一种三维复杂介质波前时间的高精度数值算法

基于水平集的波前扩展算法,如FMM(Fast Marching Method)、GMM(Group Marching Method)，作为一类计算复杂介质波前时间的有效方法而被广泛使用。该类算法都是基于程函方程的有限差分格式来计算波传播时间，在介质离散单元尺寸较大的情况下，计算精度较低。为提高波前时间的计算精度，在一个长方体单元内，将任意点的波传播时间用已知节点上波前时间的插值函数表示，然后根据Fermat原理确定未知节点上的波前时间，再结合高效率的GMM算法，形成了一种计算三维复杂介质波前时间的有效算法。数值模拟实验表明，与原GMM算法相比，该算法大大提高了波前时间的计算精度，同时具有很强的稳定性和适应性。

A HIGH ACCURACY NUMERICAL ALGORITHM FOR WAVEFRONT TIME COMPUTATION IN 3-D COMPLEX MEDIA

The wavefront marching methods based on level-sets，such as FMM(fast marching method) and GMM(group marching method) are widely used as an effective scheme of computing the wavefront time in complex media.The precision of traveltime at grid points，calculated with finite-difference solutions of Eikonal equation，is rather low when the sizes of discrete grids are large.In order to improve the precision of wavefront time calculation，a higher accuracy algorithm of wavefront time computation in 3-D inhomogeneous media is presented based on GMM method and Fermat Principle，with traveltime on arbitrary positions represented by bilinear interpolation functions of the known wavefront time on the grid nodes in each cuboid cell.Numerical simulation shows that the method can not only improve the computational accuracy greatly，but also be strong in stability and flexibility in complex media.