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.

中文翻译：

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加速高阶快速扫描方法的混合阶策略

快速扫描方法（FSM）是一种求解方程方程的方法，在基尔霍夫偏移和基于行进时间的速度建模中起着重要作用。但是，FSM用迎风有限差分方案求解了本征方程，这可能会遇到迎风奇异性并降低走时计算的数值精度。为了克服逆风奇异性问题并有效地获得准确的行驶时间，我们提出了一种改进的FSM。首先，应用基于三阶加权的基本非振荡（WENO）的Lax–Friedrichs方案来求解因式方程式方程，以实现更精确的行程时间。然后，我们设计了一种混合顺序策略来加速计算。