Waveform inversion in triclinic anisotropic media—a resolution study

Abstract

Seismic full waveform inversion (FWI) has been applied to simple elastic problems with certain symmetries, such as isotropic, transverse isotropic or vertical transversely isotropic media. In this study, the FWI concept is extended to the most general anisotropic case with 21 independent elastic material parameters and no symmetry plane (triclinic). Beside a short description of the 3-D finite-difference scheme to solve the forward problem and the FWI optimization algorithm, we present a sensitivity study for a simple anisotropic medium. This test problem consists of a homogenous triclinic anisotropic full space, which contains 21 spatially separated spheres. In each sphere one component of the elastic tensor deviates by 5 per cent from the background medium. The resolution of the different spheres, ambiguities between the different elastic parameters, as well as the effect of the acquisition geometry can be systematically investigated. Due to the high computational costs of the triclinic forward problem a few compromises have to be made regarding the acquisition geometries. Point sources are replaced by plane wave sources which lead to a limitation of incidence angles and therefore a strong decrease in resolution of the nondiagonal elastic tensor components. It is shown that, despite these limitations, a tomographic acquisition geometry would be able to resolve to some extent a monoclinic symmetry via FWI. Restricting the acquisition geometries (e.g. VSP combined with reflection seismic or reflection seismic only) significantly reduces the number of resolvable tensor elements in strict dependence of the covered incidence angles.