选择性滤波同位网格有限差分法在地震波数值模拟中的应用  

Application of selective filtering non-staggered finite difference method to seismic wave simulation

作　　者：丘磊[1] 田钢[1] 王帮兵[1] 

机构地区：[1]浙江大学地球科学系,中国杭州310027

出　　处：《地震学报》2012年第4期463-475,580,共13页Acta Seismologica Sinica

基　　金：国家科技重大专项项目(2008ZX05002)资助

摘　　要：引入计算空气声学领域的选择性滤波同位网格有限差分算法(SFFD法)用于二维地震波数值模拟.SFFD法使用经过优化的11点DRP同位网格差分格式,对空间一阶导数进行离散近似,同时采用选择性滤波方法来消除同位网格差分所产生的格点高频振荡,它既提高了数值模拟的精度,又保证了求解过程的稳定性.数值实验结果表明,SFFD法能够达到O(Δx8,Δt4)阶交错网格算法同样的精度,同时该方法还具有很强的适应性,能够应用于存在着强泊松比差异的介质模型中,完整地模拟地震波传播过程中各类型的波场,并且对复杂非均匀介质的适应能力也很好.此外,由于避免了交错网格算法在曲线坐标系和一般各向异性介质的数值模拟时所需进行的复杂的插值运算,SFFD法在这些问题上也有着很好的应用前景.In this study a selective filtering non-staggered finite difference method, called SFFD, is introduced to simulate seismic wave propagation in 2D media. SFFD utilizes optimized l 1-point DRP （dispersion relation preserving） non- staggered finite difference scheme to discretize first-order spatial derivatives. In addition, selective filtering is applied to removing grid-to-grid oscillation caused by non-staggered algorithm. The selective filtering enhances the numerical accuracy and makes the simulation stable to implement. Test result demonstrates that SFFD can achieve the same accuracy as O （△x^6,△t^4） order staggered finite difference scheme. Moreover, the proposed algorithm is able to handle the media with high Poisson＇s ratio. The media with strong inhomogeneity can also be treated by SFFD. As a non-staggered method, SFFD has potential application to seismic wave simulation in curvilinear coordinate system and general anisotropic media, in which complex interpolation must be performed for staggered scheme.

关 键 词：有限差分 选择性滤波 同位网格 数值模拟 自由界面 

分 类 号：P315.31[天文地球—地震学]