Finite‐difference solution of the eikonal equation along expanding wavefronts
Finite‐difference solution of the eikonal equation along expanding wavefronts
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DOI：
10.1190/1.1443263
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发表时间：
1992-03
期刊：
影响因子：
3.3
通讯作者：
F. Qin;Yi Luo;K. Olsen;W. Cai;G. Schuster
中科院分区：
文献类型：
--
作者：
F. Qin;Yi Luo;K. Olsen;W. Cai;G. Schuster
我们证明了用有限差分方法求解二维eikonal方程的格式对于中到大的速度差(V2/V1和GT；2)是违反因果关系的。作为另一种选择，我们提出了一种有限差分格式，在该格式中，解区域从“扩展的波前”而不是“扩展的正方形”向外扩展，因此遵循因果关系。我们的方法对于具有中等到较大速度对比度的各种速度模型似乎是稳定和相当准确的。代价是计算成本和编程工作量的大幅增加。
We show that a scheme to solve the 2-D eikonal equation by a finite‐difference method can violate causality for moderate to large velocity contrasts (V2/V1>2). As an alternative, we present a finite‐difference scheme in which the solution region progresses outward from an “expanding wavefront” rather than an “expanding square,” and therefore honors causality. Our method appears to be stable and reasonably accurate for a variety of velocity models with moderate to large velocity contrasts. The penalty is a large increase in computational cost and programming effort.