完全匹配层吸收边界在孔隙介质弹性波模拟中的应用  

Applications of the boundary absorption using a perfectly matched layer for elastic wave simulation in poroelastic media

作　　者：赵海波[1] 王秀明[1] 王东[1] 陈浩[1] 

机构地区：[1]中国科学院声学研究所,北京100080

出　　处：《地球物理学报》2007年第2期581-591,共11页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(10674148);国家自然科学基金重点项目(10534040)资助

摘　　要：模拟弹性波在孔隙介质中传播,需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射.本文在前人工作基础上,首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并详细讨论了完全匹配层的构建及其有限差分算法实现.首先,本文通过均匀孔隙模型的数值解与解析解的对比,验证所提出的数值方法的正确性;然后,本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能,将完全匹配层与廖氏和阻尼吸收边界进行了对比,研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力.数值结果表明,在孔隙介质中,完全匹配层作为吸收边界能十分有效地吸收衰减外行波,无论对体波还是面波,是一种高效边界吸收算法.In numerical modeling of elastic wave propagation in a porous medium, artificial boundaries should be treated so that they have minimum effects on elastic wave simulations. In this paper, a high-order velocitystress staggered-grid finite-difference scheme, with a perfectly matched layer （PML） absorbing boundary condition, was firstly proposed for simulating wave propagation in poroelastic media. The construction of perfectly matched layer was discussed in detail, and the implementation of high-order finite-difference scheme of the PML boundary conditions was also studied. The numerical results were validated by using analytical solutions in a homogeneous model. The paper demonstrated the performance of PML for body waves with various incident angles and various absorbing thicknesses. Also, free surface Rayleigh waves are investigated for their absorptions. The PML was compared with two kinds of absorption boundary conditions to confirm the efficiency of the PML. Our numerical results show that, the PML can efficiently absorb or reduce outgoing waves, not only for body waves, but also for surface waves. The PML method is one of the best for porous elastic wave modeling. Our algorithm will play an important role for investigating elastic wave response of inhomogeneous porous media, especially for studying borehole sonic logging response of heterogeneous porous media.

关 键 词：数值模拟 吸收边界 孔隙介质 完美匹配层 有限差分 

分 类 号：P631[天文地球—地质矿产勘探]