Finite‐element ray tracing through structurally deformed transversely isotropic formations

Abstract

Accurate ray tracing forms the central building block for prestack Kirchhoff depth migration, reflection tomography, and amplitude versus offset (AVO) analysis. We present an accurate method of tracing rays through an inhomogeneous transversely isotropic medium where the crystallographic axes of symmetry are rotated arbitrarily. We achieve this high degree of modeling diversity by discretizing our model into a piecewise homogeneous finite‐element representation of a continuously variable earth. Within each element the anisotropic parameters, together with the angle of rotation between the crystallographic and model axes, may vary arbitrarily. We obtain efficiency by approximating the exact expression for the eikonal equation given by Gassmann, which, after some minor manipulation, bears a striking resemblance to an empirical parameterization developed by Lecomte. This new algorithm produces results that compare favorably to first arrivals generated by the numerical solution of the full elastic wave equations for transversely isotropic (TI) media. In the limit of weak anisotropy, our results reduce to the well‐established Thomsen parameterization.