Wave-equation migration velocity analysis by residual moveout fitting

Introduction

In this paper I build on the framework I presented in Biondi (2010). In that report I presented a tomographic velocity estimation that aims to maximize image focusing using wave-equation operators. In SEP 140 I developed the theory and showed the results of numerical tests for a transmission tomography problem, because transmission tomography is simpler than reflection tomography. In this paper I extend that theory to the broader application of migration velocity analysis (MVA).

Conventional MVA methods are often based on the maximization of the stack power of migrated angle-domain common image gathers. However, direct maximization of the stack power as a function of velocity by wave-equation operators has well-known convergence problems (Biondi, 2006; Symes, 2008; Chavent and Jacewitz, 1995). To overcome these challenges, I propose to maximize stack power as a function of residual-moveout parameters, instead of directly as a function of velocity. In turn, the residual-moveout parameters are defined as solutions of fitting problems that maximize the correlation between the moved-out gathers and the gathers obtained by migrating the recorded data with the given velocity. These fitting problems can be quickly solved by using one-parameter gradient methods and thus do not require the explicit picking of residual-moveout parameters. The avoidance of parameter picking is an important advantage with respect to conventional wave-equation MVA methods (Sava and Biondi, 2004b,a; Sava, 2004; Biondi and Sava, 1999).

This paper presents just the theoretical development without any numerical examples illustrating the proposed method. I plan to present the application and the testing of this theory in upcoming reports.

Wave-equation migration velocity analysis by residual moveout fitting