Reverse Time Adjoint and Reverse Time Inverse Migration

H. Liu¹ and Y. Luo¹

Abstract

We present two approaches to reverse time migration technology, namely reverse time adjoint migration (RTAM) and reverse time propagation migration (RTPM). RTAM is based on the Born approximation to the wave equation and linear inverse theory. It can be regarded as the first step of the well-known least squares migration method. RTPM is also based on the Born approximation and it directly solves the wave equation backward in time. The RTPM method is often referred to as reverse time migration in the field of exploration geophysics. In this paper, both methods are formulated in terms of matrices and vectors. Rather than using the general form of matrices symbolically, all elements of the matrices are defined explicitly. This has a direct consequence in programming of these algorithms since it allows a straightforward implementation. Both RTAM and RTPM methods produce similar results when applied on the 2D Sigsbee-2B synthetic dataset. Moreover, it is worth noting that the compound operator, consisting of the forward and the adjoint, used in RTAM, is symmetric. This is another important message of this paper since any conjugate gradient algorithm can now be utilized for subsequent inversion of seismic data.

AAPG Search and Discovery Article #90188 ©GEO-2014, 11th Middle East Geosciences Conference and Exhibition, 10-12 March 2014, Manama, Bahrain