Implications of general viscoelastic ray theory for anelastic geophysical models

Abstract

Recent advances in general viscoelastic ray theory provide a new mathematical framework to trace seismic rays in an anelastic Earth. Closed-form solutions of the forward raytracing problems for horizontal and spherical anelastic media account for changes in velocity and attenuation along anelastic P and S wave ray paths that are not encountered along elastic paths (Borcherdt, 2020). The changes, induced by variations in intrinsic-material absorption in the Earth and corresponding changes in wave inhomogeneity manifest themselves as variations in ray-path location, travel-time, and amplitude-attenuation as inferred at the Earth’s surface. The new closed-form solutions provide computation algorithms for computer codes to trace anelastic seismic rays in horizontal and spherical layered models of the Earth with and without material gradients. These computer algorithms, based on exact anelastic solutions, are valid for any linear anelastic medium regardless of the amount of intrinsicmaterial absorption. The forward ray-tracing solutions and solutions of the viscoelastic Herglotz-Wiechert integral provide the framework for theoretical solutions of the viscoelastic inverse problem in horizontal and spherical media to infer both anelastic intrinsic-material absorption and wave speed from empirical measurements of travel time and amplitude of seismic waves (Borcherdt, 2020). The recent ray-theory solutions offer exciting opportunities for further developments in viscoelastic ray theory, computer codes, and capabilities to account for anelastic structure in interpretations of ever improving geophysical data sets.