I obtain images comparable to shot-profile migration results by combining wave-equation datuming and Kirchhoff migration into a layer-stripping migration method. In this case, first-arrival traveltimes produce satisfactory images because the velocity model is subdivided and traveltimes are calculated under conditions where finite-differencing the eikonal equation is valid. By dividing the imaging problem in this way, the traveltimes are better behaved and some multiple arrivals are accounted for.
In the example presented here, I downward continued the data to flat surfaces within the velocity model. This is not a limitation imposed by the method, and there is no reason that the data could not be downward continued to a datum which corresponds to some arbitrarily-shaped surface. For certain complex velocity models this could be an advantage because the careful choice of a surface can eliminate some potentially adverse propagation effects in the traveltime calculation.
The layer-stripping approach presented in this chapter is not limited to datuming and migration with finite-difference first-arrival traveltimes alone. The traveltime or parametric Green's function calculation can be done by any method, such as energetic ray tracing or band-limited traveltimes. The better the traveltime calculation method, the better the final image. However, in most cases, the advantage of the layer-stripping method is that computationally intensive traveltime methods need not be used.