Anisotropic depth migration - a new shift in seismic imaging

Finding true spatial relationships

Ron Schmid
Kelman Seismic

• The Husky/Talisman line from the Western Canadian thrustbelt region was the focus of a 1995 SEG workshop on complex structural imaging. It has excellent signal quality and the presence of alternating dipping and horizontal shale formations. Boxed regions indicate poorly migrated data zones. [93,245 bytes]
• The Husky/Talisman line after anisotropic depth processing. Significant improvement can be seen in the boxed regions. [91,299 bytes]

Prestack depth imaging has long been known and used with enormous success in the Gulf of Mexico. The technology addresses the wave front bending caused by the abrupt velocity contrast between the salt and surrounding lower velocity formations. This has allowed geologists and geophysicists to image target zones beneath salt formations.

However, depth imaging does more than merely producing a clearer picture from a previously distorted image. It also re-positions reflecting events to a more accurate representation of their true spatial relationships.

The current seismic processing doctrine is to provide the migration algorithm with a highly accurate model of the subsurface, which describes the layer geometry and detailed velocity information. This often requires the combined efforts of high level data processing and interpretive personnel and sophisticated software to derive the model directly from the data.

The validity of the velocity model is determined from inspection of the depth-migrated gathers and the stack response. The depth-migrated gathers should exhibit flat events across all offsets. The stack response provides the final seismic section for interpretation.

Experience with depth imaging technology has unquestionably produced improved imaging, yet puzzling shortcomings remain in the geometry plus velocity doctrine. For example, while well logs can directly measure rock velocity, the use of well logs for interval velocity information does not produce an optimally flat set of events on depth gathers. The subsequent stack response is degraded. Furthermore, the actual wellbore depths do not support the formation depths indicated by the depth section.

Depth imagers routinely use one velocity model for imaging and another for depth conversion to tie known formation tops. Not only are the events on the depth section wrong in the vertical sense, there is often a remnant of lateral mispostioning as indicated by wellbore dip meter measurements.

Better assumptions

In light of these important observations, it is reasonable to reassess the assumptions of the current methodology. Recent research indicates that model parameterization using isotropic interval velocities (even with velocity gradients) is not sufficient to describe wave propagation for the purposes of calculating travel times employed by migration algorithms. A more geologically reasonable assumption is that the layers are anisotropic, that is, the seismic velocities vary with direction of wave propagation.

In particular, shales are generally considered to be anisotropic. Anisotropic depth migration (ADM) honors Snell's Law, as does isotropic depth migration. It also accounts for wave front bending, due to direction of propagation relative to the bedding planes of the formations.

Consider for a moment the sensitivity of depth migration to velocity. The benefits of performing depth imaging and focusing are achieved when the velocity model approaches 3% of the true velocity. Yet the isotropic assumption used in most depth imaging ignores a factor that may modify the effective velocity by 20-30%.

Applications offshore

Most of the excellent research on seismic anisotropy involves the theoretical aspects, studying anisotropy in flat lying beds, or using shear wave anisotropy in fracture detection. However, most depth imaging is performed in structural environments, typically for thrustbelt or subsalt imaging. Therefore, truly practical depth imaging, which attempts to correct for anisotropic affects, must deal with dipping anisotropic geologic formations. Since anisotropy is an intrinsic rock property, the lessons learned from the following thrustbelt example will apply equally well in the marine exploration environment.

The following example illustrates the development of anisotropic processing from problem recognition, parameter estimation, and results on anisotropic depth migration (ADM) using an internationally known field dataset.

The Husky/Talisman line from the Western Canadian thrustbelt region forms the basis of our example and was the focus of a 1995 SEG workshop on complex structural imaging. It has excellent signal quality and the presence of alternating dipping and horizontal shale formations.

Anisotropy detection

The line was originally cast as a classic depth-imaging example in a thrust belt environment. In common with other thrustbelt regions, topography and surface referencing of travel time estimates were issues for migration purposes. However, it was generally held that dipping shale layers and thrusting of high velocity carbonates over slower velocity clastic formations was introducing non-hyperbolic moveout.

While the robustness of time imaging provided a good quality, migrated result, it was felt that depth imaging was required to correctly position events. Our observations regarding the presence of anisotropy sprang from the failure of solely isotropic depth migration techniques to adequately resolve structures within reasonable geological velocity constraints.

Key observations

Three primary observations led to the suspicion that anisotropy was affecting the imaging and position of events on this line.

• A correlation existed between dipping shales and basement structural imaging. The line exhibited alternating sequences of flat and dipping shale units in the shallow parts of the section (<2,500 meters on the seismic depth scale) with a planar, mildly dipping strong basement reflector. In every instance, horizontal shales correlated with excellent basement reflector imaging. Dipping shales correlated with poor basement reflector imaging on data that was isotropically depth migrated. Isotropic depth migration should have been able to account for the wave front bending effects (caused by the dipping shales and thrusted carbonates) to successfully image the basement reflector.

• In order to achieve an optimal isotropic depth-migrated result, we had to abandon the concept of identical geologic units having the same velocity. The geometry of events on this line juxtaposed dipping layers against stratigraphically equivalent flat events. Yet, they appeared to require different velocities for imaging purposes. Other causes, such as depth of burial and weathering were not sufficient to explain these observations. Even with a more relaxed isotropic velocity constraint, inspection of the depth-migrated gathers revealed an undesirable amount of residual moveout that could not be removed by further isotropic velocity perturbations.

• A third observation relied on inspection of events on selected depth-migrated gathers. Gathers were strategically selected, based on the angles of wavefield propagation with respect to the bedding planes of the shale events. Inspection of the residual moveout on the basement event on these gathers showed a moveout pattern predicted by anisotropic theory. That is, imaging events under dipping shales required a slower velocity than events under the identical, but flat-lying shales.

These three observations, taken separately, may be explained away by invoking some geophysical happenstance. Yet, when taken collectively, they provide compelling circumstantial evidence for the anisotropic nature of these shales.

Parameter estimation

We use Thomsen's (1986) approximations and notations for weakly anisotropic media to estimate anisotropic parameters. In the case of P-wave propagation in vertically transverse isotropic (VTI) media, depth imaging requires the estimation of three parameters:

• VP0, P-wave velocity in the direction of the symmetry axis
• Epsilon, the fractional difference between velocities perpendicular and parallel to bedding
• Delta, the variation in P-wave velocity close to the symmetry direction.

A reliable estimate of VP0 for the shale units was obtained from isotropic depth migration. In particular, we were able to capitalize on regions on the line where the shale units were flat lying and isotropic depth migration yielded flat events on depth gathers. A practical constraint on deriving the anisotropic parameters was the need for an iterative procedure. Iterations were kept to a minimum (2 or 3). Each iteration approached convergence. This implied an interactive procedure to test values of the remaining Thomsen parameters before committing to ADM iteration.

Based on a review of current literature, delta was assigned a reasonable value (nominally chosen to be a fraction of epsilon) and a range-of-values of epsilon was assessed. Subsequent work empirically demonstrated the interplay between delta and epsilon. In the case of dipping shales, delta has little effect on the lateral positioning of events but plays an important role in depth conversion.

An interactive model-building interface was designed which permitted input of bedding plane dip information and varying values of epsilon. Depth-migrated gathers were used to ascertain the most appropriate value of epsilon. The depth gathers were non-hypberbolically deNMOed (removing normal move-out) with the complex velocity model used in the migration and then reNMOed (but not re-migrated) with a velocity model which had been modified to assess different values of epsilon.

The optimum value for epsilon was determined by examining the events on the depth gathers for flatness. In addition, the gathers are restacked with the resultant stack examined for structural fit, event positioning, and horizon continuity. Many trials were quickly and inexpensively assessed, since we were dealing with a small number of strategically placed gathers, reNMOing and stacking. While the full effect of the anisotropic model parameterization was not known until an iteration of ADM was performed, the model modification (deNMO - reNMO loop) did portend the quality of the next full migration iteration.

Data example

Once a velocity model was derived another iteration of depth migration was required. We accounted for the dipping shale anisotropy in the generation of the travel times. The actual migration procedure used was a well-established Kirchhoff-type migration. Figures 1 and 2 represent the results of isotropic and anisotropic depth migration.

A key point is that the velocity used for each migration was the same. The only differences are related to the inclusion of the anisotropic parameters. In this example the model was parameterized such that every shale unit was assigned values of 10% for epsilon and 2.5% for delta. In the general case, we expect that the velocity terms will have to be slightly adjusted after the inclusion of anisotropic terms. This implies that anisotropic migration is also an iterative procedure. The box outlines serve to draw attention to regions where the data-imaging and data-focusing were improved.

The anisotropic migration allowed us to improve the imaging directly below the dipping shales. There was a clear improvement in the basement reflector imaging, positioning of faults, and overall structural fit on the final output section. Events on image gathers, which at one time showed large unresolvable residual moveout, were now much flatter.

References

Thomsen, L. (1986), "Weak elastic anisotropy," Geophysics 51, 1954 - 1966.

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