I developed an efficient, stable, and accurate algorithm to calculate first arrival traveltimes in 3D transverse isotropic media having tilted symmetry axis (TTI). This algorithm is based on a fast marching scheme to solve the eikonal equation using a higher order finite difference (FD) method generally used to calculate first arrival traveltimes in 3D isotropic media. Numerical examples demonstrate that the newly developed algorithm is able to construct accurate first arrival traveltimes in any complicated 3D TTI model that contains a large velocity gradient and an arbitrary orientation of its axis of symmetry. This algorithm can be applied to 3D Kirchhoff pre-stack depth migration and anisotropic parameter inversion in 3D TTI media.


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