertical slices at three different in-line positions, being 4.4 mm, 7.8 mm and 11.2 mm respectively. The horizontal event corresponds with a cross section of the flank. Figure 5.13d illustrates a small horizontal event, which corresponds with the skewed end of the slit. Figures 5.13e and 5.13f illustrate the full width of the slit, at differ- ent depths. Also, the shadow area is visible underneath the horizontal events. Figures 5.13g, h, i and j are horizontal slices at four different depths, being 10.3 mm,

87 5.3 3D imaging of a planar inclined slit 83 (a) (b) (c) Figure 5.12: Three different views of the image volume with two slices. One of the slices coincides with flank of the slit. In that slice, the shape of the slit is clearly recognizable. 15.2 mm, 20 and 24.9 mm respectively. Figure 5.13g illustrates a small vertical event, which is an intersection with the skewed end of the slit. Figures 5.13h and i illustrate two vertical events. It can be observed that the amplitude of figure i is weaker because its deeper, as we also observed in figure 5.12. Furthermore, the slice at 24.9 mm depth of figure 5.13j is located in the back wall. The shadow zone can clearly be identified in this figure. The results that were presented here were very interesting to analyze the 3D character- istics of the two-pass method. However, the inclined slit is not very representative for defects that are common in girth welds. Therefore, a test piece was manufactured with an actual weld. A small tungsten plate was embedded in the weld. Tungsten does not melt at the same temperature as steel. Therefore, the tungsten fragment can be considered a real weld defect. In the next section, we will present the results of the weld with the embedded tungsten fragment.

88 84 3D imaging results from measured data crossline: 14.7 mm crossline: 17.1 mm crossline: 19.6 mm 0 0 0 5 5 5 10 10 10 depth (mm) depth (mm) depth (mm) 15 15 15 20 20 20 25 25 25 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 inline (mm) inline (mm) inline (mm) (a) (b) (c) inline: 4.4 mm inline: 7.8 mm inline: 11.2 mm 0 0 0 5 5 5 10 10 10 depth (mm) depth (mm) depth (mm) 15 15 15 20 20 20 25 25 25 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 crossline (mm) crossline (mm) crossline (mm) (d) (e) (f) depth: 10.3 mm depth: 15.2 mm depth: 20 mm depth: 24.9 mm 0 0 0 0 5 5 5 5 10 10 10 10 crossline (mm) crossline (mm) crossline (mm) crossline (mm) 15 15 15 15 20 20 20 20 25 25 25 25 30 30 30 30 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 inline (mm) inline (mm) inline (mm) inline (mm) (g) (h) (i) (j) Figure 5.13: Different orthogonal slices through the 3D image volume of the inclined slit as presented in figure 5.9. The positions of the slices are in the titles above the figures.

89 5.4 3D imaging of a buried reflector in a weld 85 5.4 3D imaging of a buried reflector in a weld The results of the 3D images that were presented in the previous sections 5.1, 5.2 and 5.3 demonstrated the possibilities and characteristics of 3D imaging using the two pass method. However, the examples were not very representative for real weld defects. To test the two pass method for a more representative situation, a weld was manufactured with an intentional defect. The weld was manufactured from two 19 mm thick carbon steel plates prepared with an X-bevel with 45 V-preparation, as illustrated in figure 5.14. During the welding, a small rectangular tungsten strip of 16 x 4.3 x 1.5 mm was placed against the flank. Tungsten has a higher melting point (3410 C) than carbon steel (around 1500 C), and therefore, the tungsten fragment will cause a lack of fusion. After the weld was fin- ished, the cap was flattened to obtain good access for the probe. Figure 5.14: To evaluate the two pass 3D imaging approach for a realistic situation, a weld was manufactured. The X-weld was welded with a small tungsten strip, that causes a lack of fusion due to the difference in melting temperature. The data was collected using all 64 elements in the in-line direction and over a 40 mm aperture in steps of 1 mm in the cross-line direction. The data was processed with the 3D two pass method. In figure, 5.15 the resulting scatter plots are presented from three different views. From these views, we can see the following: The surface and the back wall can clearly be identified in the scatter plots. The presence of the tungsten plate can also be identified clearly. No shadow is present at the back wall. Apparently, the tungsten strip is small enough to allow sufficient insonification of the back wall. Apart from the tungsten plate, more indications can be observed. These indications suggest that more defects are present in the weld. Destructive testing must be performed to confirm this. To obtain more quantitative information from the image, we can observe slices through the image volume. Figure 5.16 presents some slices through the images volume of different

90 86 3D imaging results from measured data (a) (b) (c) Figure 5.15: Three different views of the scatter plot from the weld with an embedded tungsten strip. The strip is clearly visible in the 3D image.

91 5.4 3D imaging of a buried reflector in a weld 87 in-line positions. It can be seen seen that the images at the different in-line positions are not the same. This result suggests that the defect is irregular and does not have the smooth rectangular shape of the tungsten strip. During the welding process, the melt bath did not fuse with the tungsten strip due to the difference in melting temperature. As a consequence the melt bath solidified around the tungsten strip in an undefined, irregular way. If we take the envelopes of the x/z slices and sum them over the length of the defect, we get a general impression of the average hight, width and orientation of the defect. The result is presented in figure 5.16f. Here we can see that the orientation and the height of this image roughly corresponds with the cross section of the tungsten strip. We can also examine y/z slices at different cross-line direction. The result is presented in figure 5.17. It is difficult to determine the length of the defect from the individual y/z slices. Again, an average impression can be obtained if we sum the envelopes of the y/z-slice over the width of the defect. The result is presented in figure 5.17d. From this results we can see that the length of the indication also corresponds with the length of the tungsten plate. In addition, a second indication can be recognized in figure 5.17d between cross-line position 5 and 15mm at 10 mm depth. This indication cannot be explained by the presence of the tungsten strip. It is likely that this indication is a real additional defect. In figure 5.18, some x/y slices at different depth positions are presented. If we take the envelopes of the slice and sum them, we can obtain an average impression of the defects length and width (5.18d). An X-ray image is a projection of the defect in the depth direc- tion. Hence, the result of figure 5.18d can be interpreted as a quasi X-ray result. We have seen that the average dimensions of the defect obtained from the different views corresponds with the size of the tungsten plate. However, we cannot confirm this with certainty, because the exact shape and size of the defect are not known. With destruc- tive testing, more information can be obtained of the exact shape and size of the defect by macro sectioning. Still, this information will be limited, because the defect cannot be sectioned according to all the slice positions.

92 88 3D imaging results from measured data crossline: 9.9 mm crossline: 13 mm crossline: 16 mm 0 0 0 2 2 2 4 4 4 6 6 6 8 8 8 depth (mm) depth (mm) depth (mm) 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 inline (mm) inline (mm) inline (mm) (a) (b) (c) crossline: 19 mm crossline: 25 mm summed envelopes 0 0 0 2 2 2 4 4 4 6 6 6 8 8 8 depth (mm) depth (mm) depth (mm) 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 inline (mm) inline (mm) inline (mm) (d) (e) (f) Figure 5.16: xz slices, at different in-line positions. Figure f, represents the sum of the enveloped xz slices over the entire defect length. The differences in the shape at different in-line position suggest that the defect is very irregular. However, from the result of the summed envelopes, the orientation of the defect can be recognized.

93 5.4 3D imaging of a buried reflector in a weld 89 inline: 10.4 mm inline: 11.7 mm 0 0 2 2 4 4 6 6 depth (mm) depth (mm) 8 8 10 10 12 12 14 14 16 16 18 18 20 20 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 crossline (mm) crossline (mm) (a) (b) inline: 13.8 mm summed envelopes 0 0 2 2 4 4 6 6 depth (mm) depth (mm) 8 8 10 10 12 12 14 14 16 16 18 18 20 20 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 crossline (mm) crossline (mm) (c) (d) Figure 5.17: yz slices, at different cross-line positions. Figure d, represents the sum of the enveloped yz slices over the entire defect width. The length of the tungsten strip corresponds with the length of the indication in the image. Also, a second indication can be recognized between cross-line position 5 and 15mm at 10 mm depth. This indication suggest the pres- ence of an other real defect in the weld.

94 90 3D imaging results from measured data depth: 11 mm depth: 13 mm depth: 15 mm summed envelopes 0 0 0 0 5 5 5 5 10 10 10 10 crossline (mm) crossline (mm) crossline (mm) crossline (mm) 15 15 15 15 20 20 20 20 25 25 25 25 30 30 30 30 35 35 35 35 40 40 40 40 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 inline (mm) inline (mm) inline (mm) inline (mm) (a) (b) (c) (d) Figure 5.18: xy slices, at different depth positions. Figure d, represents the sum of the enveloped xy slices over the entire defect depth. This result can be interpreted as a quasi X-ray film. The dimensions of the defect in the image corresponds with size of the tungsten strip.

95 6 Artifacts and their removal In practice, multiple wave fronts from the scatterer will be received as a result of mode conversion and/or multiple bounces off the back wall and front wall. Images from mode- converted waves, can be used to support interpretation of the longitudinal wave images. Furthermore, due to the lower velocity of the transversal waves, mode-converted waves have a potentially higher resolution. The imaging process removes the propagation effects from only one insonification path with a chosen wave mode (L or T) and only one propagation path from scatterer to re- ceivers with a chosen wave mode. Due to the difference in sound velocity between L-waves and T-waves, the non-mode converted waves will image as leakage artifacts in the mode- converted images, and vice versa. This may lead to false interpretations. In this chapter such artifacts will be identified and explained with the help of an ana- lytical example. Measurements from steel test pieces with a 4 MHz linear array transducer with 64 elements will be used to demonstrate the artifacts. Furthermore, a procedure to predict the artifacts and the subsequent suppression from the input measurements will be presented and demonstrated. 6.1 Derivation of the location of artifacts Here, we will give a simplified analytical 2D example to demonstrate the position and shape of L-L energy leaked into the L-T image of a point scatterer in carbon steel. The example is not intended to explain the suppression of the artifacts, this will be addressed in the following sections.

96 92 Artifacts and their removal For this example, we will use the general imaging approach Portzgen et al. [2007] that also was presented in chapter 2. For the analytic illustration, we will concentrate on the location and shape of the artifacts. We will not so much be concerned with exact ampli- tudes. The amplitude behavior of the leaked energy will be dealt with automatically in section 6.3 on the actual removal of the leaked energy. The imaging approach consist of three steps as was also mentioned in section 2.1: [1] Removal of the propagation effects from an image point to the receivers. This step is performed in the space-frequency domain with the Rayleigh II integral for back propagation. After this step, for every source location the data consist of a single recording of the scattered field, by a virtual receiver located in the image point chosen. [2] Removal of the propagation effects from the sources to the image point. It can be demonstrated with the argument of reciprocity, that this step also involves back propagation with the Rayleigh II integral. After this step, the full data set has been reduced to a single signal generated by a virtual source in the image point and detected by a single virtual receiver located in the same position. [3] At the image point, the amplitude at t = 0 of the coinciding virtual source - virtual receiver recording, is assigned to that point as image amplitude. The three steps must be repeated for each point in the image space. The L-L and L-T imaging modes are selected by using L-wave propagation velocity in steps 1 and 2, or by using T-wave velocity in step 1 and L-wave velocity in step 2, respectively. For the first step in this example, we start with the 2D far-field approximation of the Rayleigh II integral for inverse wave field extrapolation. It is given by Portzgen et al. [2007], Berkhout [1987] (see also equation (2.2.6)): r Z j zA 1 r P (~rA ; ) P (x, 0; ) ej c dx, (6.1.1) 2 c rr where P (~rA ; ) is the Fourier transformed pressure in an image point A located at ~rA = (xA , zA ) in the object space caused by waves with angular frequency in a medium with sound velocity c. Furthermore, p P (x, 0; ) are pressure recordings at a recording plane lo- 2 cated at z = 0, and r = (x xA )2 + zA . The medium of interest for this example will be carbon steel. Hence, the waves can be transversal or longitudinal. The sound velocity c in equation (6.1.1) can be ct = 3250 m/s or cl = 5900 m/s. The choice of c depends on the wave mode of the insonification path or the scatter path. Because the imaging procedure consist of two back propagation steps, equation (6.1.1) must be applied twice. We may choose different wave modes for each step. It should be noted that in an elastic medium like steel, we cannot talk about pressure fields, neither for the longitudinal waves nor for the transversal waves. However, as both wave modes are converted back to acoustic pressure waves in the coupling with the steel to the transducer, we can continue to describe the L-waves and T-waves by scalar functions,

97 6.1 Derivation of the location of artifacts 93 O x S(xS , 0) R(xR , 0) z rSA SD rAR A(xA , zA ) SA rSD rDR RA RD D(xD , zD ) Figure 6.1: The wave field of a cylindrical compression source S will diffract in a longitudinal and a transverse wave at D. The back propagated recordings at z=0 will cause an unwanted contribution at A resulting in an artifact. that have the physical dimension of pressure. We now consider a line S located at (xS , 0), on the surface of a recording plain at z = 0, as illustrated in figure 6.1. A line diffractor D is present in the material, located at (xD , zD ). At t = 0, the source fires a short pulse that generates a longitudinal wave. The pressure field of this insonifying wave at diffractor D can be described analytically by (Berkhout [1982]): r cl r j cSD P (xS , 0; xD , zD ; ) =S() e l , (6.1.2) rSD p 2 where S() is the spectrum of the source pulse and rSD = (xD xS )2 + zD . We will assume that the source only generates longitudinal waves with sound velocity cl . The insonifying wave field will scatter at D and two waves will be generated as a result. One is the scattered longitudinal wave, the other is the scattered transversal wave. The upward traveling waves measured at z = 0 can now be described as: rSD r rSD r j( + cDR ) j( + cDR ) P (xS , 0; xR , 0; )=S(){D (xR , xS )e cl l + D (xR , xS )e }, cl t p (6.1.3) 2 where rDR = (xD xR )2 + zD , D (xR , xS ) represents the scalar amplitude of the scattered L-wave and D (xR , xS ) is a function that is proportional to the amplitude of the scattered T-wave. The amplitudes represented by D (xR , xS ) and D (xR , xS ) are depen- dent on the source position xS and the receiver position xR . D (xR , xS ) and D (xR , xS ) are dependent on the source location through a dependency of the scattered field on the angle of incidence. Since in this section we are concerned only with the shape and location of the leakage of L-L energy into the L-T image, we will ignore this dependency in the current analysis.

98 94 Artifacts and their removal The total pressure measured at the surface as described by equation (6.1.3) consist of the contribution of the longitudinal wave (the first term of equation (6.1.3)) and the transver- sal wave (the second term of equation (6.1.3)). From the wave field described by equation (6.1.3) measured at z = 0, we can compute the pressure in every point A below z = 0 at ~rA = (xA , zA ), using equation (6.1.1). We expect a high pressure and thus a high contri- bution to the image amplitude if the location of A coincides with the location of D. For the first step in the imaging process, we back propagate the measured wave field to a regular grid of image points in the object. We must choose a wave mode for the first back propagation step. Since the total scattered wave field consist of both the L- and T- waves, only the mode that corresponds with our choice will be back propagated correctly. In this example we choose the transversal wave mode with sound velocity ct to remove the prop- agation effects from receivers to image point. As a consequence, the propagation effects of the recorded L-wave field will not be removed correctly. We will demonstrate, that this incorrect back propagation leads to non-zero image amplitudes in locations other then the diffractor D, thus constituting the leakage of L-L energy into the L-T image. To focus on this leaking, we will continue our analysis with only the first term of equation (6.1.3). For the first back propagation step of the L-T imaging process, we can write equation (6.1.1) with the first term of equation (6.1.3) as: Z rSD r r j( + cDR ) j cAR P (xS , 0; xA , zA ; ) S() D (xR , xS )e cl t e t dxR , (6.1.4) p 2 with rAR = (xA xR )2 + zA (see figure 6.1), and where we used the transversal propa- gation velocity because that is the mode of the propagation that we are supposed to remove. The pressure P (xS , 0; xA , zA ; ) of the back propagated wave field after the first step of the imaging process, can now be simplified with the stationary phase method to: P (xS , 0; xA , zA ; ) S()ej (xS ,xR0 ) , (6.1.5) where xR0 is called the stationary receiver point which is the solution of the equation d (xS ,xR ) dxR = 0, with rAR rSD rDR (xS , xR ) = . (6.1.6) ct cl cl The physical interpretation of this result is that in the high frequency limit only one receiver located at the stationary point xR0 contributes to the integral in equation (6.1.4). For the location of the stationary receiver we find the relation: xA xR0 xD xR0 np 2 = p 2 , (6.1.7) (xA xR0 )2 + zA (xD xR0 )2 + zD with n = cl /ct the refraction index. To find the contribution to the image point at the location of A in the image space, the propagation effects of the insonification paths from the sources S to A also must be re- moved. In this example, the second step in the imaging process involves the same back

99 6.1 Derivation of the location of artifacts 95 propagation approach as the first step. This can be demonstrated with the argument of reciprocity. During the second step, we will back propagate the wave field that would be measured at the locations of the sources, as though they were receivers. This wave field was generated in point A as though it was a source, with a pressure described by equation (6.1.5). The second back propagation step is carried out with the velocity of the L-waves cl , hence we will image the L-T arrivals. Application of (6.1.1) again and incorporating equation (6.1.5) leads to: Z rAS j P (xA , zA ; xA , zA ; )S() D (xR , xS )ej (xS ,xR0 ) e cl dxS , (6.1.8) p 2 with rSA = (xA xS )2 + zA (figure 6.1). P (xA , zA ; xA , zA ; ) represents the pressure of the wave field in A after the two back propagation steps, as if recorded by a coinciding virtual source/receiver point in A. Making use of the high frequency approximation again, we can simplify equation (6.1.8) to: P (xA , zA ; xA , zA ; ) S()ej(xS0 ,xR0 ) , (6.1.9) d(xS ,xR0 ) where xS0 is called the stationary source point. It is the solution of the equation dxS = 0, with rSA . (xS , xR0 ) = (xS , xR0 ) + (6.1.10) cl Again, the interpretation of this result is that only one source located at xS0 contributes to the integral of equation (6.1.8). We can find this location with the following relation: xS0 xA xS0 xD p 2 = p 2 . (6.1.11) (xS0 xA )2 + zA (xS0 xD )2 + zD In the third step of the imaging process, we transform P (xA , zA ; xA , zA , ) described by equation (6.1.9) back to the space-time domain to obtain p(xA , zA ; xA , zA , t). Now we assign the amplitude of the pressure at t=0 to the image point located in A, hence I(xA , zA ) = p(xA , zA ; xA , zA , t = 0), (6.1.12) where I(xA , zA ) is the image amplitude in A. From equation (6.1.12) together with equation (6.1.9), we find that I(xA , zA ) has non-zero values when (xS0 , xR0 ) = 0, assuming a very narrow source pulse s(t). This yields the following relation: q q q q 2 2 2 2 (xS0 xA )2 + zA +n (xA xR0 )2 + zA = (xS0 xD )2 + zD (xD xR0 )2 + zD + . (6.1.13) In summary, all points (xA , zA ) in the image space that are solutions to equation (6.1.13) have non-zero image amplitudes. These points form a locus curve that defines the location and shape of the recorded L-L energy that leaked into the L-T image of the point scatterer D. In order to find these points, we must eliminate the stationary points xR0 and xS0

100 96 Artifacts and their removal from equation (6.1.13) with equations (6.1.7) and (6.1.11). A practical approach to find the non-zero locations (xA , zA ) is presented in appendix B. In case the recorded longitudinal wave was back-propagated with its true velocity cl , the refraction index n becomes one. In the limit n 1, it can easily seen that the locus curve will collapse into a point located in D, thus constituting the proper L-L image of D. In the next section we will show the predicted location and shape of leaked L-L energy into the L-T image of a point scatterer by evaluating the locus curve numerically. Further- more, examples with measured data will be given. 6.2 Analysis of the positioning of leaked L-L energy in the L-T image of a point scatterer To illustrate the shape and location of mode leakage related to a point source, we place an array of sources and receivers above three point-scatterers at 2 mm, 4 mm and 6 mm depth in a semi-infinite medium. For this illustration, we assume that the sources and receivers are located from minus to plus infinity and are closely spaced. In practice, this will not be the case, but with this illustration we can determine the shape of the artifact in an ideal case. We shall determine the shape of the artifact caused by L-L arrivals in the L-T image. We have used the approach as described in appendix B to determine the locations (xA , zA ) that form the locus curve of the artifact. In figure 6.2 the result is presented. The predicted artifacts corresponding to the point scatterers are umbrella shaped and located above the point scatterers. From equation (6.1.13) it can be derived that the depth of the artifact directly above the scatterer (hence xA = xD ) follows from, 2 zA = zD . (6.2.14) 1+n For the depths of the predicted artifacts in the examples of figure 6.2 we find with equation (6.2.14) 1.42 mm, 2.81 mm and 4.26 mm respectively. It can be seen that the shape of the artifacts depends on the depth of the scatterer. Fur- thermore, it can be proved that the deepest points of the artifact does not exceed the depth of the scatterer when taking for xS0 the limit to infinity. The deepest points of the scatterer are dependent on the aperture of sources and receivers. When the aperture with sources and receivers is limited, the artifact ends will become truncated. For the next example, real measurements were taken with an ultrasonic phased array system. The array probe consists of 64 elements with a pitch of 0.85 mm and gaps of 0.15 mm separating the elements. The center frequency of the probe is 4 MHz with a 50% bandwidth. The measurements were taken over a 20 mm thick carbon steel plate (ct = 3250 m/s and cl = 5900 m/s) with a 1.5 mm diameter bore hole drilled in the center (see figure 6.3a). The imaging approach for the examples is described in Portzgen et al. [2007].

101 6.2 Analysis of the positioning of leaked L-L energy in the L-T image of a point scatterer 97 0 1 2 depth in mm 3 4 5 6 7 0 2 4 6 8 10 distance in mm Figure 6.2: Umbrella shaped artifact caused by back propagation of the longitudinal diffracted wave with the transverse sound velocity ct . In figure 6.3b the result of the image from the L-L arrivals is presented. In figure 6.4a, the predicted artifact of L-L energy leaking into the L-T image is presented and in 6.4b the actual L-T is presented. The artifact indeed appears at the predicted location and with the predicted shape. The predicted artifact was constructed using the same range of positions for xR0 and xS0 as the actual array. The artifact in figures 6.4a and 6.4b is truncated due to practical aperture limitations. Furthermore, it can be seen in figure 6.4b that a second back wall is imaged at 14.2 mm depth. In fact, this is the L-L back wall reflection that has leaked through the L-T imaging mode. The depth of this spurious back wall image follows directly from equation (6.2.14) and is at 14.2 mm, see figure 6.4a. The last example that will be presented is from a 30 mm carbon steel block with an inclined slit (see figure 6.5a). The measurements were taken with the same equipment and with the same array transducer as the previous example. Figure 6.5b and 6.5c presents the result of the image that is obtained from the L-L arrivals. The orientation and the position of the slit is imaged correctly. The back wall is not imaged over the entire length due the the shadow effect caused by the slit preventing insonification of the back wall. Figure 6.5c is the same as 6.5b whereby the gray scale represents 20dB more sensitivity. In figure 6.5c, we can see a weak event (appointed by the arrow L-T artifact). This event is caused by the L-T arrivals and hence is the L-T artifact in the L-L image. Figure 6.5d presents the result of the image that is obtained from the L-T mode of imag- ing. The L-T energy in the image is again imaged correctly. However, as expected, energy from the L-L arrivals has leaked into this image, forming the artifacts that are identified by the arrows. The tip of the slit behaves partially as a point scatterer, hence the part of

102 98 Artifacts and their removal 0 2 4 6 distance in (mm) 8 10 12 14 16 18 20 20 25 30 35 distance in (mm) (a) Measurement set-up for the bore hole (b) Image constructed from the L-L arrivals of the bore hole Figure 6.3: Measurement set-up with a 64 element 4 MHz array probe. The probe is placed on a 20 mm thick steel block with a 1.5 mm bore hole. The image was obtained from the direct longitudinal insonification path and the direct longitudinal scatter path (the L-L arrivals). The imaging procedure as described in Portzgen et al. [2007], accounts for all possible source-receiver combinations. the artifact that corresponds to this tip has got the umbrella shape. It should be stressed at this point that the analysis of the leaking mechanism presented here only served the purpose of demonstrating and understanding the phenomenon of mode leakage. In the next section, a practical approach to removing the artifacts in the L-T images of the two examples from this section, will be presented. This method is generally valid and does not make the assumptions needed to forward model the leakage artifacts.

103 6.2 Analysis of the positioning of leaked L-L energy in the L-T image of a point scatterer 99 0 0 2 2 4 4 6 6 distance in (mm) distance in (mm) 8 8 10 10 12 12 14 14 16 16 18 18 20 20 20 22 24 26 28 30 32 34 36 20 25 30 35 distance in (mm) distance in (mm) (a) Predicted artifacts (b) L-T image of the bore caused by the bore hole hole and the back wall Figure 6.4: The predicted and actual locus curves of the artifact in the image obtained from the arrivals of the longitudinal insonification path and the scattered transversal path (the L-T image) of the test block with the bore hole, see figure 6.2.

104 100 Artifacts and their removal 0 5 10 distance in (mm) 15 20 25 30 15 20 25 30 35 40 45 distance in (mm) (a) Measurement set-up inclined slit (b) L-L image of the inclined slit 0 0 5 5 LL slit artifact 10 10 distance in (mm) distance in (mm) 15 15 LL back wall artifact 20 20 LT artifact 25 25 true back wall image true slit image 30 30 15 20 25 30 35 40 45 15 20 25 30 35 40 45 distance in (mm) distance in (mm) (c) The same image as figure b with 20dB (d) L-T image more amplification Figure 6.5: Measurement set-up with a 64 element 4 MHz array probe. The probe is placed on a 30 mm thick steel block with an inclined slit. The image obtained from the direct longitudinal insonification path and the direct scatter path (the L-L image) appears to have no artifacts. However, with a higher amplification, an artifact becomes visible. Also the image obtained from the direct longitudinal insonification path and the direct transversal scatter path (the L-T image) shows significant artifacts.

105 6.3 Suppression of artifacts 101 6.3 Suppression of artifacts Now that the cause of the artifacts is understood, methods can be designed to suppress them. In case of the examples in the previous section, it is known which arrivals caused the artifacts. The wave fronts that have caused the artifacts in the L-T images were the same wave fronts that imaged correctly in the L-L images. If we can trace back where this L-L energy was in our recorded data, we may be able to suppress it before it can leak into the L-T image. The procedure to suppress the artifacts in the L-T image can be described by the following steps: [1] Construct the L-L image from the original measurements. The correct L-L arrivals are imaged at the correct position after this step. [2] From the L-L image, determine the pure L-L image amplitudes of the object by applying a threshold to the L-L image amplitudes. Leaked L-T energy in the L-L image is supposed to be below this threshold. [3] From the pure L-L image amplitudes, calculate (analytically) or simulate (numeri- cally) a new recorded data set with L-L arrivals only. This data set does not contain any transversal waves. [4] Subtract the pure L-L data from the original recorded data. After this step, a new data set is obtained that no longer contains L-L arrivals that could leak into the L-T image [5] Construct the pure L-T image. These steps will be discussed in more detail and they will be applied to the two examples that were presented in the previous section. To suppress the artifacts in the L-T images, we start from the L-L image. The L-L image will contain the correctly imaged L-L energy, noise and maybe leaked energy from other modes such as the L-T mode (see for example figure 6.5c). The first step is illustrated again for the example with the inclined slit in figure 6.6a. Based on the results presented in figure 6.6a, in the second step we will determine the pure L-L image amplitudes. To that purpose, we will assume that the amplitudes of the incorrectly imaged arrivals from other modes in the L-L image are much lower than the cor- rectly imaged arrivals of the L-L mode itself. With this assumption, the incorrectly imaged arrivals can be regarded as noise. To get rid of the noise, we first determine the envelopes of the events in the L-L image. The result is presented in 6.6b. Then, we apply a threshold to remove all amplitudes in the image that are below the threshold value. To determine the threshold value, we used the amplitude of the back wall in the envelope of the image as reference. This will be a consistent reference. The threshold value we used was 20 dB lower then the reference amplitude. It can be derived with the use of DGS-curves (Distance Gain S ize) Krautkramer [1977], that cylindrical scatterers with a diameter less then roughly 0.25 mm will be treated as noise as a consequence. The result after the threshold was applied is presented in figure 6.6c. This result represents the reflectivity information, that can be used as a base for the model to determine genuine L-L arrivals.

106 102 Artifacts and their removal As an extra refinement to determine the pure L-L reflectivity model, we assume that the reflections and diffractions took place at sharply defined interfaces, such as the back wall and cracks. To obtain sharply defined interfaces in our reflectivity model, we select the positions of figure 6.6c where the derivative of the envelope equals zero. The result is presented in figure 6.6d. This result defines the reflectivity model, whereby total reflection corresponds with the highest value (normalized to one) and whereby lower values corre- spond to partial reflection. The range of reflectivity from zero to one is represented by the gray scale in figure 6.6d. We will use the reflectivity model for the third step of our proce- dure. Note that we have obtained the reflectivity model without any assumptions on the position and shape of the possible defects. Hence, the approach to obtain the reflectivity model is hands off and can be automated. Now that we have obtained our reflectivity model, we can calculate or simulate the L- L arrivals, whereby we assume that the medium is homogeneous and supports longitudinal wave propagation only, with sound velocity cl . Many approaches are presented in the lit- erature to calculate or simulate time domain responses from a known reflectivity model. For example, well known numerical simulation approaches are based on finite differences Youzwischen and Margrave [1999], Virieux [1986], finite element Lord et al. [1990], finite integration Schubert [2004] or (semi)-analytical approaches Sumbatyan and Boyev [1994], Kuhnicke [1996]. Also (commercial) software packages for numerical simulation of wave fields are available, such as Field II Jensen, Jensen [1996] and CIVA, Calmon et al. [2006]. Numerical simulations may be accurate, but time consuming. Therefore, we used a more efficient analytical approach to determine the L-L arrivals from the reflectivity model, called de-migration Santos et al. [2000], Tygel et al. [1996], Frazer and Sen [1985]. This approach is based on the fact that each point of the reflectivity model causes a defined hyperbola in the data, scaled with the reflectivity value from the model. The hyperbolae can be calculated analytically from the pressure distribution caused by a point source. Then, all contributions to a data point from all points in the reflectivity model are summed. The accuracy of the simulated or calculated data depends on how representative the reflectivity model is. In practice, the arrival times of diffractions and reflections are reliably predicted from the reflectivity model. However, the reflectivity values are not accurate. This is un- derstood, because reflection in carbon steel is dependent on the angle of the insonifying and scattered waves. In addition, reflection involves both wave modes that can also convert from one mode to the other Krautkramer [1977]. As a consequence, the time positions of the hyperbolae in the new data are well predicted, but the amplitudes will not be repre- sentative for the L-L arrivals in the real data. In order to suppress the L-L contributions in the original data using the simulated L-L data, the next processing step must be performed. The fourth step in the procedure involves the suppression of the L-L waves in the data based on the synthetically generated data set with L-L reflections. We will present two approaches to achieve this, one based on masking and one based on adaptive subtraction. With the masking approach, the simulated L-L waves are used to determine the posi- tion of the L-L waves in the original data. The synthetically generated L-L waves will then be used to mask the L-L energy in the original data. In figure 6.7a an unprocessed A-scan is presented from source element number 25 and receiver element number 34, obtained from the test piece with the bore hole, see figure 6.3a. The simulated A-scan for the same

107 6.3 Suppression of artifacts 103 0 0 5 5 10 10 distance in (mm) distance in (mm) 15 15 20 20 25 25 30 30 15 20 25 30 35 40 45 15 20 25 30 35 40 45 distance in (mm) distance in (mm) (a) Original L-L image of figure 6.5b (b) Envelope of the L-L image 0 0 5 5 10 10 distance in (mm) distance in (mm) 15 15 20 20 25 25 30 30 15 20 25 30 35 40 45 15 20 25 30 35 40 45 distance in (mm) distance in (mm) (c) 20 dB threshold applied on the enve- (d) Locations with the values of the pre- lope L-L image vious image where the derivative equals zero Figure 6.6: To remove the artifacts in the L-T image, the L-L arrivals that caused them must be identified and suppressed in the original data. The L-L image is used to define a reflectivity model. Then, the reflectivity model is used to calculate or to simulate the arrivals that consist of the L-L arrivals only.

108 104 Artifacts and their removal source and receiver element and with L-L waves only, is presented in figure 6.3b. The phase and amplitude of the simulated A-scan does not match the measured data very well, but the arrival time of the simulated L-L wave seems correct. To construct the mask, first the envelope of the simulated A-scan was derived. Then, the result was processed according to: pmask (t) = 1 C envelope[m(t)], (6.3.15) where pmask (t) represents the multiplication masking function, C represents an attenua- tion factor and m(t) represents the synthetic A-scan containing the modeled L-L arrivals. Furthermore, all the values of pmask (t) < 0 are set to zero. The resulting mask is presented by the dashed line in figure 6.7b. Next, the unprocessed data is multiplied by the mask, the result being presented in figure 6.7c. Here, it can be seen that only the L-L waves have been masked, and the L-T wave remains unaffected. The masking approach is straightforward and robust. Only the attenuation factor C can be adjusted to optimize the result. However, it ignores the phase information and it also masks other waves that are close to or overlapping the L-L waves. Figure 6.8a presents the result after the mask was applied to all the recordings of source elements 15, 25 and 35. It can be seen from this result, that the masking approach also masks waves that are close to or overlapping the L-L waves. A more elegant approach to remove the L-L arrivals in the original data-set with the help of the modeled L-L data, is by adaptive subtraction. In this method it is assumed that the modeled L-L arrivals have approximately correct arrival times, but that the amplitudes and the shape of the signal pulses are not necessarily correct. The purpose of adaptive sub- traction is to derive and apply a least squares matching filter to the modeled L-L arrivals, before subtraction from the input data. If we consider the modeled L-L arrivals m(t) for one source-receiver pair and if p(t) represents the original data with all arrivals, then a short convolution filter f (t) is designed such that it minimizes the residual energy: Zt2 t+t Z E= [p(t) f ( )m(t )d ]2 dt, (6.3.16) t1 tt in which the filter length is 2t. For discrete signals this minimization problem can be solved efficiently using a recursion scheme Levinson [1947], Robinson and Treitel [1980]. In practice, one filter is estimated for a group of signals within a certain time window (t1 < t < t2 ), such that distortion of interfering L-T events is minimized, assuming that the interference is not the same for a group of neighboring signals. These windows are moved in an overlapping fashion along the measurements in time and space and the re- sulting outputs of the different windows can be blended into the final subtraction result (Verschuur and Berkhout [1997]). In this way spatial and temporal variations in amplitude and phase of the predicted L-L events can be accommodated. The size of the application window and the length of the filters are parameters that can be varied to tune the solution. Figure 6.7d illustrates the result of adaptive subtraction for the A-scan of source element number 25 and receiver element number 34. In figure 6.8b, it can be seen that the adap- tive subtraction approach does not significantly affect signals that are close to, or overlap overlap with the L-L waves.

109 6.3 Suppression of artifacts 105 1 0.5 norm. amp. surface wave LL wave LT wave 0 0.5 back wall reflection 1 0 1 2 3 4 5 6 7 8 time in s (a) Unprocessed A-scan of source element 25 and receiver element 34 1 norm. amp. 0.5 mask 0 LL wave 0.5 back wall reflection 1 0 1 2 3 4 5 6 7 8 time in s (b) Simulated L-L waves (solid line) and the derived mask (dashed line) 1 norm. amp. 0.5 LL wave masked LT wave 0 back wall reflection masked 0.5 1 0 1 2 3 4 5 6 7 8 time in s (c) Unprocessed A-scan multiplied by the mask 1 0.5 norm. amp. LT wave 0 0.5 1 0 1 2 3 4 5 6 7 8 time in s (d) Resulting A-scan after adaptive subtraction Figure 6.7: Suppression of the L-L waves in the data is presented with two different ap- proaches, masking and adaptive subtraction. Both approaches use the simulated L-L waves to identify and suppress or mask the L-L wave in the original data.

110 106 Artifacts and their removal source number 15 source number 25 source number 35 source number 15 source number 25 source number 35 0 0 2 2 4 4 time in (s) time in (s) 6 6 8 8 10 10 12 12 14 14 16 32 48 64 16 32 48 64 16 32 48 64 16 32 48 64 16 32 48 64 16 32 48 64 receiver number receiver number (a) Processed data, the L-L arrivals of the (b) Processed data, the L-L arrivals of scattered and back wall have been sup- the scattered and back wall have been pressed by masking suppressed by adaptive subtraction Figure 6.8: Recordings of the array with source elements, 15, 25 and 35. The masking approach also masks signals that are close to or overlap with the L-L waves. The adaptive subtraction approach affects those signals less severely. When the L-L waves have been treated with the masking or the adaptive subtraction approach, we can proceed with the final step of our proposed procedure. The L-T images can now be constructed with the processed data, from which the L-L energy has been sup- pressed. The results of the two methods, masking and adaptive subtraction, are presented in figure 6.9 for the case of the test block with the bore hole. Figure 6.9a presents the resulting image from the data that was processed with the masking approach and figure 6.9b shows the result of the adaptive subtraction approach. In both results, the umbrella shaped artifact and the second back wall clearly have been suppressed in the L-T images. No significant difference between the two approaches can be observed in this example. For the L-T image of the inclined slit of figure 6.5, the resulting L-T images are presented in figure 6.10. Figure 6.10a illustrates the result of the data that was processed with the masking approach and figure 6.10b shows the result of the adaptive subtraction approach. It can be seen that the artifacts that were identified in figure 6.5c have been suppressed by both approaches. This example also shows the difference between the two approaches. When the L-L signals are suppressed by masking, we can see from figure 6.10a that the tip of the slit becomes slightly blurred. This occurs when signals that should contribute to the sharpness of the image are also masked. As can be seen in figure 6.10b, the result with the adaptive subtraction approach shows a sharper tip. Here, the signals contributing to the sharpness of the tip have been affected less. However, it can be seen from 6.10b that a

111 6.3 Suppression of artifacts 107 0 0 2 2 4 4 6 6 distance in (mm) distance in (mm) 8 8 10 10 12 12 14 14 16 16 18 18 20 20 20 25 30 35 20 25 30 35 distance in (mm) distance in (mm) (a) Data processed with masking (b) Data processed with adaptive substraction Figure 6.9: Images of the L-T arrivals using the processed data of the example with the bore hole. The umbrella shaped artifact and the second back wall that were visible in figure 6.3c have been removed after the data was processed with two different techniques. vague residue appears at the position where the artifacts were present. This is caused by signals from the L-L waves that were not fully suppressed. In summary, the adaptive subtraction approach may leave remnants of leakage artifacts, but it maintains the sharpness of the defect image. The masking approach is more robust and suppresses the artifacts almost fully, but the sharpness of the defect image may be affected.

112 108 Artifacts and their removal 0 0 5 5 distance in (mm) distance in (mm) 10 10 residue 15 15 spreading no spreading 20 20 residue 25 25 30 30 15 20 25 30 35 40 45 15 20 25 30 35 40 45 distance in (mm) distance in (mm) (a) Data processed with masking (b) Data processed with adaptive subtraction Figure 6.10: Image of the L-T arrivals using the processed data of the example with the inclined slit. Again, the artifacts that were visible in figure 6.5c have been removed.

113 7 Conclusion In the following sections some general conclusions will be drawn. Then, conclusions that are specific for the 2D and 3D results will be given. Finally, conclusions related to the removal of the artifacts will be given. 7.1 General conclusions In this thesis, a 2D and 3D imaging method based on inverse wave field extrapolation (IWEX) was presented, for detection and characterization of defects in carbon steel girth welds. The imaging method is based on general wave theory and earlier has been applied successfully in the application field of seismic exploration. With the development of faster computers and with advances in ultrasonic array technology, the transfer from the seismic application field to the application field of NDI became feasible. The imaging approach presented in this thesis was applied to test pieces with 2D reflectors that are representative for defects in girth welds. Also experiments were carried out on reflectors with a more 3D nature to give a proof of principle that the results obtained in 2D can be extended to 3D. The 3D imaging approach consisted of two successive 2D imaging steps. The first step was performed in the in-line direction where all transmitter - receiver combinations were taken into account. The second step was performed in the cross-line direction where the less calculation intensive zero-offset imaging approach was applied. The inverse wave field extrapolation (IWEX) imaging approach is suitable for many differ- ent weld preparations. As opposed to standard automated girth weld inspection based on zone discrimination, the inspection set-up does not change from project to project. In fact,

114 110 Conclusion the inspection set-up does not depend on the weld preparation, the only a-priori parameters that are required are the sound velocities and the wall thickness. The array design can be optimized for the required resolution. Higher frequencies (>5MHz) for better resolution and more elements to cover a wider aperture may be necessary. Because the IWEX imaging approach is independent of the weld preparation, a calibration procedure may be simple and only necessary for the sensitivity of the system. The purpose of calibration blocks will also be to give a performance demonstration as required by most codes and standards. 7.2 Conclusion on the 2D imaging of defect like reflectors From the results of the imaging of the 2D defect-like reflectors, we can draw the following conclusions: Small defects that behave as point scatterers can very well be imaged, as was illus- trated by the results of a single isolated bore hole. Images were presented from three different modes, the L-L mode, the L-T mode and the LL-LL mode. The L-L mode seems most appropriate. However, when the scatterer is located near the upper sur- face, it is better to use the LL-LL mode. The L-T mode also contains information on the scatterer. This mode can be used to verify the results of the other modes. Care should be taken to stop the leaking of L-L energy into the L-T image. This process can be carried out effectively in an automated, hands-off way. Planar defects such as lack of fusion and cold lap can be very well imaged with the L- L mode, especially when the length is larger then the wave length and the orientation is less then 45 (horizontally). It was demonstrated that surface breaking defects located at the outer surface can best be imaged with the LL-LL mode, which does not have a dead zone there. The dead zone is caused by surface waves and cross talk signals, that obscure the direct arrivals. It was also demonstrated that surface breaking defects with non-favorable orientations can be imaged and sized reasonably. This can be considered an impor- tant improvement compared to standard detection and characterization techniques for such defects, such as the corner-trap method. It was demonstrated that small defects close together, such as porosity, can be re- solved with the L-L mode, when they are more then 1 mm apart. Even better resolution may be obtained depending on the depth of the defects. The property to resolve defects is important when interaction criteria must be applied. Furthermore, the results show good agreement with analytic resolution analysis (see section 3.4). The tips of vertically orientated defects such as lack of cross-penetration can be imaged using both the L-L and the LL-LL mode. Unlike defects that are more horizontally orientated, the full extent of the defect cannot be imaged. Therefore, images of the two modes are necessary, to determine if the images represent a single defect or two individual defects. This can be done by looking for a difference in phase

115 7.3 Conclusion on the 3D imaging results 111 and by the fact that the upper tip shows up better in the L-L image and the lower tip shows up better in the LL-LL image in case of a single vertically orientated defects. In practice, the L-L mode will contain the most information. However, the L-L mode will not cover the entire volume and, therefore, other modes also must be used. Those images may contain artifacts or too much noise resulting in a less straightforward interpretation. Like with all inspection techniques, procedures must be written and training courses must be given to help the inspector with the interpretation and use of the equipment, but we maintain that the imaging based inspection technique presented here, is for more objective and far less an art, than the traditional NDI. We can conclude that the requirements for the detection and sizing of defects that were determined in section 3.2 are met, with the use of the presented measurement set-up and the 4 MHz linear phased array probe. 7.3 Conclusion on the 3D imaging results The objective of the 3D measurements was to prove that the IWEX imaging approach of ultrasonic data is also feasible in 3D. Therefore, the reflectors that were used to obtain the 3D images were designed for that purpose. One test piece was manufactured with a practically real defect. This test piece contained a weld with an embedded tungsten strip. The 3D images were constructed form the L-L mode only. From the results of the images of the 3D reflectors, we can summarize the following conclusions: 3D images were produced using the two pass method, that consists of two 2D imaging steps, one with the full-array approach (in-line direction) and one with the zero-offset approach (cross-line direction). From the results of a round bottomed hole, it was demonstrated that the resolution with the two-pass method is significantly improved in the cross-line direction. It was also demonstrated that as a result of the element size, the resolution in the in-line direction (roughly 2 mm) is better than in the in- line direction (roughly 1 mm). The resolution determined from the measurements is in agreement with the resolution analysis of section 3.4. Furthermore, we can state that this would be acceptable to comply with the required resolution specifications for defect length and height as discussed in section 3.2. It was demonstrated from the results of the three inclined round bottom cylinder holes, that the tips are imaged with a higher amplitude then the cylinder flanks. This is caused by the fact that the flanks of the holes reflect the waves in a direction outside the measurement aperture. Furthermore, the zero-offset approach is more sensitive to the orientation of reflectors then the full-array approach. From the result of the inclined slit, it was demonstrated that the scan direction is not unimportant. The first results did not show the flank of the planar inclined slit, whereas the results with the optimized scan direction showed the flank clearly. Furthermore, it was demonstrated that a shadow area appears at the back wall, because the slit obscures the insonification path. The scatter plots resulting from the 3D image volume of the test piece with the weld clearly revealed the position and size of the embedded tungsten strip. The orientation

116 112 Conclusion is less clear. However, the height of the tungsten strip was in the order of the wave length. 7.4 Conclusions on the appearance and suppression of L-L leak- age artifacts in L-T images With an analytical example, we have identified and predicted artifacts in images from L- T arrivals caused by L-L arrivals. The predicted artifacts correspond very well with the observed artifacts in actual ultrasonic images for two test blocks, one with a vertical bore hole and one with an inclined slit. A method is presented to predict and suppress the L-L arrivals from the original measure- ments in order to obtain a leakage-free L-T image. The prediction of L-L arrivals is based on a process whereby the L-L image is used to construct a reflectivity model. A thresh- olding process in the L-L image automatically selects the strongest L-L image amplitudes, while rejecting the weaker L-T image amplitudes that have leaked into the L-L image. Two different approaches have been presented to suppress the predicted L-L signals from the original data, being a masking process or adaptive subtraction. The leakage artifacts from other propagation modes now are suppressed significantly. The method was demonstrated successfully on actual measurements from the two test blocks. The presented methodology to predict and remove leakage artifacts in images from un- wanted arrivals can be adapted to other propagation scenarios. For example, it can be extended to situations with indirect insonification via the back wall or other boundaries, also in combination with various mode conversions.

117 8 Discussion and recommendations Some aspects of the work presented in this thesis have been discussed only briefly, because they were not taken into account in the current imaging methodology. In this chapter, some of these aspects and the consequences will be discussed in more detail. Recommendation for improvements and further research will follow. 8.1 Discussion on the resolution, a gap in the aperture In section 3.4 the resolution of the IWEX imaging approach was studied with the use of the point spread function (PSF). We have presented PSFs obtained for three different imaging approaches, common source imaging, zero offset imaging and full array imaging. Also, the consequences of having a limited number of source/receiver elements and elements with beam directivity were discussed. The results presented in this thesis were obtained from measurements, whereby the array probe could be placed directly above the area under investigation. However, in practice this area will usually not entirely be accessible. Most welds are produced with a reenforcement at the surface called the cap. Due to the cap, it is not possible to place the array directly over the weld. Two arrays can be placed on either side of the cap. We can regard the two arrays as a singe array with a gap in the aperture. Here, we will discuss the consequences of this gap on the resolution from the PSF. The PSF of an array with aperture length L can be calculated from equation (3.4.10), whereby we first have to calculate the Fourier trans- formed pressure P (xA , zA ; ) in a point A. We now introduce a gap of length G centered in the aperture as illustrated in figure 8.1. Then, the pressure P (xA , zA ; ) can be calculated from equation (3.4.7), minus the pressure contribution from elements that within the gap

118 114 Discussion and recommendations G L x np n p a z rD rA n A = (xA , zA ) D = (0, zD ) Figure 8.1: At the surface z = 0, the pressure is recorded of a point source D. The recorded wave field will be back propagated to a point A to determine the point spread function. G, as illustrated by the black elements in figure 8.1. We can formulate this pressure as, ( ) (N 1)/2 (K1)/2 X ej c (rnA rnD ) X ej c (rkA rkD ) P (xA , zA ; ) = S()zA p An Ak , n=(N 1)/2 rnA rnD rnA k=(K1)/2 rkA rkD rkA (8.1.1) where the subscript k denotes the elements in the gap that consist of K elements in total, hence the length of aperture G is Kp. The amplitude factors An and Ak account for direc- tivity properties and can be determined with equation (3.4.12). Equation (8.1.1) was evaluated numerically for an array with 60 elements with a pitch of 0.85 mm. The center frequency of this array transducer was 4 MHz, with a 50% band- width. The gap was created by omitting the contributions of K elements from the center of the array, where K was varied between 0 and 40. The PSF was calculated for the horizontal and vertical direction and for different diffractor depth (5, 10 and 30 mm). The directivity properties of the elements were not taken into account. The results are presented in figure 8.2. From the results of figures 8.2a, c and e, we can conclude the following for the resolution in the vertical direction: The main lobe in the near field (zA < 10mm), becomes broader when the gap length increases. The side lobes become stronger in the near field. In the far field (zA > 30mm), the vertical resolution is unaffected for the calculated gap lengths.

119 8.1 Discussion on the resolution, a gap in the aperture 115 Diffractor depth z = 5 mm Diffractor depth z = 5 mm D D 1 1 K = 0 (0 mm) K = 0 (0 mm) K = 10 (8.5 mm) K = 10 (8.5 mm) 0.75 K = 30 (25.5 mm) K = 30 (25.5 mm) 0.75 normalised point spread function normalised point spread function K = 40 (34 mm) K = 40 (34 mm) 0.5 0.5 0.25 0.25 0 0 0.25 0.25 0.5 0.75 0.5 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z in mm x in mm A A (a) (b) Diffractor depth z = 10 mm Diffractor depth z = 10 mm D D 1 1 K = 0 (0 mm) K = 0 (0 mm) K = 10 (8.5 mm) K = 10 (8.5 mm) 0.75 K = 30 (25.5 mm) K = 30 (25.5 mm) 0.75 normalised point spread function normalised point spread function K = 40 (34 mm) K = 40 (34 mm) 0.5 0.5 0.25 0.25 0 0 0.25 0.25 0.5 0.75 0.5 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z in mm x in mm A A (c) (d) Diffractor depth z = 30 mm Diffractor depth z = 30 mm D D 1 1 K = 0 (0 mm) K = 0 (0 mm) K = 10 (8.5 mm) K = 10 (8.5 mm) 0.75 K = 30 (25.5 mm) K = 30 (25.5 mm) 0.75 normalised point spread function normalised point spread function K = 40 (34 mm) K = 40 (34 mm) 0.5 0.5 0.25 0.25 0 0 0.25 0.25 0.5 0.75 0.5 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 z in mm x in mm A A (e) (f) Figure 8.2: The PSFs for a diffractor at depths, 5 mm, 10 mm and 30 mm and derived for different gap lengths. The number of elements in the gap is K and the total number of elements was 60. The pitch of the elements on the array is 0.85 mm, the directivity properties were not taken into account. The left plots illustrate the vertical PSF, and the right plots illustrate the horizontal PSF.

120 116 Discussion and recommendations From the results of figures 8.2b, d and f, we can conclude the following for the resolution in the horizontal direction: The main lobe width becomes narrower when the length of the gap increases. The side lobes become bigger when the length of the gap increases. The presence of the increased side lobes will not form a major impediment for practical situations. Two point diffractors can still be resolved reasonably well in the presence of these side lobes. The width of the main lobe determines the resolving power. In the horizontal direction, it seems that the gap will improve the resolution for the cases presented. However in the vertical direction the resolution deteriorates. Based on the results of figure 8.2, we can conclude as a rule of thumb that the gap should not exceed 25 mm for girth weld inspection, using the array transducer as described earlier. The cap of most girth weld designs will fit this requirement.

121 8.2 Imaging of LL-L arrivals 117 8.2 Imaging of LL-L arrivals The images that were presented in this thesis were mainly obtained from the direct longitu- dinal insonification path and the direct longitudinal scatter path (the L-L image), the direct longitudinal insonification path and the direct transversal scatter path (the L-T image) and the indirect longitudinal insonification path and the indirect longitudinal scatter path (the LL-LL image). Other insonification and scatter paths with different combinations of modes are of course also possible. However, the amount of energy in those recorded waves may be too low to obtain enough signal to noise ratio. For defects with a vertical orientation, it can be expected that the indirect longitudi- nal insonification path and the direct scatter path (the LL-L path) contains enough energy to construct an image with a satisfactory signal to noise ratio. In fact, the LL-L path resembles the so called tandem technique in conventional inspection. This technique is used when it is not possible to insonify the defect perpendicularly, i.e. for vertically orien- tated defects. The LL-L image was constructed for several cases of the examples that are presented in chapter 4. However, the results were not encouraging. As an example, the LL-L image for the test block with the 1.5 mm bore hole (see figure 4.1) is presented in figure 8.3a. This image does not show the bore hole properly or resembles the L-L or L-T images that are shown in figure 4.3. We can explain the poor result in the LL-L image with a geometrical argument. If we observe the recordings for a single source, we can identify the LL-L arrival of the bore hole in the data. In figure 8.4, the recordings from source element 40 are illustrated. In this data, the L-L, L-T and LL-L arrivals of the bore hole are identified. We can see that the LL-L arrival overlaps with the strong back wall reflection at the apex of the hyperbola. This can be seen better at the right side of figure 8.4, where the LL-L arrival and the back wall reflection are illustrated with lines. Because the back wall reflection has the same arrival time as the LL-L diffraction for some combinations of source-receiver elements, we can expect that the back wall amplitude contributes strongly to the image amplitude of the image point located at the position of the bore hole. We will demonstrate now that the back wall reflection contributes to many points in the image volume. We follow the LL-L path for a point A somewhere in the imaging volume. The travel time of the LL-L path is given by: 1 tLLL (xA , zA ) = (rSA + rAR ), (8.2.2) c p LL-L path, rSA = (xA xS )2 + (2d zA )2 where tLLL (xA , zA ) is the travel time of thep 2 where d is the wall thickness, and rAR = (xR xA )2 + zA , (see figure 8.5). The travel time of a back wall reflection td with the same source-receiver combination is given by: 1 td = rd , (8.2.3) c p where rd = (xR xS )2 (2d)2 , (see figure 8.5). In case tLLL (xA , zA ) td , then the signal caused by the direct back wall reflection, will always appear in the data at the same time as a scatterer that is located in A, for the given source-receiver combination. Hence,

122 118 Discussion and recommendations 1 2 2 0.9 4 4 0.8 6 6 0.7 distance in (mm) 8 distance in (mm) 8 0.6 10 10 0.5 12 12 0.4 14 14 0.3 16 16 18 0.2 18 20 0.1 20 0 20 25 30 35 20 25 30 35 distance in (mm) distance in (mm) (a) Unprocessed LL-L image of the bore (b) LL-L image constructed from the hole processed data Figure 8.3: LL-L images from the data that was obtained from the test piece with the bore hole (see figure 4.1). Due to the presence of the back wall response, all points in the image will get a high contribution. When the back wall reflections are suppressed, an image from the bore hole appears. a signal is present at that time regardless the presence of a scatterer. As a consequence, the image amplitude is determined by the back wall reflection and not by the presence of a scatterer. We now calculate the positions of point A in the image space, that fulfill the condition tLLL (xA , zA ) td . From equations (8.2.2) and (8.2.3), it follows directly that, rd rSA + rAR . (8.2.4) The distances rd , rSA and rAR form the legs of a triangle as is illustrated in figure 8.5. With the help of angle between rSA and rAR we find using the cosine rule: rd2 = rSA 2 2 + rAR 2rSA rAR cos. (8.2.5) If we take the square of both sides of equation (8.2.4), we find for the condition: rd2 rSA 2 2 + rAR + 2rSA rAR . (8.2.6) From equation (8.2.6) and equation (8.2.5), we can conclude that the the condition is fulfilled for all source-receiver combinations located at xS and xR , and points A located at

123 8.2 Imaging of LL-L arrivals 119 source number: 40 back wall reflection LLL scatter path 2 LL diffraction 4 LT diffraction time in (s) 6 8 LLL diffraction 10 12 8 16 24 32 40 48 56 64 8 16 24 32 40 48 56 64 receiver number Figure 8.4: Recordings of all 64 elements with source element 40 of the measurements from the test piece with a bore hole (see figure 4.1).The left side of the figure illustrates the data with high sensitivity so that the weak diffraction signals from the arrivals are visible. The right side of the figure illustrates the data with lower sensitivity. Here, the solid and dotted line indicate the arrival time of the back wall reflection and the LL-L diffraction of the bore hole. The two arrivals are almost the same at the apex.

124 120 Discussion and recommendations x S(xS , 0) R(xR , 0) A(xA , zA ) z rAR SA d d RA rd rSA rAR Figure 8.5: The back wall reflection from source S measured by receiver R will cause a contribution to a point A, also when no scatterer is present in point A. (xA , zA ) that form a triangle of which cos 1 or . Using figure 8.5 we can write for angle , = + SA RA . (8.2.7) It follows from equation (8.2.7) that all points in the image space of which SA RA , the back wall reflection arrives at approximately the same time. These points can easily be determined from tanSA = x2dzA xS A and tanRA = xRzxA A (figure 8.5), this yields zA xA xR + (xS xR ). (8.2.8) 2d With equation (8.2.8), all xA coordinates can be determined at all depth levels zA for all combinations of xS and xR where the back wall reflection arrives at the same time of a scatterer. The poor result illustrated in figure 8.3a can be explained by the fact that for many points in the images space, combinations of xS and xR can be found that satisfy equation (8.2.8). We have demonstrated with our analysis, that the back wall reflection will cause a poor LL-L image. If the back wall reflection is suppressed from the original data, then we may obtain a better result. The back wall reflection can be suppressed with the use of the masking or adaptive subtraction approach, as was also used to suppress the L-L artifacts in L-T images (see section 6.3). If the back wall reflection is suppressed, signals caused by the LL-L arrivals from the bore hole with the same travel time will also be suppressed. However, the signals that do not have the same travel time will be unaffected and produce an image of the bore hole (figure 8.3b).

125 8.3 Recommendations for further research 121 8.3 Recommendations for further research The results that were presented in this thesis were mainly generated with the L-L, the L-T and LL-LL arrivals. Although images of other arrivals may contain artifacts, not all arrivals that contain information on the defect have been used. Further research can be done on the L-LL arrivals, that can be compared with the tandem configuration. Despite the fact that L-LL images inherently suffer from poor resolution due to stretch effects, the images may be optimized by suppressing the back wall reflections and by only using those transmitter - receiver combinations that would give the best resolution. All the images in this theses were obtained from raw unprocessed data. For better re- sults, the raw data can be processed to increase the signal to noise level and to suppress near field effects. For example, surface waves are very well predictable and can be sup- pressed in the raw data or treated with the adaptive subtraction method. Also, the strong cross talk at the start of the A-scans may be treated. Furthermore, the resolution of the images may be improved by treating the A-scans with a deconvolution approach to min- imize the length of the wavelet under the condition of an acceptable noise level. In the field of seismic imaging, several approaches for deconvolution have been proposed already (Berkhout [1984] and Robinson and Treitel [1980]), resulting in improved resolution and minimization of side lobes. Further research on the effect of the gap in the aperture as a result of the cap weld rein- forcement. In some special practical cases the weld cap may be grind flush. However the majority of the pipelines will have girth welds with a cap. To obtain an optimal insonifica- tion of the weld volume, flexible arrays may be useful to cover the weld cap. Alternatively, plastic wedges can be used to optimize the directivity of the elements towards the weld volume. However, such a wedge will also create an extra interface giving rise to more mul- tiple reflections that may cause unwanted artifacts in the images. In most of the results presented, the aperture of the array was sufficient. However, in the case where the wall thickness exceeds 20 mm, artifacts are visible in the images as a result of the limited aperture. These artifacts were described earlier in seismic exploration. A remedy for these artifacts is to taper the Rayleigh II back propagation operator. This technique should be explored and optimized for the ultrasonic application field. Other processing tools that were developed in seismic exploration can also be applied on the ultrasonic data. In seismic exploration, methods were developed to suppress the effects of spatial aliasing Spitz [1991], Bancroft [1995], Zwartjes [2005]. With these tech- niques, the separation between the elements may be enlarged so that with a fixed number of channels, the aperture can be increased. Also methods were developed to account for the directivity of the array elements, resulting in an improved resolution. These methods involve deconvolution and they should be explored for the ultrasonic application field. In principle, welds in more complex geometries like transition welds or nozzles also can be inspected with the the IWEX imaging approach. Images from reflections via the bound- ary are in that case less straight forward but not impossible. The propagation operators must be estimated from images of the first arrived signals (the L-L arrivals). This will be

126 122 Discussion and recommendations the procedure for severe wall thickness variations or severe cases of high - low. For the SAFT application, the influence of geometry variations and surface roughness has already been studied by Lorenz [1993]. More complex weld materials like austenitic, alloys or plastic welds may also be inspected. Again, the propagation operator may not be straight forward then. However they can be obtained from the data. Compare the complexity with seismic exploration, where no a- priori knowledge is available and all properties of the subsurface like composition, density and sound velocity, must be estimated from the same single data set. The imaging theory presented in this thesis is based on linear wave theory that makes use of the Born approximation. In practice, this would mean that signals resulting from reverberations between individual defects are neglected. This approximation may hold in most cases. However, an interesting approach for imaging that should be applied on ultrasonic data would be based on non-linear wave theory Marklein et al. [2006] such as full wave form inversion. Imaging based on total inversion aims to find a property model that explains the recorded data in a non-linear iterative way (van den Berg and Kleinman [1997] and Abubakar et al. [2005]). The resolution that can be achieved with total inver- sion will be better than the resolution obtained from linear techniques (Simonetti [2006a] and Simonetti [2006b]). Although total inversion requires even more computer intensive calculations, it will be the final frontier for imaging ultrasonic data. Large defects can leave a shadow area (see for example figures 5.10). The presence of such a shadow area indicates the presence of a large defect. Further research can be done to analyze the information of the defect that can be obtained from the shadow area. For example the shadow area may contain information on the shape of the defect. 8.4 Final remarks The potential for improved probability of detection and unambiguous interpretation of results is very high. However, in order to be successfully applied in practice, more hurdles must be taken. Acceptance of the technique by both the industries and NDI providers is essential. Hopefully, this thesis and the publications that were written in the scope of this research will contribute to that process. Standards and codes are also essential for guidance on the use of IWEX imaging and for acceptance by industries.

127 Bibliography Abramowitz, M., and Stegun, I. A., 1964, Handbook of mathematical functions: Dover Publications N.Y. Abubakar, A., Habashy, T. M., van den Berg, P. M., and Gisolf, D., 2005, The diagonalized contrast source approach: an inversion method beyond the born approximation: Inverse Problems, , no. 21, 685702. Aki, K., and Richards, P., 2002, Quantitative seismology: University Sience Books. API, 1999, Welding of pipelines and related facilities, nineteenth edition, standard 1104: American Petroleum Insitute. Armitt, T., September 2006, Phased arrays not the answer to every application: We.3.1.3. Azar, L., Shi, Y., and Wooh, S., 2000, Beam focusing behavior of linear phased arrays: NDT&E international, 33, 189198. Bancroft, J. C., 1995, Aliasing in prestack migration: CREWES Research Report, 7, 25.1 25.16. Berkhout, A. J., 1982, Seismic migration, imaging of acoustic energy by wave field extrap- olation: Elsevier, second edition. Berkhout, A. J., 1984, Seismic resolution,resolving power of acoustical echo techniques: Geophysical press. Berkhout, A. J., 1987, Applied siesmic wave theory: Elsevier.

128 124 BIBLIOGRAPHY Bleistein, N., and Handelsman, R., 1969, Uniform asymptotic expansions of double inte- grals: journal of mathematical analysis and applications, 27, 434453. BS, 1996, Acceptance and rectification of welds, section 6: Britisch Standard. Burch, S., and Burton, J., 1984, Ultrasonic synthetic aperture focusing usingplanar pulse- echo transducers: Ultrasonics, pages 275281. Calmon, P., Mahaut, S., Chatillon, S., and Raillon, R., 2006, Civa; an expertise platform for simulation and processing ndt data: Ultrasonics, doi: 10.1016/j.ultras.2006.05.218, 15. Chiao, R., and Thomas, L., 1994, Analytic evaluation of sampled aperture ultrasonic imag- ing techniques for nde: IEEE transactions on UFFC, 41, no. 4, 484493. Claerbout, J., 1985, Imaging the earths interior: Blackwell scientific publications. Davies, J., Simonetti, F., and Cawley, P., 2006, Review of synthetically focused guided wave imaging techniques with application to defect sizing: Review of Quantitative Non- destructive Evaluation Vol 25, 142149. de Raad, J., and Dijkstra, F., 1995, Mechanized ut now replace rt on girth welds during pipeline construction: Pipeline Technology, II. de Raad, J., and Dijkstra, F., 1998, Mechanised ut on girth welds during pipeline construc- tion - a mature alternative to radiography: Insight, 40, no. 6, 435438. DNV, 1996, Non destructive testing, appendix D6 of Rules for submarine pipeline systems: Det Norske Veritas. Dube, N., E.A., and Moles, M., September 1998, Mechanized ultrasonic inspection of large diameter gas pipeline girth welds: Erhard, A., and Ewert, U., may 1999, The tofd method, between radiography and ultrasonic in weld testing: Jahres Tagung. Fenster, A., 2001, Three dimensional ultrasound imaging (topical review): Phys. Med. Biol., 46, 6799. Findlay, N., and van der Ent, J., 2001, Automated ultrasonic rotoscan weld inspection -agl - roma to brisbane stage & gas looping pipeline constructed by clough/lucas: Frazer, L., and Sen, M., 1985, Kirchhoff-helmholtz reflection seismograms in a laterally inhomogeneous multi-layered elastic mediumi. theory: Geophys. J. R. astr. Soc., 80, 121147. Gibson, B., Larner, K., and Levin, S., 1983, Efficient 3-d migration in two steps: Geophys- ical Prospecting, 31, 133. Ginzel, E., 2000, Amplitude sizing and mechanised ultrasonic inspection using linear scan- ning: www.NDT.net, 5, no. 4.

129 BIBLIOGRAPHY 125 Ginzel, E., 2006, Automated ultrasonic testing for pipeline girth welds: Olympus NDT Canada. Gisolf, A., and Verschuur, D., 2005, Acoustical imaging in complex media (college docu- mentation ap3531): Section Acoustical Imaging and Sound Control. Gross, B., Connelly, T., van Dijk, H., and Gilroy-Scott, A., 2001, Flaw sizing using mech- anized ultrasonic inspection on pipeline girth welds: www.NDT.net, 6, no. 7. Harvey, C., Pilcher, J., and Eckersley, R., 2002, Advances in ultrasound: Clinical Radiology, 57, 157177. Heckauser, H., September 2006, Trusts and beliefs in ut of girth welds: We.4.7.1. Holmes, C., Drinkwater, B., and Wilcox, P., 2005, Post-processing of the full matrix of ultrasonic transmit-receive array data for non-destructive evaluation: NDT&E Interna- tional, 38, 701711. Huang, J., Que, P., and Jin, J., 2004, Adaptive dynamic focusing system for ultrasonic nondestructive testing op pipeline girth welds: Review of scientific instruments, 75, no. 5, 13411346. Hughes, S., 2001, Medical ultrasound imaging: Physics Education, pages 468475. Jakubowicz, H., and Levin, S., 1983, A simple exact method of 3-d migration - theory: Geophysical Prospecting, 31, 3456. Jensen, J., Linear description of ultrasound imaging systems:, Technical report, Technical University of Denmark. Jensen, J., 1996, Field: A program for simulating ultrasound systems: Volume 34, Supple- ment 1, Part 1,, 351353. Jesse, T., and Smith, S., 2002, Real-time rectilinear volumetric imaging: IEEE UFFC, 49, no. 1, 114124. Johnson, J., and Barna, B., 1983, The effects of surface maping corrections with synthetic aperture focusing techniques on ultrasonic imaging: IEEE transactions on sonics and ultrasonics, SU-30, no. 5, 283293. Krautkramer, J., 1977, Ultrasonic testing of materials: Springer-Verlag Berlin Heidelberg New York, second edition. Krom, A., Lont, M., van den Heuvel, M., and van Nisselroij, J., may 2000, Comparing the integrity and economics of pipeline girth welds using different non-destructive testing techniques and acceptance criteria: Kuhnicke, E., 1996, Semianalytical method to calculate acoustic waves in layered elastic media: Ultrasonics, 34, 483486. Lee, J., and Choi, S., 2000, a parametric study of ultrasonic beam profiles for linear phased array transducer: IEEE UFFC, 47, no. 3, 644650.

130 126 BIBLIOGRAPHY Levinson, N., 1947, The wiener rms (root mean square) error criterion in filter design and prediction: Journal of Mathematics and Physics, 25, 261278. Loewenthal, D., Lu, L., Roberson, R., and Sherwood, J., 1976, The wave equation applied to migration: Geophysical Prospection, 24, 380399. Lord, W., Ludwig, R., and You, Z., 1990, Developments in ultrasonic modeling with finite element analysis: Journal of Nondestructive Evaluation, 9, no. 2/3, 129143. Lorenz, M., 1993, Ultrasonic imaging for the characterization of defects in steel components: Ph.D. thesis, Delft University of Technology. Lozev, M., 2005, Optimized inspection of thin walled pipe welds using advanced ultrasonic techniques: Journal of Pressure Vessel Technology, 127, 237234. Mland, E., 1988, Artefacts in zero-offset migration: Geophysical Prospection, 36, 633 643. Mahaut, S., Godefroit, J.-L., Roy, O., and Cattiaux, G., 2004, Application of phased array techniques to coarse grain components inspection: Ultrasonics (Elsevier), 42, 791796. Marklein, R., Miao, J., Rahman, M., and Langenberg, K., September 2006, Inverse scat- tering an imaging in ndt: Recent application and advances: Th.3.3.2. Mayer, K., Marklein, R., Langenberg, K., and Kreutter, T., 1990, Three-dimensional imag- ing system based on fourier transform synthetic aperture focusing technique: Ultrasonics, 28, 241255. Moles, M., and Labbe, S., November 2005, Special phased array applications for pipeline girth weld inspection: Moles, M., Dube, N., and Ginzel, E., June 2003, Pipeline girth weld inspection using ultrasonic phased array: Moles, M., Dube, N., Labe, S., and Ginzel, E., 2005, Review of ultrasonic phased arrays for pressure vessel and pipeline weld inspection: Journal of Pressure Vessel Technology, 127, 351356. Morgan, L., June 2002, The performance of automated ultrasonic testing (aut) of mecha- nised pipeline girth welds: Moura, E. P., 2004, Pattern recognition of weld defects n preprocessed tofd signals using linear classifiers: Journal of Nondestructive Evaluation, 23, no. 4, 163172. NEN3650, 1992, Non destructive testing, appendix D6 of requirements for steel pipeline transportation systems: NEN. Ogilvy, J., 1983, Diffraction of elastic waves by cracks: application to time of flight diffrac- tion: Ultrasonics, 21, 259269. Portzgen, N., Dijkstra, F., Wassink, C., and Bouma, T., June 2002, Phased array technol- ogy for mainstream applications:

131 BIBLIOGRAPHY 127 Portzgen, N., Gisolf, A., and Blacquiere, G., 2007, Inverse wave field extrapolation: a different ndi approach to imaging defects: IEEE transactions on UFFC, 54, no. 1, 118 126. Portzgen, N., September 2004, Practical results of ultrasonic imaging by inverse wave field extrapolation: Portzgen, N., September 2006, Practical results of ultrasonic imaging by inverse wave field extrapolation: Th.2.3.1. Ravenscroft, F., 1991, Diffraction of ultrasound by cracks: comparison of experiment with theory: Ultrasonics, 29, 2937. R/D-Tech, 2004, Introduction to phased array ultrasonic technology applications: R/D- Tech. Reynolds, A., 1978, Boundary conditions for the numerical solution of wave propagation problems: Geophysics, 43, no. 6, 10991110. Robinson, E., and Treitel, S., 1980, Geohysical signal analysis: Prentice Hall. Santos, L., Schleicher, J., Tygel, M., and Hubral, P., 2000, Seismic modeling by demigra- tion: Geophysics, 65, no. 4, 21811289. Schnneider, W., 1978, Intergral furmulatin for migration in two and three dimensions: Geophysics, 43, no. 1, 4976. Schubert, F., 2004, Numerical time-domain modeling of linear and nonlinear ultrasonic wave propagation using finite integration techniques -theory and applications: Ultrason- ics, 42, 221229. Simonetti, F., 2006a, Breaking the resolutin limit: a new perspective for imaging in nde: review of QNDE, 25, 700707. 2006b, Multiple scattering: The key to unravel the subwavelength world from the far-field pattern of scattered wave: physical review, E 73, (036619)113. Spitz, S., 1991, Seismic trace interpolation in the f-x domain: Geophysics, 56, no. 6, 785 794. Sumbatyan, M., and Boyev, N., 1994, Mathematical modelling for the practice of ultrasonic inspection: Ultrasonics, 32, no. 5, 511. Thomson, R., 1984, Transverse and longitudinal resolution of the synthetic aperture focus- ing technique: Ultrasonics, 22, 915. Tygel, M., Schleicher, J., and Hubral, P., 1996, A unified approach to 3-d seismic reflection imaging, part ii: Theory: Geophysics, 61, no. 3, 759775. van den Berg, P. M., and Kleinman, R. E., 1997, A contrast source nversion method: Inverse Problems, , no. 13, 16071620. Cerveny, C., 2001, Seismic ray theory: Cambridge University Press.

132 128 BIBLIOGRAPHY Verschuur, D., and Berkhout, A., 1997, Estimation of multiple scattering by iterative in- version, part ii: Practical aspects and examples: Geophysics, 62, 15961611. Virieux, J., 1986, P-sv wave propagation in heterogeneous media: Velocity-stress finite- difference method: Geophysics, 51, no. 4, 889901. Volker, A., 2002, Assessment of 3-d seismic acquisition geometries by focal beam analysis: Ph.D. thesis, Delft University of Technology. von Bernus, L., Bulavinov, A., and Dalichow, M., 2006, Sampling phased array - a new technique for signal processing and ultrasonic imaging: Insight, 48, no. 9, 545549. Wells, P., 2000, Current status and future technical advances of ultrasonic imaging: IEEE engineering in medicine and biology, pages 1420. Whittingham, T., 1999, Transducers and beam forming in medical ultrasonic imaging: Insight, 41, no. 1, 812. Wilcox, P., Holmes, C., and Drinkwater, B., September 2006, Enhanced defect detection and characterisation by signal processing of ultrasonic array data: Fr.1.1.4. Wooh, S., and Shi, Y., 1999, Optimum beam steering of linear phased arrays: Wave motion, 29, 245265. Youzwischen, C., and Margrave, G., 1999, Finite difference modeling of acoustic waves in matlab: CREWES Research report, 11. Zwartjes, P., 2005, Fourier reconstruction with sparse inversion: Ph.D. thesis, Delft Uni- versity of Technology.

133 A High frequency approximation According to Bleistein and Handelsman [1969], an integral such as equation (6.1.4) can be approximated in the high frequency limit. The general formulation is: Z lim F (x, )ej (x) dx = r 2j F (x0 , ) j (x0 ) q e , (A.0.1) 2 (x) | d dx 2 |x 0 where x0 is called the stationary point, given by:

134 d (x)

135 = 0, (A.0.2) dx x0 and where:

136 h 2 d (x)

137 i = sign

138 . (A.0.3) dx2 x0

139 130 High frequency approximation

140 B Derivation of the locus curves of L-L leakage artifacts in L-T images In this appendix, a practical method is given to find the solutions (xA , zA ) of equation (6.1.13). First an expression for zA will be derived from equations (6.1.7) and (6.1.13) in the form zA = f (xA , xS0 , xR0 ). We can write the relation of equation (6.1.13) as, q q R= x2S0A + zA 2 +n x2AR0 + zA 2 , (B.0.1) with xS0A = |xS0 xA |, xAR0 = |xA xR0 | and with R defined as, q q R x2S0D + zD 2 + x2DR0 + zD 2 , (B.0.2) with xS0D = |xS0 xD | and xDR0 = |xD xR0 |. Note that the definition of R does not depend on xA or zA . With the aid of figure 6.1, we define xAR0 tan (R0A ) = . (B.0.3) zA With the definitions of R and , we can write equation (6.1.13) as follows, p q 2 R nzA 2 + 1 = (zA xS0R0 )2 + zA , (B.0.4) with xS0R0 = |xS0 xR0 |. Taking the square of both sides of equation (B.0.4) yields a second order polynomial in zA ,

141 132 Derivation of the locus curves of L-L leakage artifacts in L-T images 2 AzA + BzA + C = 0, (B.0.5) with A = 1 + 2 n2 ( 2 + 1), (B.0.6) p B = 2xS0R0 + 2Rn 2 + 1, (B.0.7) and C = (R2 + x2S0R0 ), (B.0.8) of which the solution of zA is straight forward, bearing in mind that zA is always positive. To evaluate independent on xA and zA , we use equation (6.1.7) to find R0A . This yields, 1 R0A = sin1 ( sin(R0D )), (B.0.9) n with R0D = tan1 ( xDR0 zD ) (see figure 6.1). Hence R0A can be written independent of xA and zA . With equation (B.0.9) and the solution of equation (B.0.5), the first expression for zA = f1 (xS0 , xR0 ) is found. Note that this expression does not depend on xA . With the aid of figure 6.1 and with equation (6.1.11) we can see that S0A = S0D , hence the tangents of these angles must also be equal, this yields, xS0A zA = zD , (B.0.10) xS0D with xS0D = |xS0 xD |. Equation (B.0.10) is the second expression for zA = f2 (xA , xR , xS ). To find (xA , zA ), an iterative approach can be used. First, (xD , zD ) is given and xS0 and xR0 are chosen. In practice, there is a limited number of combinations since the ultrasonic array has a fixed number of elements. With xS0 and xR0 , R can be determined from equation (B.0.2) and from equations (B.0.3) and (B.0.9). Then zA = f1 (xS0 , xR0 ) can be solved from equation (B.0.5). With zA = f1 (xS0 , xR0 ), xA can be determined by: xA = xR0 f1 (xS0 , xR0 ). (B.0.11) With xA , xS0A can be determined and zA = f2 (xA , xS0 , xR0 ) can be solved from equation (B.0.10). The value of zA = f2 (xA , xS0 , xR0 ) must be the same as the result of zA = f1 (xS0 , xR0 ). For all values of xS0 a corresponding xR0 can be found on the aperture such that both expressions for zA (f1 (xS0 , xR0 ) and f2 (xA , xS0 , xR0 )) are equal. The values of zA and xA that correspond with the pairs of xS0 and xR0 that makes f1 (xS0 , xR0 ) = f2 (xa , xS0 , xR0 ) are the solutions that form the artifact.

142 C Technical drawings of test pieces Figure C.1: Technical drawing of the test piece with the three inclined bore holes. This test piece was used for section 5.2. The measures are in (mm), the sections A-A and B-B are illustrated in figure C.2

143 134 Technical drawings of test pieces (a) section A-A (b) section B-B Figure C.2: Sections of the technical drawing of the test piece with the three inclined bore holes, see figure C.1. The measures are in (mm).

144 135 (a) top view (b) view A (c) view C Figure C.3: Technical drawing of the test piece with the planar inclined notch. This test piece was used for section 5.3. The measures are in (mm).

145 136 Technical drawings of test pieces

146 D Symbols and Abbreviations D.1 Symbols In the following symbols that occur frequently are briefly explained. Symbols that occur infrequently are not listed. Their meaning will be clear from the text. Scalars symbol description a element size c sound wave velocity cl longitudinal sound wave velocity ct transversal sound wave velocity d wall thickness f frequency n element number p seismic wave field in the space-time domain pmask multiplication masking function t time xn x-coordinate of the n-th element

147 138 Symbols and Abbreviations xm discrete x-coordinate of an image point xA x-coordinate of a point A xD x-coordinate of a diffractor D xS x-coordinate of a source S xR x-coordinate of a receiver R xR0 stationary source point yA y-coordinate of a point A zs discrete z-coordinate of an image point z0 depth of a recording plane zA z-coordinate of a point A zD z-coordinate of a diffractor D An directivity amplitude factor C attenuation factor G Greens function G+ causal Greens function G anti-causal Greens function (2) H1 first order Hankel function of the second kind I image amplitude K number of elements in a gap L length of the array M total number of image points N total number of elements P seismic wavefield in the space-frequency domain Pn Fourier transformed pressure at the n-th element P SF point spread function Qm,n scalar inverse propagation operator Qm,n scalar inverse propagation operator with half the sound wave veloc- ity R scattering coefficient S source wavelet signature wavelength wave field angle n angle between diffractor point D and the n-th element angular frequency k discrete angular frequency component

148 D.1 Symbols 139 x heart to heart distance between two elements r distance between an observation point and a source point rm,n distance between a discrete image point an the n-th element rnA distance between the n-th element and an image point A rnD distance between the n-th element and a diffractor point D rAR distance between an image point A and a receiver R rDR distance between a diffractor point D and a receiver R rSA distance between a source point St and an image point A rSD distance between a source point S and a diffractor point D amplitude factor D scalar amplitude of a scattered L-wave D scalar amplitude of a scattered T-wave longitudinal scalar potential function transversal scalar potential function Vectors symbol description ~a vector with image amplitudes ~n direction vector normal to a surface ~r position vector of an observation point ~rA position vector of a point A ~ P Fourier transformed pressure vector ~zo P Fourier transformed pressure vector with zero-offset data ~m Q vector inverse propagation operator ~l U displacement vector for longitudinal waves ~t U displacement vector for transversal waves Matrices symbol description P Fourier transformed pressure matrix Pw Fourier transformed pressure matrix with the source wavelet signa- ture Q matrix inverse propagation operator Q matrix inverse propagation operator with half the sound wave ve- locity

149 140 Symbols and Abbreviations R matrix with scattering coefficients D.2 Abbreviations abbreviation description API American petroleum institute AS Australian standard AUT automated ultrasonic testing AVG amplitude verstarkung grosse BS British standard CSA Canadian standard DAC distance amplitude correction DGS distance gain size DNV Det Norske Veritas ECA engineering critical assessment FSH full screen height ISO international standard organization IWEX inverse wave field extrapolation LCF lack of cross penetration L-L longitudinal insonification and scatter path L-T longitudinal insonification paht and transversal scatter path LL-L indirect longitudinal insonification path and direct scatter path LL-LL indirect longitudinal insonification path and indirect scatter path NDI non-destructive inspection NDT non-destructive testing PSF point spread function SAFT synthetic aperture focussing technique TFM total focussing method ToFD time of flight diffraction

150 Summary Imaging of Defects in Girth Welds using Inverse Wave field Ex- trapolation of Ultrasonic Data Ultrasonic non-destructive testing is a renowned method for the inspection of girth welds. However, defect sizing and characterization remains challenging with the current inspection philosophy. In addition, data display and interpretation is not straightforward and requires skill and experience from the inspector. A better and more reliable inspection result would contribute to safer pipeline construction and economic benefits (like low false call rates and the possibility to use smaller wall thickness). In seismic exploration, images of the subsurface have been obtained using acoustic data, for many years. The main objective of this thesis is to apply the imaging concepts developed in seismic exploration to the application field of ultrasonic NDI in 2D and to give a proof of concept in 3D. The 2D inverse wave field extrapolation (IWEX) imaging approach is presented, which is based on the Rayleigh II integral for back propagation. A 3D imaging approach is pre- sented called two pass imaging. This approach consist of two 2D imaging steps performed in two orthogonal directions. For homogeneous media, this two-pass process is known to be exact. With a linear array, a surface is scanned. In the direction parallel to linear array (the in-line direction) full offset imaging can be performed. In the direction perpendicular to the linear array (the cross-line direction) zero-offset imaging can be performed.

151 142 Summary The current traditional inspection philosophy is based on zonal discrimination. This phi- losophy is well regulated in codes and standards. From these codes and standards, a rough requirement was derived for the resolution of the IWEX imaging approach. The resolution that can be obtained with IWEX imaging is investigated on the basis of point spread func- tions. Aperture limitations and directivity effects of the ultrasonic elements are taken into account. Result of 2D images from different insonification and scatter paths are presented. The data was obtained from measurements on various test blocks with machined reflections us- ing a linear array. The test blocks also contain reflectors that are representative for actual weld defects. To demonstrate the proof of principle of 3D IWEX imaging, test blocks were manufactured with suitable reflectors to study the characteristics of 3D imaging. Also, a final experiment was performed on a test block with an intentional defect in a real weld. The results are presented and discussed. The IWEX imaging approach basically removes propagation effects from source to scatterer and from scatterer to receiver. In ultrasonic data from carbon steel, two wave modes exist with different sound velocities (longitudinal and transversal). To construct an image, one of these modes must be chosen for the back propagation. As a consequence, the energy in the data from the other mode is not treated correctly and will produce leakage artifacts in the image. Artifacts in L-T images caused by L-L arrivals are discussed and illustrated with an analytical example. In addition, a procedure is presented and demonstrated to suppress these artifacts. It is concluded that the IWEX imaging approach is suitable to detect, size and characterize defects that are common in girth welds. The L-L image (direct longitudinal insonification path and direct longitudinal scatter path) will usually contain the most information. How- ever, for the area just below the surface, the LL-LL image (insonification and scatter paths via the back wall) must be used. To confirm the L-L and the LL-LL images, the L-T image (direct longitudinal insonificaton path and direct transversal scatter path) can be used, after the artifacts are suppressed with the proposed procedure. It is also concluded that 3D IWEX imaging is feasible and that it contributes to an improved resolution in the lateral direction. Finally, recommendations are given for further research. Although ultrasonic imaging based on inverse wave field extrapolations offers a huge potential for ultrasonic NDI, still work must be done to apply IWEX in practice. Evaluation programs are necessary for the ac- ceptance of the imaging technique. In addition, new codes and standards must be written for industrial use.

152 Samenvatting Afbeelden van defecten in lasnaden gebaseerd op inverse golfveld extrapolatie van ultrasone data Tegenwoordig is niet-destructief onderzoek (NDO) gebaseerd op ultrasone metingen een veel gebruikte en geaccepteerde inspectie methode voor het onderzoek naar fouten in las- naden. Echter, fout grootte bepaling en karakterisatie van fouten blijft gecompliceerd met de huidig inspectie filosofie. Daarnaast vereist het vaardigheid en ervaring van de inspecteur om de resultaten van metingen te interpreteren. Dit komt omdat de data vaak in ruwe vorm wordt gepresenteerd. Een beter en betrouwbaarder inspectie resultaat zou bijdragen aan de veiligheid van de bouw van een pijpleiding. Bovendien zou het ook economische voordelen hebben, omdat fouten minder vaak ten onrechte worden afgekeurd en omdat een nauwkeurigere inspectie het gebruik van dunnere wanddiktes (en dus minder materiaal) mogelijk maakt. Bij seismisch bodemonderzoek worden sinds geruime tijd representatieve afbeeldingen van de aardbodem gemaakt met akoestische data. Het doel van dit proefschrift is om de afbeeld- ingtechnieken ontwikkeld voor het seismisch bodemonderzoek, toe te passen op ultrasone data. De afbeeldingtechniek is gepresenteerd in 2D en gedemonstreerd in 3D. Het 2D afbeeldingsalgoritme is gepresenteerd op basis van inverse golfveld extrapolatie (IWEX), met behulp van de Rayleigh II integraal voor terug propagatie. De afbeeld- ingsmethodiek voor 3D afbeeldingen is gebaseerd op een twee stappen proces (de two pass methode). Dit proces bestaat uit twee 2D afbeelding stappen in twee orhogonale richtingen.

153 144 Samenvatting Met een lineair ultrasoon array taster wordt daarvoor een oppervlak afgescand. In de richt- ing parallel aan het array (de in-lijn richting) wordt een 2D afbeelding vervaardigd met alle mogelijke zender-onvanger combinaties (full offset imaging). Daarna wordt in de richting loodrecht op het array een 2D afbeelding gemaakt. Bij deze stap zijn alleen de meetposi- ties beschikbaar waarbij de zender en ontvanger op dezelfde locatie staan (zero-offset data). De huidige inspectie filosofie is gebaseerd op het zone concept. Dit concept is goed gereg- uleerd in codes en standaarden. De vereiste resolutie van de afbeeldingstechniek is gebaseerd op acceptatiecriteria die beschreven zijn in deze codes en standaarden. De haalbaarheid van deze resolutie is geanalyseerd met behulp van zogenaamde point spread functies. Daar- bij is rekening gehouden met praktische beperkingen zoals de gelimiteerde apertuur en de beperkte spreidingshoek van de array elementen. Er kunnen afbeeldingen gemaakt worden van verschillende belichtingspaden en verschil- lende diffractie paden. 2D resultaten van verschillende paden zijn in dit proefschrift gep- resenteerd. De data is verkregen door metingen aan de proefstukken met een lineair array. Voor de verificatie van de 2D situatie zijn metingen gedaan aan proefstukken met reflec- toren die representatief zijn voor veel voorkomende defecten in lasnaden. Voor verificatie van de 3D situatie zijn proefstukken gebruikt met groeven en boringen. Ook is er een echte las vervaardigd met een opzettelijke fout (een wolfraam plaatje was meegelast). De IWEX afbeeldingstechniek compenseert het effect van golfveld propagatie van zender naar defect en van defect terug naar ontvanger. In koolstofstaal kunnen twee golfsoorten voorkomen met verschillende geluidsnelheden (longitudinaal (L) en transversaal (T)). Voor het verkrijgen van een afbeelding moet er een keuze worden gemaakt tussen de modes (L of T). Echter, de data bevat de informatie van beide modes. Als gevolg daarvan, wordt informatie van de niet gekozen mode verkeerd afgebeeld. Dit leidt tot lek van geluidsen- ergie in de afbeelding van de gekozen mode. In dit proefschrift worden lek artefacten in L-T afbeeldingen als gevolg van L-L golven besproken en gellustreerd aan de hand van een analytisch voorbeeld. Tevens wordt er een procedure voorgesteld en gedemonstreerd voor het onderdrukken van dergelijke lek artefacten. Er is geconcludeerd dat IWEX afbeeldingen geschikt zijn voor de detectie, fout grootte bepaling en karakterisatie van fouten die voorkomen in lasnaden. Meestal levert de L-L afbeelding het beste resultaat. Daarnaast is de LL-LL afbeelding (belichting en ontvangst via de bodem) noodzakelijk voor fouten die zich onder het bovenoppervlak bevinden. Ter ondersteuning van de resultaten van de L-L en LL-LL afbeeldingen kan de L-T afbeeld- ing worden gebruikt. Daarvoor moeten eventuele lek artefacten worden onderdrukt. Ook kan geconcludeerd worden dat het goed mogelijk is om 3D afbeeldingen te maken met de gepresenteerde methode. Vooral in de laterale richting levert dit een verbeterde resolutie op. Tot slot zijn er aanbevelingen gedaan voor verder onderzoek. Voordat IWEX in de praktijk kan worden toegepast, moeten er ondanks de goede vooruitzichten nog een aantal zaken worden bekeken. Evaluatie programmas zijn nodig voor de acceptatie van de techniek. Daarnaast zullen er nieuwe codes en standaarden moeten worden geschreven om IWEX op industriele schaal toe te mogen passen.

154 Curriculum vitae Niels Portzgen, was born on 2 december 1975 in Terneuzen, the Netherlands. He received his M.Sc. degree in Applied Physics in 2000 from Delft University of Technology. He is currently working for Applus RTD, a Dutch nondestructive testing company. The emphasis of his work is on ultrasonic phased array technology and applications. The PhD research was performed in the scope of this work. Therefore, he was stationed one day in the week at the group of acoustical imaging and sound control of the Delft University of Technology.

155 146 Curriculum vitae Publications Potzgen N., Wassink C.H.P., Dijkstra F.H., Bouma t., Phased Array Technology for mainstream applications, proceedings of the 8th ECNDT Barcelona, June 2002 Bouma T., Potzgen N., Dijkstra F.H., Advances in Non-Destructive Testing (NDT) of Pipeline Girth Welds, proceedings of the Pipe Dreamers Conference Yokohama, November 2002 Potzgen N., Dijkstra F.H., Gisolf A., Blacquiere G., Advances in imaging of NDT results, proceedings of the 16th WCNDT Montreal, August 2004 Dijkstra F.H., Potzgen N., van Merrienboer H.A.M., Ultrasonic inspection of pipeline split-tees, proceedings of the 16th WCNDT Montreal, August 2004 Potzgen N., Volker A.W.F., Fingerhut M., Tomar M., Wassink C.H.P., Finite difference simulation of ultrasonic NDE methods for the detection and sizing of stress corrosion cracking (SCC), proceedings of QNDE Brunswick, August 2005 Potzgen N., Practical results of ultrasonic imaging by inverse wave field extrapolation, proceedings of the 9th ECNDT Berlin, September 2006 Potzgen N., Gisolf A., Blacquiere G., Inverse Wave Field Extrapolation: a Different NDI Approach to Imaging Defects, IEEE trans. on UFFC, vol. 54, no. 1, January 2007, pp 118-127 Potzgen N., Baardman R., Verschuur D.J., Gisolf A., Wave equation based 3D imaging of ultrasonic data, Theory and Practice, proceedings of QNDE Colorado, July 2007

156 Acknowledgements When I started working for the RTD development department in 2000, doing a PhD re- search was not my intention. The idea of combining my job with a PhD research was born when I learned more about ultrasonic array technology. I realized that the potential of this technology offered more then duplicating an already existing inspection philoso- phy. Casper Wassink, Frits Dijkstra and Maarten Robers were the first colleagues that supported this idea. I would like to thank them for the constructive discussions and for their help to find contacts. The idea of a PhD research became a project with the support of Tjibbe Bouma who was the department manager and with the approval of prof. Dries Gisolf and Gerrit Blacquiere (part time prof. in 2000). Special thanks go out to Gerrit Blacquiere for his support and advice. The weekly appointments with Gerrit often lead to discussions that helped me understand the theory. The research was partially subsidized by the Dutch government. I would like to thank Ahmed Polat (Senter Novem) for his support to obtain the subsidy and his involvement during the research. Some practical work during the research was performed by trainees. I would like to thank Damie van Leeuwen, Sandra Blaak and Rolf Baardman for their valuable contributions. For the practical work, both hardware and software were required. Within a company driven by operations, these two essential elements were very hard to get. I would like to thank my colleagues Nico t Hooft, Tom van Overbeek, Herman van Noort, Ton Kuiters, Carlos Paiva and Hans van Veldhuizen for their help to get the hardware, the software and the rest of the measurement set-up available and running. Certainly, I will remember the time on Fridays in the group at the university. The dis-

157 148 Acknowledgements cussions with Sandra, Maurice, Gertjan, Ayon and the other members of this group were always fun, especially during lunch. I also would like to thank Erik Verschuur (who knows all about seismic exploration) for his time to review the article and this thesis. Ook wil ik mijn vader, moeder en broer bedanken voor hun vertrouwen en steun. Meer dan eens hebben jullie mij met beide benen op de grond gehouden. In het bijzonder wil ik tenslotte Patricia bedanken. In de periode dat dit onderzoek heeft plaatsgevonden ben je van mijn vriendin mijn vrouw geworden en heb je twee prestaties geleverd die het schrijven van dit proefschrift veruit overtreffen.

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