Abstract
A Kirchhoff method that avoids possible singularities on the surface of integration and is more accurate than previous Kirchhoff methods has been developed for seismic migration in laterally inhomogeneous media. It is based on a newly derived integral solution to the acoustic wave equation. This solution indicates that wave fields in an inhomogeneous medium can be expressed as a summation of ray solutions determined by the transport and extended eikonal equations. The extended eikonal equation is, in turn, solved by an asymptotic series. For implementation, a perturbation scheme is developed for solving the ray and transport equations. In addition to computing higher‐order terms of the asymptotic series, this scheme can be used to avoid most of the ray tracing required for wave extrapolation in a medium where vertical variations may be large but lateral variations are small compared to velocity itself. Where an analytic ray solution for the reference velocity used in the perturbation scheme exists, ray‐Kirchhoff migration in such a medium can be carried out without numerical ray tracing.
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