A comparison of four depth-migration methods

Summary A Common Basis Though relatively expensive compared to ray-based migration methods, the methods based on wavefield extrapolation are more accurate in seismic imaging of complex geologic structures. This paper describes implementations of four such related one-way methods for depth migration of prestack and poststack data: phaseshift-plus-interpolation, split-step Fourier, implicit w-x finite-difference, and Fourier finite-difference. All the algorithms work in the frequency domain, resulting in natural and similar parallelization of the codes. These straightforward implementations of one-way methods yield accurate imaging in complicated structures such as the Marmousi model, where most ray-based methods require complicated ray-tracing efforts to image the target-zone. With the advance of computer technology, we expect the above migration methods to play a more important role in the near future, even in the imaging of 3-D prestack data. Let’s start with the 2-D acoustic wave equation. Given a homogeneous velocity structure, in the frequencywavenumber domain we have