非周期均匀化在弹性方程中的应用  

The application of non-periodic homogenization of elastic equation

作　　者：张凌云 孙和平 徐建桥[1] ZHANG LingYun;SUN HePing;XU JianQiao(State Key Laboratory of Geodesy and Earth′s Dynamics,Institute of Geodesy and Geophysics,Chinese Academy of Sciences,Wuhan 430077,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院测量与地球物理研究所大地测量与地球动力学国家重点实验室,武汉430077 [2]中国科学院大学,北京100049

出　　处：《地球物理学报》2020年第1期131-140,共10页Chinese Journal of Geophysics

基　　金：国家重点基础研究发展计划(973计划)(2014CB845902);国家自然科学基金(41474062)联合资助

摘　　要：对于谱元法中介质的非均匀分布尺度小于最小的理论波长以及复杂的间断面网格化难题,建立从微观到宏观的升尺度均匀化方程以及在不丢失波场计算精度对局部区域的微小尺度进行均匀化.利用传统的简正模计算方法求解本征频率和本征函数,给出了均匀化的结果,证明了均匀化计算方法的可行性和正确性;分析了基频简正模频率、理论地震图与均匀化参数,均匀化阶数之间的联系.并成功将之应用到SEM1D实验中,为下一步CSEM三维均匀化奠定基础.It is a problem that in the case of heterogeneity scales much smaller than the minimum wavefield length and complicated mesh of discontinuity for spectra element method.The purpose of this paper is to understand and to build the effective medium through upscaling rules and equations allowing to average the small scales of the original medium without losing the accuracy of the wavefield computation.Traditional normal modes method was used to get the eigenfrequencies and eigenfunctions and the results show that this method is correct and practicable.Relations among the eigenfrequencies and eigenfunctions of fundamental spheroidal modes,seismograms and homogenization parameters and order were analyzed.This has been extended to SEM1D and it will lay a foundation for the homogenization of CSEM in the next work.

关 键 词：非周期 均匀化 简正模 谱元法 

分 类 号：P312[天文地球—固体地球物理学]