A new finite-difference technique is presented for solving the eikonal equation for inhomogeneous, transversely isotropic media. The method is an extension of other recently developed, isotropic finite-difference algorithms. An expanding-wavefront scheme on a triangular mesh of points is employed, in order to ensure causality and minimize grid anisotropy. Several examples are presented to illustrate the method for varying degrees of anisotropy and inhomogeneity. This technique is particularly well suited to tomographic and migration/inversion applications, since the traveltimes can be efficiently calculated on a dense grid of points for a smoothly varying background.
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