Exact traveltime computation in multi-layered transversely isotropic media with vertical symmetry axis

Abstract

An approach to calculate the accurate ray paths and traveltimes in multi-layered VTI media (transversely isotropic media with a vertical symmetry axis) is proposed. The expressions of phase velocity, group velocity and Snell's law used for computation are all explicit and exact. The calculation of ray paths and traveltimes for a given elementary wave is equivalent to that of a transmission problem which is much easier to be treated with the formulae proposed. In the section of numerical examples, the processes of implementation are described at length using a multi-arrival example and a head-wave example. Lastly, the exact and approximate traveltime curves for the same elementary wave are calculated from the exact formulae and Thomsen's approximations, respectively. The comparison of the curves reveals the increase of errors arising from the repeated use of approximations and indicates the limited applicable range of approximations. It is emphasized that one should keep in mind the applicable range of an approximation when using it. © 2008 Seismological Society of China and Springer-Verlag GmbH.