Dip angle-compensated one-way wave equation migration

Abstract

Conventional migration algorithms based on one-way wave equations in a Cartesian coordinate system often under estimate amplitudes, especially at large propagation or reflection angles. This has a deleterious effect on seismic images and should be corrected. We illustrate the nature of the problem by working in the more natural spherical coordinate system and offer two simple solutions to the problem: (1) a wave combination scheme where the wave extrapolation is done independently for each Cartesian coordinate and the resulting wavefields are summed and (2) a simple wave projection scheme whereby the conventional one-way propagator is corrected by means of a factor 1/cos(θ), where θ is the angle of the wave measured from the vertical axis or the reflector angle. The wave combination scheme is applicable to waves with propagation angles beyond 90°, but will roughly triple the computation time compared with conventional one-way propagators in the 3D case. The wave projection scheme is more economical and can easily be implemented in the wavenumber (or slowness) domain at no extra computational cost. These schemes are valid both in depth-dependent media and in laterally heterogeneous media. In addition, the proposed amplitude-preserving schemes can be applied to all methods based on the conventional one-way wave equation. We then develop and implement the second approach to demonstrate its validity by means of numerical examples.