三维倾斜横向各向同性介质的统一表示和模拟  

General Expression and Modeling of 3D Tilted Transversely Isotropy Media in Circle Coordinate

作　　者：朱兆林[1] 马在田[1] 杨文采[2] 

机构地区：[1]同济大学海洋地质国家重点实验室,上海200092 [2]中国地质科学院地质研究所,北京100037

出　　处：《同济大学学报（自然科学版）》2007年第11期1556-1561,共6页Journal of Tongji University:Natural Science

摘　　要：倾斜横向各向同性介质的对称轴与坐标轴有一定的旋转角度,不同的旋转方向其刚性矩阵有不同的形式.一般研究横向各向同性介质沿三个坐标轴方向旋转得到的倾斜横向各向同性介质,为了方便统一描述这类不同旋转方向的各向异性介质,提出了循环坐标系统的概念.在循环坐标系统下,容易实现各种倾斜横向各向同性介质公式的统一描述,运用到正演模拟中,可以用同一单斜介质系统的波动方程实现不同倾斜横向各向同性介质的模拟程序.最后,用三维交错网格有限差分模拟算法进行了方法的试验,结果成功地实现了三维倾斜横向各向同性介质的正演波动模拟,证实了上述概念的可行性.Tilted transversely isotropic media refer to a case of transversely isotropy with tilted symmetry axes, which have rotating angles with different stiffness matrix in different rotating directions. The cases where transversely isotropy rotates along three axes are often studied, and the concept of circle co- ordinate system is presented in order to depict them generally. In the circle ccordinate, many basic formulas of tilted transversely isotropy can be expressed easily, and a kind of monoclinic media＇s wave equations can be used to simulate wavefield in different tilted transversely isotropic media. The modeling algorithm is staggered grid finite difference method. The numerical steps are implemented by using second order difference in time and high-order staggered grid difference in space. Numerical results of a model show that the above concepts are reasonable and feasible, and 3D anisotropic staggered gird difference method is implemented preferably.

关 键 词：倾斜横向各向同性介质 循环坐标系统 交错网格 有限差分 正演模拟 

分 类 号：P315.3[天文地球—地震学]