2911 1386 higginbotham · avo (amplitude variation with offset) has been a corner-stone of prospect...

1386 The Leading Edge November 2010

SPECIAL SECTION: R e v e r s e t i m e m i g r at i o nR e v e r s e t i m e m i g r at i o nSPECIAL SECTION: R e v e r s e t i m e m i g r at i o nSPECIAL SECTION: R e v e r s e t i m e m i g r at i o n

The most advanced prestack depth-migration (PSDM) technologies available today, such as wave-equation

migration (WEM) and reverse time migration (RTM), are primarily used for offshore applications like subsalt imaging. However, E&P efforts in many onshore basins can also benefit from PSDM, and there is considerable momentum in many basins to adopt this technology as the default imaging tool (Young et al., 2009). This paper highlights the application of wave-equation depth-imaging technologies (WEM and RTM) with several onshore U.S. case studies. Below we list some benefits that users of PSDM technology might expect to enjoy:

• A true depth picture. Local velocity anomalies induce false time structures. Unless dense well control is available, PSDM (and the associated velocity model) provides the best connection between seismic reflection time and drill-ing depth. With Kirchhoff time migration, the imaging velocity need only be correct locally; with PSDM, rays or waves are propagated from the source to target to receiver, so the velocity must be correct from top to bottom. This feature of time migration makes it robust in regions where velocity is hard to estimate, but the time-migration veloc-ity may not help in tying wells in depth. If well control is present, a PSTM image can be stretched to fit the wells in depth; in areas with lateral velocity variation, however, focusing on PSTM images will be compromised and dip-ping events mispositioned. Anisotropic PSDM techniques are often required to improve the tolerance of well ties. With PSDM, that approach is well grounded in physics as opposed to more empirical approaches used with time imaging.

• The depth velocity model has interpretive value. Accurate ve-locity estimation is the key to PSDM success. But savvy prospectors may use velocity models themselves for vari-ous elements of optimization of drilling activities, fault seal analysis, and petrophysical attributes such as pore-pressure determination. The high spatial resolution velocity models generated for PSDM are particularly useful.

• A better focused image. Even subtle lateral velocity varia-tions cause a loss of clarity on time-migrated images. Steep dips and faults (and stratigraphic details) are particular-ly sensitive to this effect, and PSDM usually produces a clearer image of these features, in almost any basin.

• More accurate attributes. Most AVO and azimuthal frac-ture attributes (fracture density and fracture orientation) are computed on prestack time data or time-migrated data, and relate surface offset/azimuth to reflection angle, by assuming a local V(z) profile. Lateral velocity variation causes focusing and refraction effects that may degrade the accuracy of these attributes. PSDM, applied in the true reflection-angle domain, may allow attribute technologies to be applied even in complex geology.

JOE HIGGINBOTHAM, MORGAN BROWN, COSMIN MACESANU, and OSCAR RAMIREZ, Wave Imaging Technology

PSDM had a spotty track record for onshore applications in the 1990s as PSDM images were reputed to be low-fre-quency, noisy, and with poor depthing. Fast-forwarding to the present time, we feel that PSDM is positioned to become the default onshore imaging technology. Young et al. present compelling case studies to this end. To achieve default sta-tus, PSDM needs to be as good or better than PSTM, in ev-ery project. To this end, the ever-declining cost of ever more powerful computers has driven a long-term trend toward intensive, iterative depth velocity analysis (which improves event focusing) and toward higher-frequency depth migra-tion. Nearly every onshore play type in the United States can benefit from depth imaging. Below we list several such plays:

• Unconventional resources. Each “shale play” differs from the others in subtle ways, but each can benefit from PSDM. One common thread among all shale plays is the need to clearly image macrofaults and microfractures to mitigate drilling and environmental hazards and to maximize the effectiveness of hydraulic fracturing. The Marcellus Shale has significant surface topography and velocity lensing as-sociated with salt tectonics. The Eagle Ford Shale often has velocity-driven “fault shadow” effects common to other Gulf Coast plays. The Woodford, Fayetteville, and Niobrara shales suffer from structural complexity and ve-locity anisotropy above the target. Furthermore, as each shale play matures, operators will need more and more di-agnostic information from seismic data, and PSDM will play a central role.

• Subthrust imaging. From Wyoming to the San Joaquin Val-ley of California to the West Texas overthrust, subthrust plays require depth imaging, not just to remove false time structures, but also to maximize resolution of faults and steep dips, which may contain stranded resources.

• Fault shadow. In some environments, particularly in the U.S. Gulf Coast, seismic velocity may vary rapidly across faults that have a pore-pressure differential. The velocity lensing that results —known as fault shadowing—causes time distortions and degrades event focusing. PSDM, combined with high-effort depth-migration velocity anal-ysis, is known to solve the fault-shadow problem.

• Permian Basin/Midcontinent. Although the Permian Basin and Midcontinent regions are primarily considered “easy” to image, subtle lateral velocity variation and anhydrite/salt dissolution may nonetheless necessitate PSDM. The recent relatively high price of oil has refocused the indus-try’s attention on these oil-rich plays, raising the bar for geoscientists to maximize exploration success.

Wave-equation depth velocity model buildingCurrently, most onshore depth-migration projects use Kirch-hoff (ray-based) PSDM tools. Given the successes realized in areas with complex focusing, like the Gulf of Mexico subsalt,

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isotropy or azimuthal anisotropy parameters; η generally manifests itself as a “hockey stick” on a prestack or mi-grated gather, since the apparent velocity used to flatten a gather increases as a function of angle or offset.

In complex geology, an angle gather may not have recog-nizable residual moveout when the acquisition geometry is irregular or when the migration velocity is far from optimal, whereas the MVFA-focusing information clearly indicates velocity errors. For this reason in particular, experience tells us that our two-stage workflow is preferred for land seismic applications.

Reverse time migration (RTM)Perhaps the simplest of all depth-migration algorithms, re-verse time migration (RTM), is also the most theoretically accurate, but also the most expensive. However, continued commoditization of high-performance computing hardware, as well as third-party software packages, have put RTM ca-pabilities into the hands of firms with modest computer re-sources.

Practically speaking, RTM combines the best attributes of one-way WEM algorithms (natural handling of amplitude- focusing effects and sharp lateral velocity variations) and of Kirchhoff algorithms (ability to image steep or overturned dips). However, RTM is sensitive to velocity errors and an-isotropy, as the energy which illuminates the steep or over-turned reflectors takes a long travel path through the Earth, and often propagates at or near the horizontal. Provided that

why are wave-equation technologies not used more frequent-ly onshore? The primary answer is that Kirchhoff PSDM offset gathers are still most commonly used to build depth velocity models. However, given the rise of third-party RTM tools, many firms are applying a final RTM, after building a velocity model with Kirchhoff tools. This approach could suffer from a consistency problem: if wave-equation migra-tion algorithms are needed to image some reflectors, it stands to reason that only a wave-equation velocity update can reli-ably measure velocity errors near these reflectors. For land seismic processing in particular, we advocate a two-stage it-erative velocity estimation scheme using wave-equation mi-gration exclusively:

1) Migration velocity focusing analysis (MVFA), described by Higginbotham et al. (2008), using the time-shift imag-ing condition for WEM (e.g., Sava and Fomel, 2006) to measure image focusing as a function of time. MVFA can detect errors in migration velocity under velocity lenses such as salt (Brown et al., 2009) and is robust to large er-rors in migration velocity and irregular acquisition geom-etry. We demonstrate MVFA’s efficacy in Figure 1.

2) WEM angle-gather updating. By using an efficient scheme to compute WEM reflection angle gathers (Macesanu et al., 2010), we are able to measure residual curvature of events as a function of incidence angle, and back-project the velocity error to update the migration velocity model in a spatially dense fashion. The gathers also enable the computation of the Thomsen parameter η for VTI an-

Figure 1. MVFA was applied at four potential drilling locations on the BP velocity benchmark model. The pink curves represent the migration velocity at the four locations. The green curves represent the true velocity. The red energy clouds are the velocity indicated by MVFA analysis.



RTM is performed from topography, the algorithm is suitable for land processing.

Wave-equation AVA and fracture attributesAVO (amplitude variation with offset) has been a corner-stone of prospect generation and reservoir derisking in sedi-mentary basins like the Gulf Coast for many years. However, the scientific basis of almost all AVO work rests on linear-izations of the Zoeppritz equations about perturbations in elastic properties like VP, VS, and density. The resulting AVO equations are actually written in terms of incidence angle at the reflector; in practice, offset and angle are connected by a V(z) assumption. In all but the most well-behaved, compac-tion-driven basins, the V(z) assumption is often violated, and sometimes severely, scrambling the offset-to-angle mapping.

As described in an earlier section, we use an efficient (Macesanu et al.) scheme to compute full-volume, true 3D angle gathers. The angle information is computed at the re-flector and is more accurate than the simple V(z) offset-to-angle transformation. Higginbotham et al. describe an ad-vanced inversion scheme for AVA (amplitude variation with angle) parameters, which uses the entire angle gather, not just “far/mid/near stacks”, and which presents an iterative scheme to recover a “mudrock line” which best fits the data volume, subject to constraints.

Surface azimuth angle gathers have been used effectively to delineate fractures due to apparent azimuthal anisotropy and/or azimuthal AVO. Lateral velocity variation and/or dip may scramble the relationship between surface azimuth angle

and reflection azimuth angle. We can also compute WEM reflection azimuth angle gathers. These gathers boast theo-retical advantages over conventional gathers, both in terms of kinematics and amplitude preservation. What’s more, we can combine incidence angle decomposition with azimuth angle decomposition to compute AVAZ (amplitude variation with azimuth angle) and/or azimuthal velocity attributes, us-ing a WEM algorithm rather than a Kirchhoff algorithm.

ExamplesOur first example uses the BP velocity benchmark model data and was adapted from Brown and Higginbotham (2009). Although not an onshore example, it nicely demonstrates MVFA’s ability to resolve velocity errors in difficult imaging areas. The true velocity in this model has several zones of anomalously low P-wave velocity under the salt, simulating likely zones of overpressure, which are often found in the Gulf of Mexico.

MVFA can resolve velocity anomalies under complex features like salt because it uses a wave-equation propaga-tor rather than a simple kinematic propagator. Also, because it uses wavefield focusing rather than incidence angle to measure velocity error, it may be more robust to the limited incidence angle coverage typical of the Gulf of Mexico sub-salt. In this example, we assumed that we knew the velocity perfectly down to the base of salt, but inserted a single V(z) function below the salt as a starting point for subsalt velocity analysis. Figure 1 illustrates the result of applying MVFA at four potential drilling locations under the salt. Two are

Figure 2. 3D slice view of south Texas WEM image, overlain by final depth-migration velocity model. Black arrows indicate the location at which the data slices are extracted. Green circles highlight velocity anomalies associated with sealing faults. (Data courtesy of ECHO Geophysical.)



over (unknown) overpressure anomalies. The MVFA gath-ers, at x = 9000 m and x = 12,250 m, show overpressure anomalies, and the MVFA energy peaks do indeed indicate a subsalt slowdown, even though we migrated with too high a velocity. On the other two MVFA gathers, the energy peaks also line up with the true velocity, but are indicating that the velocity model is correct (an important check). While we do not claim that MVFA is a cure-all solution for subsalt veloc-ity estimation, this approach can steer us in the right direc-tion, and is well-suited for the first phase of our two-phase WEM velocity analysis program.

Our second example illustrates the performance of our two-stage velocity update workflow on an onshore data set from Live Oak County, Texas, USA. Figure 2 shows a WEM image overlain by the final depth-migration velocity model obtained after eight iterations of MVFA (analysis performed at every shot point) and four iterations of WEM angle gather update (analysis performed at every image point). We have successfully measured sharp velocity variations across faults and a strong velocity inversion under the top Wilcox reflec-tion. In addition to causing time sags and inhibiting the focusing of time-migrated images, variations shown in the velocity model may indicate sealing faults and zones of pro-spectivity (green circles on Figure 2). The data are under-sampled in terms of source and receiver coverage, and WEM angle gathers with the initial velocity did not look good enough for velocity analysis, but MVFA successfully pulled the velocity in the right direction. Subsequent WEM angle

Figure 3. Example from Paradox Basin, Utah. (left) 3D view of PSDM image. (right) Corresponding 3D view of time-migration image. The green ovals on the PSDM image highlight areas which show improved imaging over time migration (red ovals). (Data courtesy of Whiting Petroleum.)

updating filled in the fine-scale details. Our next example is taken from the Paradox Basin,

Utah. Figure 3 compares PSDM to time migration on this example. The Cane Creek Formation consists of overpres-sured, oil-bearing shales/siltstones, embedded between thick salt layers. The lateral velocity variation is subtle at first glance, but significant enough to degrade time imaging in many cases. The degradation is maximized in regions with the largest dips, because velocity follows structure. Explorers drilling horizontal wells in this play need to visualize faults and steep dips near the faults to minimize risk, and in this case, the PSDM image provided a clearer view.

Our final comparison of depth migration and time mi-gration (Figure 4) is taken from southern Wyoming, in a compressional tectonic regime. Reverse faults and “pop-up” features predominate. Time migration images the fairly sim-ple areas quite well, but in this case is not able to correctly image some important reverse faults and steeply dipping fea-tures, which are clear on the PSDM image. The lateral veloc-ity changes here are not radical, but are sufficient to make PSDM an excellent choice.

Next, we illuminate the benefits of RTM with two on-shore examples. The first example (Figure 5) is taken from the famous Spindletop Dome in Jefferson County, Texas. RTM is generally known for its ability to image steep or overturned salt flanks, which it did quite well in this example. However, RTM also excels at imaging steep faults, both fault-plane re-flections and fault truncations. Figure 5 compares RTM to



time migration on inline and crossline slices near the salt, where steeply dipping beds and radial faults represent the remaining stranded oil and gas reserves. RTM has imaged fault planes and produced a sharp image of many fault trun-cations. The improvements increase deeper in the section.

Figure 6 compares RTM to WEM on the Wyoming example shown in Figure 4. Most modern one-way WEM algorithms generally have a dip limitation of about 70°. The Wyoming example does not have dips this steep, so we see that WEM does image the steep flank of the anticline. How-ever, for far-offset receivers, the path from either the source to the reflector or from the reflector to the receiver of a 45° reflection may propagate at an angle greater than 70°. So the WEM algorithm acts as a far-offset filter on the steeply dipping events. As we expect, the RTM image is stronger in places with the highest dips. The additional energy on the RTM image may prove crucial to a seismic interpreter.

Our final two examples illustrate the performance of WEM angle gathers in the computation of rock physics at-tributes. Figure 7, taken from the same south Texas data as shown in Figure 2, shows that the WEM image over the most productive well (produced more than 5 billion ft3) covered by the survey does not yield an obvious seismic “bright spot.” The rock physics of these overpressured Wilcox-age sands is not identical to the typical Gulf of Mexico class 3 AVO sand. However, by applying a prestack inversion for elastic reflec-tivities, using WEM angle gathers, rather than PSTM near/mid/far stacks, we compute a pseudo-Poisson’s reflectivity attribute that (a) stands out roughly 100 fold from the back-ground events, and (b) conforms to the interpreted faults.

Figure 8 illustrates WEM azimuth angle gathers applied to the Wyoming example shown in Figures 4 and 6. The data were migrated with the final velocity model, but decom-posed into six azimuth volumes spanning the range 0–180°

using WEM angle de-composition technology. Azimuthal anisotropy often manifests itself as “sinusoidal” variations in reflector depth with azi-muth angle. Vertically ori-ented rock fractures may cause azimuthal anisotro-py, and as the rocks in this area are “tight”, natural fractures are principally important to prospectiv-ity. Simply interpreted, the phase of the sinusoid aligns with the orientation of the fractures, and the amplitude of the sinusoid may be proportional to the density of fractures. In this case, the peak of the sinusoid aligns with the strike direction, indicat-

Figure 4. Wyoming thrust example. (left) PSDM crossline slice. (right) PSTM crossline slice. Pink polygon on PSTM highlights area where steep dips and faults are not optimally imaged by time migration. (Data courtesy of Nadel and Gussman, Rockies.)

Figure 5. Spindletop Dome RTM example. (left) PSTM image of radial faults. (right) RTM image of radial faults.

Figure 6. Wyoming RTM/WEM comparison. (left) RTM 3D slice view. (right) WEM 3D slice view. Green oval highlights region on RTM image that is improved over the WEM image (red oval). (Data courtesy of Nadel and Gussman, Rockies.)



Figure 7. South Texas AVA attribute example. (left) WEM image 3D slice view, with interpreted faults. Depth slice illustrates productive wells in survey; green arrow indicates location of most productive well. (right) Pseudo-Poisson’s ratio attribute 3D slice view with same faults and well location. (Data courtesy of ECHO Geophysical.)

Figure 8. Wyoming WEM azimuth angle example. (left) 3D common-azimuth angle image. (right) Azimuth-angle gather for (x,y) location specified by crosshairs on left panel. Arrows indicate “slow” and “fast” directions consistent with an interpretation of fracture-induced azimuthal anisotropy. (Data courtesy of Nadel and Gussman, Rockies.)



ing that flexure from the creation of the anticline may have induced fractures.

ConclusionsIn this article, we demonstrate by way of example that ad-vanced PSDM workflows are not only applicable, but prob-ably indispensible, for successful prospecting in many on-shore basins. Accurate and spatially dense velocity analysis is absolutely critical for PSDM; we outlined a two-stage veloc-ity estimation procedure using a variant of depth focusing analysis followed by a WEM angle-gather-flattening tech-nique. Furthermore, if the final migration is a wave-equation migration (WEM or RTM), we advocate using a wave-equa-tion-based velocity estimation approach. We demonstrated on two examples from the western United States that PSDM can significantly improve the resolution of faults and steep dips, even when the lateral velocity variation is not radical. We demonstrated on several examples, that RTM can fur-ther improve over the steep dip resolution of WEM, and can image faults much better than time migration. Lastly, we demonstrated the use of WEM angle gathers for attribute calculations (AVA and azimuthal fracture detection). WEM angle gathers promise increased accuracy over surface offset or azimuth gathers, and more natural handling of ampli-tudes than Kirchhoff gathers.

ReferencesBrown, M. P. and J. H. Higginbotham, 2009, Sub-salt overpressure

detection before drilling using wave equation migration technolo-gies: 79th Annual International Meeting, SEG, Expanded Ab-stracts, 1800–1803.

Higginbotham, J. H., M. P. Brown, and R. G. Clapp, 2008, Wave equation migration velocity focusing analysis: 78th Annual Inter-national Meeting, SEG, Expanded Abstracts, 3083–3087.

Macesanu, C., J. H. Higginbotham, and M. P. Brown, 2010, Angle decomposition in one-way wave-equation migration: 80th Annual International Meeting, SEG, Expanded Abstracts, 3242–3246.

Sava, P. and S. Fomel, 2006, Time-shift imaging condition in seismic migration: Geophysics, 71, no. 6, S209–S217.

Young, J., G. Johnson, S. Klug, and J. Mathewson, 2009, The case for depth imaging all 3D data: 79th Annual International Meeting, SEG, Expanded Abstracts, 522–526.

Acknowledgments: We thank Bob Clapp of Stanford University for many useful conversations, and for his development of the multidi-mensional slice viewer used here. We also thank the editors of this special section, John Etgen and Reinaldo Michelena, for clarity-enhancing reviews of the manuscript. We finally acknowledge ECHO Geophysical, Nadel and Gussman, Rockies, LLC, Whiting Petroleum, and BP for allowing us to show the data examples.

Corresponding author: [email protected]

2911 1386 higginbotham · avo (amplitude variation with offset) has been a corner-stone of prospect...

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