Robust seismic‐images amplitude recovery using curvelets

Abstract

In this paper, we recover the amplitude of a seismic image by approximating the normal (demigration‐migration) operator. In this approximation, we make use of the property that curvelets remain invariant under the action of the normal operator. We propose a seismic amplitude recovery method that employs an eigenvalue like decomposition for the normal operator using curvelets as eigen‐vectors. Subsequently, we propose an approximate non‐linear singularity‐preserving solution to the least‐squares seismic imaging problem with sparseness in the curvelet domain and spatial continuity constraints. Our method is tested with a reverse‐time ‘wave‐equation’ migration code simulating the acoustic wave equation on the SEG‐AA salt model.