A shortest-path-aided fast-sweeping method to improve the accuracy of traveltime calculation in vertically transverse isotropic media

The high accuracy and efficiency of traveltime calculation are critical in seismic tomography, migration, static corrections, source locations and anisotropic parameter estimation. The fast-sweeping method is an efficient upwind finite-difference approach for solving the eikonal equation. However, the fast-sweeping method is accurate only along the axis directions. In two-dimensional or higher dimensional cases, the accuracy is severely decreased in the diagonal directions due to the numerical errors in these directions. These similar numerical errors also arose in higher order fast-sweeping method and anisotropic fast-sweeping method. To improve the accuracy of traveltime calculation in two-dimensional or higher dimensional space, a shortest-path-aided fast-sweeping method is proposed. The shortest-path-aided solution is embedded into the sweeping process of the standard fast-sweeping method to improve the traveltime accuracy in the diagonal directions. Shortest-path-aided fast-sweeping method is very easy to implement nearly without additional computational cost and memory consumption. Furthermore, this method is easy to extend from two-dimensional to higher dimensional, from low-order to higher-order and from isotropic to anisotropic cases.