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Summary Traveltime computation in anisotropic media is essential for depth imaging and tomography. The fast marching method is an appealing method in isotropic media and it computes traveltime by solving the eikonal equation with finite difference method. However, it is not applicable in anisotropic media due to the nonlinearity introduced in anisotropic eikonal equation. To address this challenge, we present a Fermat’s principle based fast marching method to compute traveltime in TI media. This method computes traveltime along the expanding wavefront using Fermat’s principle instead of solving the eikonal equation. Thus, it does not suffer from the nonlinearity of eikonal equation in TI media. To compute traveltime using Fermat’s principle, we adopt the moveout approximation to get the explicit expression of group velocity in TI media and this group velocity expression describes the ray propagation. This method is applicable in both VTI and TTI media. Numerical examples on both VTI and TTI models demonstrate the feasibility of this method. |
