I demonstrate how wave-equation datuming can be applied to improve imaging in two of the most challenging environments facing geophysicists: overthrust areas with substantial surface topography and areas of complex velocity structure. I look at these challenges from the point of view that problems arise because the data have not been collected at the ideal recording surface. In the case of overthrust data, problems occur because data are collected along an irregularly sampled rugged surface. In the case of complex velocity structure, problems occur because the data are recorded too far away from the imaging target.
I compare Kirchhoff, phase-shift and finite-difference wave-equation datuming operators by formulating them as adjoint operators and casting them in a unified theoretical framework. This, and a series of synthetic examples allows me to compare and contrast the three different methods. The evaluation leads me to conclude that the Kirchhoff method is best because it is the the most efficient method for application to prestack data, and it can be easily applied to three-dimensional data. Furthermore, the Kirchhoff implementation handles the exact topographic elevations, and its application is not confined to a regular computational grid.
When data are distorted by rugged acquisition topography, I apply wave-equation datuming early in the processing flow to upward continue the data to a flat datum. This approach does not require a detailed a priori knowledge of the near-surface velocity, and it streamlines subsequent processing because the data are regridded onto a regularly sampled datum. Wave-equation datuming unravels the distortions caused by rugged topography, and unlike the static shift method, it does not adversely effect subsequent wave-based processing. The image obtained after wave-equation datuming exhibits better reflector continuity and more accurately represents the true structural image than the image obtained after static shift.
To image complex structures, I develop a hybrid datuming and migration algorithm which is based on breaking up the complex velocity structure into small regions where first-arrival traveltimes are well behaved and coincide with the most energetic arrivals. The traveltimes are used first for imaging, and second for downward continuation of the entire survey to the boundary of the next region. Because traveltimes are computed for small depth domains, the adverse effects of caustics, headwaves, and multiple arrivals do not develop. This results in images comparable to those obtained by shot-profile migration, and superior to those created using maximum-amplitude traveltimes and band-limited traveltimes.