地震波数值模拟中的最优Shannon奇异核褶积微分算子  

Optimal Shannon singular kernel convolutional differentiator in seismic wave modeling

作　　者：龙桂华[1,2] 赵宇波[1] 赵家福[1] 

机构地区：[1]中国科学院深圳先进技术研究院,中国广东深圳518055 [2]中国科学院地质与地球物理研究所,中国北京100029

出　　处：《地震学报》2011年第5期650-662,共13页Acta Seismologica Sinica

基　　金：广东省自然科学基金项目(10478922035-X00491);国家自然科学基金项目(40874024;41104039);国家重点基础研究发展计划"973"计划(2007CB209603)联合资助

摘　　要：如何有效协调地震波数值模拟过程中的计算精度和计算效率,一直是许多地球物理工作者密切关注且努力寻求解决的问题.这一问题求解的好坏,将直接影响到人们正确认识地下构造的地球物理响应.本文从离散Shannon奇异核理论出发,推导了基于Shannon奇异核的交错网格褶积微分算子,分析并求出了影响算子精度窗函数的最优化参数.通过将最优褶积微分算子与不同长度的交错网格有限差分算子进行比较,发现该算子8点格式的精度相当于16阶交错网格有限差分.对于同长度的算子,交错网格褶积微分算子可以在一个波长内具有较少的采样点数.将本文算子运用于Corner-Edge固液介质模型,其数值试验结果同样表明,该方法计算精度高,稳定性好,可作为研究复杂介质中地震波传播的又一有效数值方法.One of many problems that geophysicists concern with and endeavor to solve for a long time has been lacking of new methods that can well balance the incompatible relation between accuracy and computation efficiency in seismic modeling. In order to solve this problem and correctly recognize the geophysical response of the subsurface structures, we derived a kind of numerical method named staggered-grid convolutional differentiator to solve the one-order velocity-stress equation in elastic media based on discrete Shannon singular kernel theory, whose optimal coefficients are obtained with nonlinear optimization method. Accuracy comparison between optimal staggered-grid convolutional differentiator and staggered-grid finite differentiators with different lengths indicates that the accuracy of the 8th-order scheme differentiator proposed in this paper is comparable with 16th-order staggered-grid finite difference, which, in other words, means that optimal staggered-grid convolutional differentiator has fewer points per wavelength when the two differentiators have the same length. Numerical modeling in Corner-Edge model also demonstrates that the optimal staggered-grid convolutional difference method is of high efficiency and robustness, and this method can be chosen as an alternative approach to compute the wave field in complex media.

关 键 词：交错网格 Shannon奇异核 褶积微分算子 地震波模拟 

分 类 号：P315.01[天文地球—地震学]