Accurate Depth Migration Research Articles

Seismic velocities in the North West Shelf Region, Australia, From Near-vertical and Wide-angle Reflection and Refraction Studies

A significant limitation of conventional seismic reflection technology is that it poorly constrains seismic velocities in the deep part of the section. These velocities are needed for seismic migration, to convert from time to depth, and to estimate the likely rock composition at depth. Seismic observations at large offsets can compensate for this limitation. The Australian Geological Survey Organisation recorded high-quality refraction and wide-angle reflection seismic data using ocean-bottom seismographs (OBS) along 5 profiles on Australia’s North West Shelf, to maximum offsets of 300 km. The OBS transects coincide with previously acquired deep-crustal seismic-reflection profiles. Consequently, velocity information can now be derived from two independent data sets: common-depth point (near-vertical) reflection data and refraction/wide-angle reflection data. Residual (difference between these two velocity data sets) velocity images can be produced and analysed. Even within the top 5 km of the section residuals between the OBS- and CDP-derived interval velocities vary from -0.5 to +3.5 km/s and increase further with depth. Consequently, the depth equivalent of 4 s two-way time will vary by up to 1.2 km or 10%. The practical implications of co-processing of seismic velocity information are: improved seismic velocity estimation, more accurate depth migration and depth conversion of seismic data and less distortion of amplitudes and shapes of geological structures after depth conversion.

Improving plane‐wave decomposition and migration

Plane‐wave data can be produced by slant stacking common geophone gathers over source locations. Practical difficulties arise with slant stacks over common receiver gathers that do not arise with slant stacks over common‐midpoint gathers. New techniques such as hyperbolic velocity filtering allow the production of high‐quality slant stacks of common‐midpoint data that are relatively free of artifacts. These techniques can not be used on common geophone data because of the less predictive nature of data in this domain. However, unlike plane‐wave data, slant stacks over midpoint gathers cannot be migrated accurately using depth migration. A new transformation that links common‐midpoint slant stacks to common geophone slant stacks allows the use together of optimized methods of slant stacking and accurate depth migration in data processing. Accurate depth migration algorithms are needed to migrate plane‐wave data because of the potentially high angles of propagation exhibited by the data and because of any lateral velocity variations in the subsurface. Splitting the one‐way wave continuation operator into two components (one that is a function of a laterally independent velocity, and a residual term that handles lateral variations in subsurface velocities) results in a good approximation. The first component is applied in the wavenumber domain, the other is applied in the space domain. The approximation is accurate for any angle of propagation in the absence of lateral velocity variations, although with severe lateral velocity variations the accuracy is reduced to 50°. High‐quality plane‐wave data migrated using accurate wave continuation operators results in a high‐quality image of the subsurface. Because of the signal‐to‐noise content of this data the number of sections that need to be migrated can be reduced considerably. This not only saves computer time, more importantly it makes computer‐intensive tasks such as migration velocity analysis based on maximizing stack power more feasible.

On: “Accurate depth migration by a generalized phase‐shift method” by Dan Kosloff and David Kessler (GEOPHYSICS 52, 1074–1084, August 1987).

I would like to point out that the “generalized phase‐shift method” (Kosloff and Kessler, 1987) introduced for solution continuation — and referred to as a new method — is essentially identical to the “generalized Haskell matrix/layer eigenstate propagator (GHM/LEP)” method I presented earlier (Pai, 1985). Unfortunately, Kosloff and Kessler did not reference that paper.

Transformation of Faults in Seismic Migration and Modelling

Faults, thrust faults and intrusion boundaries as usually picked on seismic data are features quite different from normal reflection horizons. Their definition is by terminations of reflecting interfaces rather than by discernible reflected energy off the fault or intrusion boundary. Reflections off faults or intrusion boundaries are, in general, (except for cases of accurate depth migration) not located where the corresponding terminations of horizons line up. Frequently, they are not discernible. Faults or intrusion boundaries that are not actual reflections may not be migrated or modelled. They have to be transformed from time to depth or depth to time domain. The transform parameters can only be derived from horizons available in both time and depth.

Accurate depth migration by a generalized phase‐shift method

A new depth migration method derived in the space‐frequency domain is based on a generalized phase‐shift method for the downward continuation of surface data. For a laterally variable velocity structure, the Fourier spatial components are no longer eigenvectors of the wave equation, and therefore a rigorous application of the phase‐shift method would seem to require finding the eigenvectors by a matrix diagonalization at every depth step. However, a recently derived expansion technique enables phase‐shift accuracy to be obtained without resorting to a costly matrix diagonalization. The new technique is applied to the migration of zero‐offset time sections. As with the laterally uniform velocity case, the evanescent components of the solution need to be isolated and eliminated, in this case by the application of a spatially variant high‐cut filter. Tests performed on the new method show that it is more accurate and efficient than standard integration techniques such as the Runge‐Kutta method or the Taylor method.

Applications of operator separation in reflection seismology

The principle of operator separation, a generalization of operator splitting, is applied to some problems in reflection seismology. In particular, the examples of wave‐equation migration of seismic data in a three‐dimensional medium and accurate depth migration in a laterally varying medium are considered in light of this theory. For the case of a stratified three‐dimensional medium, the standard dimensional splitting technique used in the downward‐continuation step of the migration process can be replaced with full dimensional separation. The computational implications of this result are that the wave field array need only be transposed once during the downward continuation rather than 2n times, where n is the number of finite‐difference steps taken in the calculation. For the example of downward continuation in a laterally varying medium, the ideas of operator separation can be used to split the downward continuation operator into two parts, one that looks like the conventional downward‐continuation operator for a stratified medium, and a second that represents the correction for the effects of lateral variation.