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Global finite elemtent simulation of short period seismic waves

短周期地震波全局有限元模拟

基本信息

批准号：
12640406
负责人：
OKAMOTO Taro
金额：
$ 2.3万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

(1)We developed a 2D finite element method for the simulation of seismic waves in heterogeneous media. We use a hybrid, seismo-acoustic approach so that we can simulate the scttering of the seismic waves (in elastic media) and the sound (pressure) wave (in fluid media), as the seismo-acoustic scattering is very important for seismic waves travel through the oceanic regions or through the deep core-mantle boundary. In order to do that, we discrimate between solid elements and fluid elements so that the boundary nodes have two values (displacement and pressure), and the solid-fluid boundary conditions are exactly satisfied right at the boundary of elements. We also incorporated the anelastic attenuation by complex-valued elastic moduli (this is possible because we selected the frequency domain formulation instead of the time domain formulation). We evaluated the various aspects of our method (seimo-acoustic scattering, feasibility for irregular shapes and interfaces, and anelastic attenuation).(2)We developed a parallel, distributed computation program of the above finite element method. This is required because the very large complex-valued sparse linear system must be solved to model the global wave field. Our approach is to distribute the elements of the stiffness matrix and vectors among processors and to apply a distributed GP-BiCG algorithm to solve the system iteratively. We showed that we are able to solve a problem of about 3,000,000 degrees of freedom in a relatively short time (about 1000s) with a small PC cluster of 10 processors. We plan to apply these method to model the far-field body waves such as Pdiff.

(1)建立了非均质介质中地震波模拟的二维有限元方法。我们使用一种混合的地震声方法，这样我们就可以模拟地震波（在弹性介质中）和声波（压力）波（在流体介质中）的散射，因为地震声散射对于地震波穿过海洋区域或穿过深核-地幔边界非常重要。为此，我们区分固体单元和流体单元，使边界节点有两个值（位移和压力），并在单元边界处精确满足固流边界条件。我们还通过复值弹性模量纳入了非弹性衰减（这是可能的，因为我们选择了频域公式而不是时域公式）。我们评估了我们方法的各个方面（半声散射，不规则形状和界面的可行性，以及非弹性衰减）。(2)开发了上述有限元方法的并行分布式计算程序。这是必须的，因为必须求解非常大的复值稀疏线性系统来模拟全局波场。我们的方法是在处理器之间分配刚度矩阵和向量的元素，并应用分布式GP-BiCG算法迭代求解系统。我们展示了我们能够在相对较短的时间内（大约1000秒）用10个处理器的小型PC集群解决大约3,000,000个自由度的问题。我们计划将这些方法应用于Pdiff等远场体波的建模。