True‐amplitude seismic migration: A comparison of three approaches

Abstract

Knowledge of elastic parameter (compressional and shear velocities and density) contrasts within the earth can yield knowledge of lithology changes. Elastic parameter contrasts manifest themselves on seismic records as angle‐dependent reflectivity. Interpretation of angle‐dependent reflectivity, or amplitude variation with offset (AVO), on unmigrated records is often hindered by the effects of common‐depth‐point smear, incorrectly specified geometrical spreading loss, source/receiver directivity, as well as other factors. It is possible to correct some of these problems by analyzing common‐reflection‐point gathers after prestack migration, provided that the migration is capable of undoing all the amplitude distortions of wave propagation between the sources and the receivers. A migration method capable of undoing such distortions and thus producing angle‐dependent reflection coefficients at analysis points in a lossless, isotropic, elastic earth is called a “true‐amplitude migration.” The principles of true‐amplitude migration are simple enough to allow several methods to be considered as “true‐amplitude.” I consider three such migration methods in this paper: one associated with Berkhout, Wapenaar, and co‐workers at Delft University; one associated with Bleistein, Cohen, and co‐workers at Colorado School of Mines and, more recently, Hubral and co‐workers at Karlsruhe University; and a third introduced by Tarantola and developed internationally by many workers. These methods differ significantly in their derivations, as well as their implementation and applicability. However, they share some fundamental similarities, including some fundamental limitations. I present and compare summaries of the three methods from a unified perspective. The objective of this comparison is to point out the similarities of these methods, as well as their relative strengths and weaknesses.