We propose an expanded finite-difference (EFD) approach to calculate first traveltimes at any point of a regular grid for anisotropic media. The Huygens ' principle is applied as it was previously done in isotropic cases. This approach takes explicitly into account all kind of waves in a high frequency approximation, as long as they are the fastest, with for instante diffracted waves and headwaves. To illustrate our proposal, 2D calculations for anisotropic materials with cubic, hexagonal, tetragonal or orthorhombic symmetry are studied. Based on the same algorithm used in isotropic media, this approach should be extended to 3D cases and possibly for any symmetry system.


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