The failure of standard processing and imaging methods in complex areas can be thought of as arising from the fact that the data have not been collected at the ideal recording datum. In the case of land data, the failure can occur when data have been collected along an irregularly-sampled rugged surface, not on a level and regular grid. In the case of complex velocity structure, the problem can occur because the data have been recorded too far away from the imaging target, and not at the ideal subsurface location.
Under certain conditions the rugged topography problem can be compensated for by redatuming with static shift; however, when the assumptions behind the static correction are invalid, subsequent processing and imaging is degraded. Alternatively, the data can be processed from a nonflat datum, but this requires special algorithms that can accommodate irregular and rugged geometry. This can be a problem because most algorithms are optimized for regularly-sampled data referenced to a flat datum. If the data are referenced to a flat datum, structures are not distorted by topography, and interpreter input is facilitated both in the processing and imaging stages.
To ameliorate these problems in areas of rugged topography, I apply wave-equation datuming to transform the data to an ideal, regularly sampled, flat datum. This is the most accurate method of redatuming because it preserves the wavefield nature of the data and thus does not adversely affect subsequent wave-equation processing steps. Another advantage of wave-equation datuming over static shifts is that it is capable of regridding the data to a regular computational mesh. Once the data are redatumed, a wide range of processing algorithms can be applied. There is no restriction imposing the use of specialized algorithms that can handle nonflat irregular geometry. Once the data are properly redatumed, incorporation of geological information in velocity model building and assessment of processing validity is easier because structures are readily identified and correctly interpreted.
In areas of complex velocity structure, the migration result is improved if the data are downward continued through complex overlying structures, and the imaging is performed from a datum that is closer to the target zone. In this way, the deleterious effects of complex overburden are stripped away. The greatest benefit of this layer-stripping approach is that the complex velocity model is broken up into smaller portions. This is a great benefit for Kirchhoff imaging methods which employ summation trajectories based on single-valued first-arrival traveltime tables. The imaging of a limited portion of the complex structure from a nearby reference datum allows the traveltime calculation to be performed for a restricted time range, for which the traveltime calculation accurately parameterizes the most energetic portion of the seismic wavefield. Because the first-arrival traveltime calculation is not allowed to evolve for too long, caustics and headwaves do not develop to the point where they degrade the imaging result.