Elastic-wave inverse scattering based on reverse time migration with active and passive source reflection data

Summary

We develop a comprehensive theory and microlocal analysis of reverse-time imaging—also referred to as reverse-time migration or RTM—for the anisotropic elastic wave equation based on the single scattering approximation. We consider a configuration representative of the seismic inverse scattering problem. In this configuration, we have an interior (point) body-force source that generates elastic waves, which scatter off discontinuities in the properties of earth’s materials (anisotropic stiffness, density), and are observed at receivers on the earth’s surface. The receivers detect all the components of displacement. We introduce (i) an anisotropic elastic-wave RTM inverse scattering transform, and for the case of mode conversions (ii) a microlocally equivalent formulation avoiding knowledge of the source via the introduction of so-called array receiver functions. These allow a seamless integration of passive source and active source approaches to inverse scattering.

We develop a program and analysis for elastic wave-equation inverse scattering, based on the single scattering approximation, from two interrelated points of view, known in the seismic imaging literature as “receiver functions” (passive source) and “reverse-time migration” (active source).

We consider an interior (point) body-force source that generates elastic waves, which scatter off discontinuities in the properties of earth’s materials (anisotropic stiffness, density), and which are observed at receivers on the earth’s surface. The receivers detect all the components of displacement. We decompose the medium into a smooth background model and a singular contrast and assume the single scattering or Born approximation. The inverse scattering problem concerns the reconstruction of the contrast given a background model.