弹性波的三维有限元模拟  

THREE-DIMENSIONAL FINITE ELEMENT MODELLING OF ELASTIC WAVES

作　　者：邓玉琼[1] 张之立[2] 

机构地区：[1]美国哥伦比亚大学Aldridge应用地球物理实验室 [2]国家地震局地球物理研究所

出　　处：《地球物理学报》1990年第1期44-53,共10页Chinese Journal of Geophysics

摘　　要：本文讨论了弹性波瞬态传播问题的三维有限元计算方法及当前存在的实际困难.针对要求计算机内存大和计算时间长的问题,采取了改进措施.由于采用了集中质量矩阵和修正的中心差分时间积分显格式相结合的方法,可以使计算机内存和计算时间大为减少;由于采用结点定位法,最适合用于目前发展的并行计算机系统,可使计算速度大大增快;还采用了有效激发震源法,有效激发区是随时间步进的增加而逐步增大,这不仅能节省计算时间,而且使波场的传播过程一目了然,本文计算了由两种介质组成的三维楔形问题,得到若干典型剖面的瞬时波场图及随时间变化的合成地震图.In this paper, the three-dimensional iinite element algorithm for solving transient elastic wave propagation problems and the existing practical difficulties are discussed. An algorithm, the combination of finite element in space with lumped mass matrix representation and a modified explicit central difference time integration, may overcome partially the difficulties of requiring an enormously large computer incore storage and a large amount of computing time. For a structure with 30×30×30 hexahedron elements, the present algorithm can reduce the computer in-core storage down to 1/5000 time of the conventional algorithm of 'block-by-block'. The nodal-point-oriented approach, which particalarly suits for the computation on the parallel computer systems is used. We also adopt an effective excitation method (EE method) in the entire marching process. With this EE method, the region of excitation motion expands with increasing in time yteps, and the computing time can be further reduced. As a demonstrative example, a three-dimensional wedge shaped structure with two kinds of medium has been considered. The forcing function is taken as the first derivative of the Gaussian function. For some profiles of this wedge problem, the snapshot view of wave patterns and the .synthetic seismogram for the calculated displacement fields are also presented.

关 键 词：弹性波 三维有限单元法 结点定位 有效激发震源 瞬时波场 合成地震图 

分 类 号：P315.31[天文地球—地震学]