Prestack plane‐wave Kirchhoff migration in laterally varying media

Abstract

Conventional Kirchhoff migration methods are applied to seismograms in the offset‐time (x − t) domain. We describe the theory, numerical details, and examples of a prestack depth migration method in the plane‐wave domain that is valid in laterally inhomogeneous media. The theory is based on a Kirchhoff‐Helmholtz formulation of the wavefield and uses plane‐wave‐transformed shot gathers for migration. We use geometric ray theory for the source wavefield continuation operator and a plane‐wave expansion of the receiver wavefield in the integrand of the Kirchhoff‐Helmholtz integral. The source and receiver plane‐wave traveltimes are computed at each grid point in the subsurface using a finite‐difference approximation of the eikonal equation with appropriate initial and boundary conditions. We developed an efficient technique to compute imaging time by a combination of these two times. The technique allows us to design algorithms for migrating shot gather or constant ray‐parameter sections efficiently. We evaluate the efficiency and accuracy of the algorithm with three sets of synthetic data examples with varying degrees of complexity. We also compare the performance of the parallel algorithms using Parallel Virtual Machine (PVM). Migration of a marine data set results in excellent images of a mud volcano and the top of an accretionary prism of an active continental margin on the Nicoya Peninsula of Costa Rica.