The Pseudo-Laplace Filter for Vector-Based Elastic Reverse Time Migration

Abstract

The scalar images (PP and PS) can be effectively obtained in vector-based elastic reverse time migration by applying dot product–based scalar imaging conditions to the separated vector wavefields. However, the PP image suffers from polarity reversal issues when opening angles are greater than 9 0 ∘ and backscattering artifacts when opening angles are close to 18 0 ∘ . To address these issues, we propose the pseudo-Laplace filter for the dot product–based scalar imaging condition. Based on the analysis of the Laplace filter in the scalar image of vector-based wavefields, the second-order parallel-oriented partial derivatives of Cartesian components cross-correlation results are selected to construct the pseudo-Laplace filter. In contrast, second-order normal-oriented partial derivatives of the Cartesian component’s cross-correlation results are omitted. The theoretical analysis with the plane wave assumption shows that the proposed pseudo-Laplace filter can solve the problems of backscattering artifacts and polarity reversal in PP images by the scalar imaging condition. Due to additional polarity correction and backscattering attenuation, numerical examples show excellent performance in PP images with a pseudo-Laplace filter. Furthermore, the application of the pseudo-Laplace filter requires trivial additional computation or storage.