Scattering Radiation Pattern Atlas: What Anisotropic Elastic Properties Can Body Waves Resolve?

Full-waveform inversion (FWI) optimizes the subsurface properties of geophysical Earth models in such a way that the modeled data, based on these subsurface properties, match the observed data. The anisotropic properties, whether monoclinic, orthorhombic, triclinic, or vertical transversally isotropic (VTI), of the subsurface, be it a fractured reservoir or the core-mantle boundary, are necessary to describe the observed wave phenomena. There are no principal limitations on the complexity of the anisotropy that can be inverted using FWI. However, the question remainswhat kind of anisotropic descriptions of the elastic properties of the Earth can or cannot be inverted reliably from seismic waveforms? We reveal the resolution that can be achieved through reconstructions of each elastic parameter by building vertical resolution patterns from the scattering radiation patterns of body waves. A visual analysis of these patterns indicates trade-offs, that is, perturbations of parameters that have the same reflection-based scattering patterns as other perturbations. Each trade-off leads to an apparent ambiguity in the inversion, which must be addressed by additional assumptions, constraints, or regularizations. For orthorhombic media, we find the exact trade-offs that exist between parameters. Our parameterization isolates the VTI parameters, and therefore, we also obtain trade-offs for every scattering mode for VTI media. We discover that only monoclinic parameters are recoverable from the first-order scattering of monotypic waves. We summarize the trade-offs in tables for easy reference. This paper is intended to be useful for researchers setting up anisotropic FWI problems, and interpreting or controlling the quality of such inversions.