Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method  

基于贴体旋转交错网格的起伏地表地震波有限差分数值模拟（英文）

作　　者：Cheng Jing-Wang Fan Na Zhang You-Yuan Lü Xiao-Chun 成景旺;范娜;张友源;吕晓春

机构地区：[1]长江大学地球物理与石油资源学院,湖北武汉430100 [2]油气资源与勘探技术教育部重点实验室(长江大学),湖北武汉430100 [3]华北水利水电大学资源与环境学院,河南郑州450011

出　　处：《Applied Geophysics》2018年第3期420-431,共12页应用地球物理（英文版）

基　　金：supported by the National Nature Science Foundation of China(Nos.41504102 and 41604037);National Science and Technology Major Project(No.2016ZX05015-006);Yangtze University Youth Found(No.2015cqn32)

摘　　要：Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.有限差分法计算效率高,在地震数值模拟中被广泛应用,但其不能灵活处理起伏地表。基于贴体网格的曲线坐标变换可用来解决该问题,如基于插值近似的标准交错网格(SSG, standard-staggered-grid)有限差分法、基于MacCormack类的同位网格中心差分法和满足交错分布的全交错网格有限差分法。与上述差分方法相比,旋转交错网格(RSG,rotated-staggered-grid)有限差分法满足曲线坐标系下波动方程的空间分布,不需要额外增加内存和计算量,实现过程简单。为此本文提出了采用旋转交错网格(RSG,rotated-staggered-grid)求解曲线坐标系下一阶应力-速度方程的方法,同时引入一种适合RSG的高精度单边仿真型有限差分(UMFD,unilateral mimetic finite difference)算子来处理起伏地表的自由边界条件。数值模拟结果显示,在RSG有限差分中,采用UMFD法处理自由边界得到的数值解比真空法精度高,且当最短波长内网格点较少时,在一定程度上能有效避免面波频散现象;RSG有限差分法、谱元法和MacCormack类同位网格法三种方法的模拟结果具有较高的一致性,但RSG有限差分法的计算效率比谱元法和MacCormack类同位网格法高。

关 键 词：FINITE DIFFERENCE FORWARD modeling GRID staggered rotated body-fitted SURFACE free BOUNDARY 

分 类 号：P631.4[天文地球—地质矿产勘探]