Elastic least-squares reverse time migration from topography through anisotropic tensorial elastodynamics

Abstract

Least-squares reverse time migration is an increasingly popular technique for subsurface imaging, especially in the presence of complex geological structures. However, elastic least-squares reverse time migration algorithms face significant practical and numerical challenges when migrating multi-component seismic data acquired from irregular topography. Many associated issues can be avoided by abandoning the Cartesian coordinate system and migrating the data to a generalized topographic coordinate system conformal to surface topology. We introduce a generalized anisotropic elastic least-squares reverse time migration methodology that uses the numerical solutions of tensorial elastodynamics for propagating wavefields in computational domains influenced by free-surface topography. We define a coordinate mapping assuming unstretched vertically translated meshes that transform an irregular physical domain to a regular computational domain on which calculating numerical elastodynamics solutions is straightforward. This allows us to obtain numerical solutions of forward and adjoint elastodynamics and generate subsurface images directly in topographic coordinates using a tensorial energy-norm imaging condition. Numerical examples demonstrate that the proposed generalized elastic least-squares reverse time migration algorithm is suitable for generating high-quality images with reduced artefacts and better balanced reflectivity that can accurately explain observed data acquired from topography in a medium characterized by arbitrary heterogeneity and anisotropy. Finally, the computational cost of our method is comparable to that of an equivalent Cartesian elastic least-squares reverse time migration numerical implementation.