'Shortest path' ray tracing for most general 2D/3D anisotropic media

Abstract

This paper presents a simple method for seismic ray tracing in a general anisotropic medium, which may include complex structures and compound materials, such as water, isotropic and anisotropic rocks, fine-layers and parallel small cracked blocks. The anisotropy may be defined by up to 21 density-normalized elastic moduli which vary with spatial position. The method presented is a direct extension of the irregular network 'shortest path' method for an isotropic solid. For this extension, we first apply analytic solutions of the wave velocities (phase velocity and group velocity) for a general anisotropic medium as a 'transform' or 'mapping' operator to convert the elastic-moduli-described medium into the direction-dependent group-velocity models for the three independent wave modes (qP, qS1, qS2). We then utilize the 'shortest path' method to trace raypaths through such group-velocity models for the three modes. We also give an alternative derivation of Fermat's principle of stationary time in anisotropic media. With this method, the travel times and ray paths of the first arrivals emanating from a source to multiple receivers can be simultaneously obtained for the three modes. Some 2D/3D numerical experiments are performed to show the accuracy and applicability of the method. From these results, one can see that the method may be applied to kinematic modelling and inversion in 2D and 3D seismic or seismological applications.