Finite difference calculation of first traveltimes in anisotropic media

I propose a finite difference approach, in a general sense, to calculate the traveltimes of the first arrivals in anisotropic media at any point of a regular grid. This method is based on the application of Huygens principle and is similar to an earlier developed method for isotropic cases. The procedure takes explicitly into account the existence of different waves, in the high-frequency approximation, and can deal with any peculiar waves such as diffracted waves or headwaves which may sometimes be the fastest ones. 2-D calculations for anisotropic materials with cubic, hexagonal, tetragonal or orthorhombic symmetry are presented. However, since this approach is based on the same algorithm as used in isotropic media for both 2-D and 3-D cases, it may be extended to 3-D anisotropic media. Moreover, the general algorithm does not depend on the symmetry system and is therefore applicable in any other case of anisotropy. I suggest, in a first attempt, to apply the finite difference calculation of traveltimes for qP waves, because q S waves may have very peculiar propagation in anisotropic media. Key words: anisotropic media, finite differences, first traveltimes.