Least‐squares DMO and migration

Abstract

Conventional processing, such as Kirchhoff dip moveout (DMO) and prestack full migration, are based on independent imaging of subsets of the data before stacking or amplitude variation with offset (AVO) analysis. Least‐squares DMO (LSDMO) and least‐squares migration (LSMig) are a family of developing processing methods which are based on inversion of reverse DMO and demigration operators. LSDMO and LSMig find the earth model that best fits the data and a priori assumptions which can be imposed as constraints. Such inversions are more computer intensive, but have significant advantages compared to conventional processing when applied to irregularly sampled data. Various conventional processes are approximations of the inversions in LSDMO and LSMig. Often, processing is equivalent to using the transpose of a matrix which LSDMO/LSMig inverts. Such transpose processing is accurate when the data sampling is adequate. In practice, costly survey design, real‐time coverage quality control, in‐fill acquisition, redundancy editing, and prestack interpolation, are used to create a survey geometry such that the transpose is a good approximation of the inverse. Normalized DMO and migration are approximately equivalent to following the application of the above transpose processing by a diagonal correction. However, in most cases, the required correction is not actually diagonal. In such cases LSDMO and LSMig can produce earth models with higher resolution and higher fidelity than normalized DMO and migration. The promise of LSMig and LSDMO is reduced acquisition cost, improved resolution, and reduced acquisition footprint. The computational cost, and more importantly turn‐around time, is a major factor in the commercialization of these methods. With parallel computing, these methods are now becoming practical.