二维各向异性介质中地震波场的高阶同位网格有限差分模拟  

Two-dimensional seismic wave simulation in anisotropic media by non-staggered finite difference method

作　　者：祝贺君[1] 张伟[1,3] 陈晓非 

机构地区：[1]北京大学地球与空间科学学院计算地球动力学实验室,北京100871 [2]中国科学技术大学地球和空间科学学院,蒙城地球物理国家野外观测研究站,合肥230026 [3]Graduate School of Oceanography,University of Rhode Island,USA

出　　处：《地球物理学报》2009年第6期1536-1546,共11页Chinese Journal of Geophysics

基　　金：地震行业科研专项基金(20070804);国家自然科学基金项目(40521002)资助

摘　　要：本文将DRP/opt MacCormack有限差分格式用于模拟二维各向异性介质中的地震波传播.DRP/optMacCorma ck是一种同位网格下的差分格式,避免了传统的交错网格在计算各向异性问题时由于变量插值而导致的误差.而且相对于低阶同位网格差分格式,它具有低色散、低耗散的优点.此格式将中心差分算子分成前向和后向两个空间单边差分,然后在4-6步Runge-Kutta时间积分中使用单边差分组合.在具有垂直对称轴的横向各向同性(VTI)模型下,通过对比DRP/opt MacCormack有限差分和谱元方法的模拟结果,验证了前者具有很高的精度和稳定性.由于实际地质条件下TI介质的对称轴通常是倾斜的(TTI),本文在二维三分量框架下模拟TTI介质中的地震波场.结果显示横波分裂和切平面/反平面运动耦合的特征.数值实验表明DRP/opt MacCormack是一种有效的研究各向异性介质中地震波传播规律的差分格式.In this paper, a DRP/opt MacCormack finite difference scheme is used to simulate seismic wave propagation in two-dimensional anisotropic media. DRP/opt MacCormack is a non- staggered finite difference scheme which avoids the stress/strain interpolation in traditional staggered finite difference method. Compared to low-order non-staggered finite different scheme, it has low dispersion and dissipation. This scheme divides center difference to forward and backward one-side difference operators which are combined in 4-6 steps Runge-Kutta time integration. In a transverse isotropic media with vertical axis （VTI）, we validate the high accuracy and stability of DRP/opt MacCormack scheme by comparing with spectral element method. In the realistic geological situations, the symmetric axes of transverse isotropic media are tiled （TTI）, we simulate three components seismic wavefields in two dimensional TTI media. The results show shear wave splitting and decoupling of in-plane/anti-plane movements. The numerical simulations show that DRP/opt MacCormack scheme is an efficient tool to study the wavefields in arbitrary anisotropic media. This scheme is suitable for media with arbitrary topographic variations and can be easily implemented in three-dimensional simulations.

关 键 词：有限差分 DRP/opt MacCormack格式 理论地震图 各向异性 TTI介质 

分 类 号：P631[天文地球—地质矿产勘探]