A Hybrid-Order Strategy to Accelerate a High-Order Fast Sweep Method

The Fast Sweep Method (FSM) is an approach to solve eikonal equation, and it plays a significant role in Kirchhoff migration and traveltime based velocity modelling. However, FSM solves the eikonal equation with an upwind finite difference scheme, which may suffer from upwind singularity and decrease the numerical accuracy of traveltime calculation. To overcome the upwind singularity problem and obtain accurate traveltime efficiently, we propose an improved FSM. First, a third-order weighted essentially non-oscillatory (WENO) -based Lax-Friedrichs scheme is applied to solve the factored eikonal equation to achieve a more accurate traveltime. Then, we design a hybrid-order strategy to accelerate the computation. Theories and numerical examples indicate that this method could calculate the traveltime accurately and the total iteration number will reduce significantly.