Approximate explicit ray velocity functions and travel times for P‐waves in TI media

Abstract

Summary Seismic anisotropy in sedimentary rocks is becoming more and more important in modern seismic processing and interpretation. The assumption of transversely isotropic (TI) media is a good approximation for most real anisotropic sedimentary rocks of interest to geophysicists. In homogeneous TI media, the ray velocity surface for SHwaves is an ellipse, while those for P- and SV-waves are non-elliptical, and no exact explicit ray velocity functions exist for P- or SV-waves in TI media. In this paper, approximate explicit analytical P-wave ray velocity functions in transversely isotropic media have been developed. The functions include a new dimensionless constant, A, which can be determined using elastic constants C11, C33, C44, and C13, or Thomsen’s parameters e, δ, α0, and β0. The accuracy of the functions has been tested for all the materials published by Thomsen (1986). The formula for calculating the travel times between any two points in homogeneous transversely isotropic (TI) media and the reflection travel times from a single horizontal reflector overlain by transversely isotropic media with vertical symmetrical axis (VTI) have been derived from the ray velocity functions. The results show that the reflected travel time formulae works well for both large and small offsets.