Finite difference 3D common-shot migration of data from the West Delta area of the Gulf of Mexico

Abstract

The advent of the network, or “cluster,” of modern personal computers has enabled prestack 3D “wave equation” methods, such as common-shot migration, to become practical alternatives to standard Kirchhoff depth migration. Clusters have overcome hardware limitations (cost-effective memory and speed) that previously limited the widespread use of these wave equation algorithms. Prestack Kirchhoff migration is efficient and easily adapts to various data acquisition geometries, while its steep-dip and high-resolution imaging capabilities are unparalleled. Traveltime calculations, typically by ray tracing, are fundamental to conventional Kirchhoff migration. However, propagating wavefronts become complicated when traveling through complex geology; for example, a simple spherical wave propagating near its source eventually separates into several (or many) distinct “branches” as the wave encounters large lateral velocity variations. Computing 3D traveltime fields that faithfully represent such wave propagation and actually using these in 3D Kirchhoff migration is difficult and computationally expensive. Conventional Kirchhoff migration instead uses simplified, single-valued traveltime fields produced by criteria such as first arrival or maximum energy. Where several raypaths encounter a grid node, for example, the maximum-energy criterion selects the traveltime from the raypath with largest amplitude. The single-valued traveltime approximation may be poor in complex geology, where the traveltime fields really are multibranched or multivalued. Prestack wave equation imaging, on the other hand, such as finite difference common-shot migration, uses numerical modeling of the one-way wave equation instead of ray tracing. These wave equation methods can be more accurate than ray methods for modeling wave propagation in complex media. The result can be a superior image in areas of complex geology, such as beneath salt bodies. The most serious limitation of these one-way wave equation methods is that they are dip-limited relative to Kirchhoff methods, especially for strong lateral velocity variations. Most of today's prestack wave equation methods use accurate “dual-domain” techniques …