Global finite elemtent simulation of short period seismic waves

(1)建立了非均匀介质中地震波的二维有限元模拟方法。我们使用地震-声学混合方法，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-声波散射对于地震波穿过海洋区域或穿过深部核幔边界是非常重要的。为此，我们对固体单元和流体单元进行了区分，使得边界节点有两个值(位移和压力)，并且固体-流体边界条件正好在单元边界上得到精确满足。我们还加入了复值弹性模数的滞弹性衰减(这是可能的，因为我们选择了频域公式而不是时间域公式)。我们评估了我们方法的各个方面(地声散射，不规则形状和界面的可行性，以及滞弹性衰减)。(2)我们开发了上述有限元方法的并行、分布式计算程序。这是必需的，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算法来迭代求解该系统。我们展示了我们能够用10个处理器的小型PC集群在相对较短的时间(大约1000秒)内解决大约3,000,000个自由度的问题。我们计划用这些方法来模拟远场体波，如Pdiff。

(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.