A decade of tomography

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1 GEOPHYSICS, VOL. 73, NO. 5 SEPTEMBER-OCTOBER 2008 ; P. VE5 VE11, 10 FIGS / A decade of tomography Marta Jo Woodward 1, Dave Nichols 2, Olga Zdraveva 3, Phil Whitfield 4, and Tony Johns 3 ABSTRACT Over the past 10 years, ray-based postmigration grid tomography has become the standard model-building tool for seismic depth imaging. While the basics of the method have remained unchanged since the late 1990s, the problems it solves have changed dramatically. This evolution has been driven by exploration demands and enabled by computer power. There are three main areas of change. First, standard model resolution has increased from a few thousand meters to a few hundred meters. This order of magnitude improvement may be attributed to both high-quality, complex residual-moveout data picked as densely as 25 m to 50 m vertically and horizontally, and to a strategy of working down from long-wavelength to short-wavelength solutions. Second, more and more seismic data sets are being acquired along multiple azimuths, for improved illumination and multiple suppression. High-resolution velocity tomography must solve for all azimuths simultaneously, to prevent short-wavelength velocity heterogeneity from being mistaken for azimuthal anisotropy. Third, there has been a shift from predominantly isotropic to predominantly anisotropic models, both VTI and TTI. With four-component data, anisotropic grid tomography can be used to build models that tie PZ and PS images in depth. INTRODUCTION The seismic exploration industry was revolutionized in the early 1990s by the transition of imaging from two to three dimensions, from time to depth, and from poststack to prestack. During much of the decade, the industry worked to replace interactive NMO velocity analysis with something more suitable to the resolution and large data-volume challenges of the new regime. Early strategies of velocity scanning in time gave way to smoothed 1D inversions and Deregowski loop approaches Deregowski, By the late 1990s, the industry was implementing ray-based, prestack depth migration PSDM domain tomographies to perform full migration velocity analysis Stork, 1992; Wang et al., Some of these were highly constrained and interpreted layer-based approaches, solving for velocity gradients between horizons Bloor, 1998 ; others were less constrained and more data-driven, grid-based approaches Woodward et al., The basics of the tomography products from the late 1990s have survived to this day, but the problems they solve have become bigger, the resolution expectations have become more demanding, and the earth models have progressed from predominantly isotropic to predominantly anisotropic. This evolution has been enabled by the approximately thousandfold increase in industry computing power that accompanied the transition from serial to parallel computing. In this article, we review the basics of our implementation of grid tomography. Next, we give some examples that illustrate the historic changes in the problems it solves. Finally, we speculate on what lies beyond ray-based grid tomography. RAY-TRACE GRID TOMOGRAPHY PSDMs contain redundant images of the earth s subsurface one image volume for each offset or opening angle for Kirchhoff and wave-equation migrations, respectively. Hereafter, we refer to offset alone for brevity. The depth variation of reflection events across offset is residual moveout RMO. When there is no RMO, the earth model has optimized the data focusing; when there is RMO, we can trace rays through the model to determine which parts of the model to change to flatten the moveout and improve the focusing. We analyze RMO on common-offset image volumes sorted to common-image-point CIP gathers. Standard industry grid tomography generates and solves ray-traced residual-migration equations to produce earth models that flatten RMO on CIP gathers. There are three basic components of depth-domain ray tomography, each of which can have its own style. The first component is the data the representation of the RMO. For ray-based tomography, Manuscript received by the Editor 22 January 2008; revised manuscript received 7April 2008; published online 1 October WesternGeco, Imaging R&E, Houston, Texas, U.S.A. martajo@slb.com. 2 WesternGeco, Research, Houston, Texas, U.S.A. nichols0@slb.com. 3 WesternGeco, Data Processing, Houston, Texas, U.S.A. ozdraveva@slb.com; johns5@slb.com. 4 WesternGeco, Data Processing, Gatwick, U.K. pwhitfield1@slb.com Society of Exploration Geophysicists. All rights reserved. VE5

2 VE6 Woodward et al. there are two options: 1 simple or single parameter, in which the moveout is characterized by a best-fitting parabola or hyperbola, and 2 complex or multiparameter, in which an image depth is picked independently for many offsets or represented by a higher-order polynomial curve. As computer power has increased and as resolution expectations have grown, the industry standard has moved from single parameter to multiparameter. Today, we can pick single-parameter moveout for preliminary, low-resolution work on a survey, but our later iterations rely on complex multiparameter moveout. The left panel in Figure 1 shows complex moveout picked for three azimuths 30, 90, and 330 of a rich-azimuth data set. The picker first fits a line or a parabola to each event and then applies a trace-by-trace shift to match the offsets further. Note the events do not always correlate across azimuth. Because different azimuths illuminate different reflectors in the earth, dense picking of all possible reflectors requires independent picking of all azimuths in the CIP gathers. Key events common to the gathers of all azimuths can be picked along horizons for quality control QC purposes. We use a single-parameter representation to compress 4D multiparameter moveout for 3D or 2D visual QC. The right panel in Figure 1 shows a single-parameter moveout QC plot for a high-resolution project. Blue is positive moveout, red is negative moveout, and white is zero moveout. Although the picks appear to be horizon based, they were not. The density of the picks and the data quality were sufficiently high for the continuity of reflectors to be captured automatically. The ultimate resolution of a velocity model depends on the seismic frequency more explicitly, the seismic wavelength, the acquisition geometry, and the earth how the density and dips of the reflectors illuminate the model. Resolution in depth will increase with pick density in depth until thin velocity layers stop registering pickable RMO, because of the frequency and offset limitations of the seismic data Clapp, We generally pick RMO at a depth interval as fine as 30 m up shallow. Higher resolution can be achieved up shallow with the wide-offset, horizontal raypaths of refraction tomography Tanis et al., Many papers describe the elliptical wavepath that characterizes the illumination volume corresponding to a picked event in ray tomography Woodward, 1992; Fliedner et al., Lateral resolution increases with CIP gather density until the gather spacing drops below the width of the first Fresnel zones of the dominant-frequency wavepaths. Resolution is greater up shallow, where the velocity is slower and the Fresnel zones are narrower; resolution is lesser down deep, where the velocity is higher and the Fresnel zones are broader. A spatially continuous CIP-gather grid cannot increase model resolution beyond the bandwidth limitations of the data. Velocity perturbations smaller than a Fresnel zone will produce frequency dispersion instead of pickable RMO because their phase-delay signatures are not linear with frequency. When perturbation signatures cannot be represented by a depth error, a full-waveform inversion approach must be used. Of course, greater pick density always improves the signal-to-noise ratio of the picks. In practice, we generally pick on CIP-gather grids as fine as m. The second component of any ray tomography is the model. Just as with data picks, models can range between two extremes. At one extreme, models can be purely layer based, with properties defined on horizon maps and interpolated linearly between the horizons. Models such as these have relatively few parameters to solve; they are strongly constrained by the user, and they rely heavily on an interpretation. They were probably the standard in the late 1990s and are still useful in areas with poor data quality requiring many a priori constraints. At the other extreme, models can be purely gridded. Today, we mainly use hybrid gridded models. We divide the model into layers at interfaces in which we have sharp, ray-bending velocity contrasts, such as at the water bottom, at salt boundaries, and at carbonate boundaries. Within layers, we use continuously interpolated property grids. We place surfaces where we believe we can add more detail to the layer boundaries by interpreting seismic images than by analyzing RMO. Property grids within layers are made dense enough to capture the resolution we think we can achieve or that we need to meet our imaging goals. Surface grids are sampled as finely as interpretable to capture the rugosity of their corresponding geologic structures. Because errors in surfaces are compensated for by erroneous property updates on their underlying grids, poorly determined surfaces restrict the resolution that is attainable beneath them. When high-resolution updates are produced below poorly picked surfaces, they can contain erratic bull s-eye features. For extremely rugose surfaces, the bandlimited nature of the seismic source will result in a ray solution that is unrepresentative of the wave-propagation data. The third component of a ray tomography is made up of the residual migration equations and their solver. We ray-trace the source and receiver rays corresponding to our depth picks through the model to generate equations that relate changes in the model to changes in the RMO. These are residual migration equations based on the formulation of Stork 1992 : z h z h z z h t i i i v 2 cos cos. 1 Figure 1. Left Superimposed independent multiparameter RMO picks for three azimuths red 30, black 90, and blue 330 on six CIP gathers. The picker first fits a line or parabola to the events and then applies a trace-by-trace shift to further match the offsets. Right Single-parameter picks of RMO for 2D section QC. Red is 1 blue is 1 and white is 0. The parameter is the residual slowness or NMO correction of Al-Yahya 1989 and Etgen Picks are typically separated by 50 m in x and y, m in z. The prime indicates a residually migrated reflector depth, z h is depth as a function of offset or angle h, i indicates a node on the property grid, is the angle of incidence for the reflection, is the reflector dip, v is the effective velocity at the reflector, and t/ i is the change in traveltime corresponding to a change in property at node i. These are linear tomography equations, in that the t/ i terms are calculated under the assumption that raypaths do not change as we change the model. Although is most often velocity or slowness,

3 A decade of tomography VE7 it can be any earth property, such as Thomsen parameters or Thomsen, Our goal is to find property perturbations that minimize the RMO of depth picks residually migrated with a model including those perturbations, i.e., that minimize z h z 0, where z h is a nonnear-offset pick and z 0 is a near-offset pick. This is a floating datum criterion, in that all of the picks move to minimize their relative depth errors rather than a static depth error. We have one equation for each nonnear-offset pick. The basic tomography update equation is formed by subtracting equation 1 for corresponding nonnear- and near-offset picks and accumulating the picked depth errors on the right side: L z. The geometry and background model terms in equation 1 are contained in L. Of course, reflection seismic problems are severely underdetermined, and we need to regularize the problem. Instead of equation 2, we solve PLSW P z using LSQR and damped least squares. Our update is SW. In equation 3, P is a row weighting diagonal matrix; SW is a preconditioner that constrains the shape of our update, following the approaches of Harlan personal communication, 1995 and Fomel 1997 ; S is a smoother applied as a 3D convolution, with user-specified wavelengths in x, y, and z; and W is a column weighting diagonal matrix. Because we use damped, reweighted least squares, our objective function is PLSW P z The row-weighting matrix P allows us to vary the significance of RMO for different segments of the data. The column-weighting matrix W acts through the damping-parameter penalty term, allowing us to vary the penalty on update magnitudes in different regions of the model. Note the L-1.5 norm on the measure of the updated RMO. We use iteratively reweighted least squares Scales and Gersztenkorn, 1988 to push our norm toward a median and away from a mean. For any one iteration of PSDM and RMO picking, we solve equation 2 many times, iteratively reparameterizing the problem by refining the smoother S Harlan, personal communication, 1995; Bube and Langan, We start out by solving with a long-wavelength smoother in x, y, and z; we subtract the RMO predicted linearly by the corresponding smooth update SW ; and finally we reduce the wavelengths in S and solve again. We repeat this process until we reach a predetermined smoothness or resolution in the update or until it is obvious we have violated the linear assumptions of our ray-traced residual migration equations. We choose between the set of updates of different smoothness. At this point, we remigrate and begin a new iteration. Figure 2 illustrates an overview of this workflow. RESOLUTION EXAMPLES The basics of this workflow have not changed over the past 10 years. What have changed dramatically are the size and the resolution requirements of the projects. Figure 3 shows a 9 4-km snapshot of our first 3D grid tomography result, computed in 1998 Woodward et al., 1998; Sayers et al., The panels show the velocity resolution increasing through three PSDM iterations of tomography. The first iteration solved for wavelengths down to 8000 m in x and y and down to 2000 m in z. The second iteration solved down to m; the third iteration solved down to m. We picked complex RMO every 200 or 300 m in depth on a m gather grid. The model was about 25 blocks. We solved the equations in serial mode on a single CPU on a SUN or SGI computer. The model was isotropic. At the time, we were delighted with the way the geometry of the shale diapir automatically took shape in our model with no laborious interpretation, constrained only by the smoother S and the RMO data picks. We were also pleased with the close match between the final velocity model and the checkshot, obtained long after we completed the project. The tomography caught the velocity inversion well, which in this case probably corresponds to an overpressure zone. We attribute this success to a strategy of working our way down from long wavelengths to short wavelengths: We get the average part of Velocity model PreStk depth mig. Are CIPS flat? Yes PreStk. depth mig. image Solve3D 3D For for smooth Smooth Updates updatesto to Interval interval Velocity velocity Iterate to shorter wavelengths or next layers No Autopick residual moveout and dip in z + 3D ray-trace linear tomography equations CIP S Figure 2. Grid tomography workflow. Data are prestack depth migrated with an initial model. RMO is picked automatically from the gathers; dips are picked automatically from a stack cube. Aray tracer first finds the source/receiver pair corresponding to each offset/angle pick, then calculates linear equations relating changes in RMO to changes in the property field s being updated. The equations are solved to produce a set of possible updates of decreasing smoothness. After choosing an update from the set, the loop is iterated to shorter spatial wavelengths and/or different layers. Remigration relinearizes the problem. Initial image Three tomographic velocity updates with increasing detail = Depth (km) Well validation 0 Interval velocity from 1 stacking velocity 2 Checkshot 3 Tomography Interval velocity (km/s) ϕ ν θ ν i h Z h Z h Final image Figure 3. First grid tomography result from 1998, demonstrating the strategy of building a model up from long wavelength to short wavelength. Top panels show left initial model, middle three increasingly detailed updates produced by three iterations through the loop of Figure 2, and right the final model. The final model is validated by the interval velocity graph on the bottom, comparing stacking blue, checkshot green, and tomographic red velocities. r

4 VE8 Woodward et al. the model correct before we add detail. The fundamental principle underlying the approach is Occam s razor, or simplicity that it is best to flatten the RMO with the smoothest possible model. Figure 4 shows a result from Here, the model was 42 blocks, the pick interval in depth ranged from 30 to 200 m, and the gather grid was m almost 0.5 million gathers. The high-density, single-parameter-pick QC plot of the right panel in Figure 1 was pulled from a representative line in this project. The problem was almost 500 times larger than the first example, and it ran in parallel on 100 or 200 CPUs. The level of detail in the top panel is quite remarkable because the velocity field was resolved down to wavelengths of 400 m in x and y and 300 m in z. The water and salt layers are shown as purple masks; the sediment velocities range from a low of about 1800 m/s in blue to a high of about 3800 m/s in orange. Note the low-velocity zones over the salt peaks, perhaps because of rock failure, stress changes, and geomechanical effects Sayers, This relationship is demonstrated even for the small salt spike in the valley on the lower left, a detail most would have hesitated to force into the model a priori. Note also how the velocity field follows the lithologic layers in panoramic view in the top panel and in close-up view in the lower panels, where velocity overlies seismic data unfortunately with a different color scale. None of this detail was interpreted into the model: The smoother had a varying aspect ratio in xy:z but no steering-filter dip constraints Clapp et al., The detail arises from the dense, multiparameter RMO picks and from the long-wavelength to short-wavelength workflow. Clearly, layers a few hundred meters thick can be resolved, given high-quality data and a suitable geometry. MULTIPLE AZIMUTHS Another change in the demands on today s grid tomography has been the increase of seismic data sets acquired with multiple azimuths. The biggest driver for this is the superior illumination and multiple suppression that wide-azimuth acquisition offers for subsalt imaging in the Gulf of Mexico Kapoor et al., 2007, but it is also important for land, ocean-bottom cable or node-acquisition geometries, and for the combination of surveys shot over the years at different azimuths. Just as for high-resolution work, multiple azimuths challenge velocity analysis by the increase in data they multiply the input data by a factor of three or more but they also require changes to the workflow. Although the different azimuths can be migrated, picked, and ray-traced separately, their corresponding tomography equations must be solved simultaneously. The goal of the tomography is to make all azimuths flat with a single model, not to create a model for each azimuth. We demonstrate multiazimuth tomography with a North Sea example Dazley et al., 2007; Whitfield et al., The data consist of five overlapping surveys with varying acquisition azimuths, covering 2000 km 2. A layer-stripping, hybrid grid-tomography approach was used to be consistent with the clearly differentiated geology of the North Sea. We focus on grid tomography applied to the second layer: a Cretaceous chalk interval varying from 1 to 2 km in thickness Figure 5. The initial chalk model was a smoothly varying vertical gradient function left panel. Because earlier studies predicted short-wavelength velocity variations in this chalk interval, tests were run to study the importance of azimuth in the velocity analysis. After a long-wavelength iteration was completed using only 90 azimuth data, butterfly mirror image in offset plots were made to compare remigrated moveout between all of the azimuths. The left panel of Figure 6 shows butterfly plots for nine gathers and two azimuths after the single-azimuth update. The offsets increase to the left for the 45 azimuth on the left halves of the gathers and to the right for the 90 azimuth on the right halves; the azimuths meet in the middle at the near offset. The 90 azimuth gathers are flattened at the base of chalk, as expected, but the 45 gathers are not. When the moveout dependence on azimuth was observed initially, it was thought to be evidence of azimuthal anisotropy. However, Initial chalk layer velocity Final chalk layer velocity 2 3 Velocity (km/s) 4 5 Figure 4. High-resolution result. Sediment velocities in the top panel range from about 1800 blue to 3800 m/s orange. The water and salt layers are indicated by purple masks. The lower panels show close-ups from the same line, with velocity overlying seismic data. In these panels, the salt mask is orange and the color scale is different but with the same range. Distance scales are unavailable. Courtesy Devon Energy Corp. 6 3km Figure 5. left Initial and right final chalk layer velocities. The top chalk is indicated by the green line and the base chalk by the violet line. Courtesy Total E&P Nederland B.V.

5 A decade of tomography VE9 that was not the case. Simultaneous inversion of all of the azimuths to shorter wavelengths in two subsequent production iterations produced the corresponding flattened-gather butterfly plots in the right panel of Figure 6. The lesson here is that velocity heterogeneity can appear as apparent azimuthal anisotropy when surveys with different azimuths are analyzed separately. All azimuths must be picked independently, but their equations must be solved simultaneously. It also underscores how much better constrained a model is for multiple azimuths than for single azimuths. There is a much greater possibility that the optimal focusing model will correspond to the true earth model. The final chalk-velocity model is shown in the right panel of Figure 5. Figure 7 shows a depth slice at 1600 m through the first model left panel and the final model right panel, with the 45 and 90 azimuths marked by arrows. This figure illustrates how velocity heterogeneity can produce different moveout on different azimuths. Multiazimuth PSDM stacks for the initial and final chalk-velocity models are compared in Figure 8; the ellipses highlight the imaging improvement at the target level below the chalk.as in the preceding example, the PSDM CIP gathers were analyzed on a m grid, and multiparameter RMO was picked. The project solved for wavelengths down to 600 m in x, y, and z. Smoothly varying vertical transversely isotropic not azimuthal anisotropy parameters were also derived for the model, but from geostatistics rather than from tomography. smaller in magnitude than. The Thomsen parameter was extended to be consistent with the laterally varying field derived in the preceding time work. Continuing with the process, in the fourth step the P-velocities and Thomsen parameters were held fixed and the S-velocities were updated with several iterations of anisotropic grid tomography. Fifth, depth mis-ties were picked between interpreted geologic features on anisotropically migrated PZ and PS images. These were input to a grid-tomography iteration without RMO-gather data to produce an S-velocity update that tied the PZ and PS images in depth. For step six, the Thomsen parameters and were scaled globally by an average of the pretomography percent-depth mis-ties to compensate for the S-velocity update. This first-order correction to the anisotropy approximately reflattened the PS gathers. For step seven, a final iteration of PS tomography was performed to provide a spatially variable residual update to further flatten the PS gathers. The PZ data were much less sensitive to this final update, as expected. Figure 9 shows the final P-velocity and V P /V S ratio superimposed on the final PZ and PS images. Figure 10 shows the final and fields: their values range from zero yellow to 0.16 blue. In previous work, we have usually performed migration scans to optimize. Butterfly CIP gathers: 45 /90 azimuths MULTIPLE PROPERTIES The other increasingly standard complication of the basic grid-tomography workflow is a shift from predominantly isotropic to predominantly anisotropic models, both transverse isotropy with a vertical axis VTI and tilted transverse isotropy TTI. Even large multiclient Gulf of Mexico earth models, in which isotropy was long considered to be sufficient, now contain property grids for Thomsen s anisotropy parameters and, along with P-velocity. Our example for building an anisotropic model is the offshore Trinidad Pamberi project Johns et al., This was a four-component 4-C depth project that followed an anisotropic time-imaging project. Converted-wave projects generally require that anisotropy be determined because of the greater sensitivity of S-waves than P-waves to anisotropy and because of the need to get anisotropy right to align PZ and PS images. Conversely, the extra measurement also provides more data for constraining the anisotropic parameters. One well was available, with logs to a depth of 2.5 km; total project depth was 6 km. We chose to use a VTI model instead of a TTI model because the reflectors were flat or mildly dipping. The work was done in seven steps. First, an isotropic P-velocity model was built with several iterations of standard grid tomography. RMO offsets were approximately limited to equal depth. Second, the P velocities were scaled to tie the well; and were estimated by interactive 1D forward modeling to flatten gathers at the well. An alternative would have been to use constrained tomography. Third, the 1D function was extended horizontally as a constant away from the well and as zero below the well. This simple approach was chosen because only one shallow well was available, because the 1D function gave a good tie at the well, and because was Velocity (km/s) Figure 6. Butterfly mirror image in offset plots showing CIP-gather pairs for 45 left half of gathers and 90 right half of gathers azimuths. The nine gathers in the left panel were migrated with a longwavelength update using only 90 azimuth data picks. The nine gathers in the right panel were migrated with a final tomography result using data from all azimuths after Whitfield et al., Courtesy Total E&P Nederland B.V Figure 7. Depth slice at 1.6 km through the first and final chalk models, with azimuths indicated by arrows.after Whitfield et al Courtesy Total E&P Nederland B.V

6 VE10 Woodward et al. This was one of the first projects in which we used the tomography to solve for a Thomsen parameter. 3km 4km Figure 8. Depth stack showing chalk and the target below the chalk for the left long- and right short-wavelength models. The top chalk is indicated by a red line; the base chalk is indicated by a lavender line. The ellipses highlight the improved imaging at the target. After Whitfield et al Courtesy Total E&P Nederland B.V. km 0 3 BEYOND RAY TOMOGRAPHY Ray tomography breaks down when we cannot pick RMO. One example of this is below salt, either where the illumination angles are reduced so severely as to prevent RMO discrimination or where poor salt-body definition and poor subsalt illumination result in very-lowquality data. Recent industry solutions for this problem have centered on velocity scan picks being translated into RMO and input to existing tomography algorithms Wang et al., As computer power continues to increase, interactive interpretation-driven, beam-based migration schemes or other scenario-testing workflows may become viable alternatives. Tomographic update of salt-body boundaries is another area of development, as is incorporation of alternative data types such as gravity and magnetotellurics. Ray-trace tomography and RMO picking also break down for high-frequency velocity variations that are smaller than a Fresnel zone. Full waveform inversion schemes, in which we back project differences between migrated or unmigrated wavefield data and forward-modeled data, appear to be on the verge of becoming computationally feasible Sava and Biondi, 2004; Albertin et al., 2006; Sirgue et al., 2007; Song and Childs, Even when RMO can be picked, these methods offer the advantage of not requiring the often labor-intensive and error-prone picking process. Ever-increasing computer power continues to drive the industry toward more fully automated model-building workflows. CONCLUSIONS 6 0 km 15 0 km Velocity (km/s) 1.0 V 5.0 P /V S Figure 9. Final PZ and PSV PSDM stacks. P-velocity is overlaid on the PZ image; V P /V S is overlaid on the PSv image. Courtesy EOG Resources Inc. 0 Much of the last decade s model-building focus has been on elaborating RMO-based ray tomography and reducing turnaround time. The method has evolved from building narrow-azimuth, isotropic, low-resolution models to building wide-azimuth, anisotropic, highresolution models. Heavily interpretation-constrained models such as layered property gradients and single-parameter RMO data have been replaced when possible with more purely data-constrained property grids and complex RMO. This evolution has been enabled by an exponential increase in computer power and necessitated by the disappearance of easy-to-find oil. Integrating increasing amounts of data of many types, interactive scenario testing, and automation will undoubtedly continue to be major trends in the near future. km km 15 0 km 15.0 ε.16 Figure 10. Final and property fields, with values ranging from zero yellow to 0.16 blue. Courtesy EOG Resources, Inc..0 δ.16 ACKNOWLEDGMENTS The authors thank Devon Energy Corporation for permission to publish the high-resolution data example, Total E&P Nederland B.V. for permission to publish the multiazimuth example, and EOG Resources Inc. for permission to publish the anisotropic example. We also thank David Watts for his work on the high-resolution example, Carmen Vito for his work on the anisotropy example, Colin Sayers and Ran Bachrach for their geomechanic insights, and our colleagues at WesternGeco who worked on the presented projects. We also thank Miles Wortham for his patient help with the graphics.

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