Accommodating lateral velocity changes in Kirchhoff migration by means of Fermat’s principle

When velocity varies laterally as well as with depth, an exact Kirchhoff depth migration requires that rays be traced from each depth point in the section to each source/receiver location. Because such a procedure is prohibitively expensive, Kirchhoff migration is usually carried out by using a velocity function that depends only on depth. This paper introduces a new method, based on Fermat’s principle, which is a compromise between these two extremes. The slowness (reciprocal velocity) function is written as the sum of two functions, the first of which is large and depends only on depth, while the other is small and varies both with depth and position along the line. Raypaths are traced for the first slowness function and are used to calculate migration curves. For each depth point these same raypaths are used to calculate traveltime perturbations due to the laterally varying part of the slowness. The traveltime perturbations are added to the migration curve to obtain an approximation to the exact migrat...