模拟地震波传播的三维逐元并行谱元法

Three-dimensional element-by-element parallel spectral-element method for seismic wave modeling

高效地震波场正演模拟对于复杂模型中地震波传播与成像研究至关重要.本文在谱元法原理框架内,对已有逐元谱元法改进,提出一种新的逐元并行谱元法求解三维地震波运动方程,并得到地震波场.逐元并行谱元法的核心思想在于在单元上进行质量矩阵与解向量的乘积运算,并将此运算平均分配至每一个CPU计算核心,此处理有利提升谱元法的并行计算效率.同时,根据Gauss-Lobatto-Legendre(GLL)数值积分点与插值点重合的特点,将稠密单元刚度矩阵的存储转化成单元雅克比矩阵行列式的值及其逆的存储,大幅减少谱元法计算内存开销.此外,在模型边界上利用逐元并行谱元法求解二阶位移形式完美匹配层(PML)吸收边界条件,消除边界截断而引入的虚假反射.通过逐元并行谱元法得到的数值解与解析解对比,以及实际地震波场模拟,数值结果证实了逐元并行谱元法用于地震波场模拟的高效性.

High-efficient seismic wave forward modeling is important for the investigation of seismic wave phenomenon in complex media and the imaging of subsurface structures of the Earth.In the framework of spectral-element method(SEM),we improve the computation efficiency of the previous element-by-element method and propose a new element-by-element parallel spectral-element method(EBE-SEM)for solving 3D seismic wave equation to obtain seismic wavefield.The essential idea of EBE-SEM is that the products of stiffness matrix and solution vector are operated on element level,and the products are equally distributed to each CPU processor.This strategy can greatly increase the parallelization of SEM.Because Gauss-Legendre-Lobatto integration points coincide with the interpolation points in SEM,the storage of dense element stiffness matrix can be transformed to the storage of the determinant and inversion of element Jacobian matrix,and therefore the efficiency of EBE-SEM can be further increased.To eliminate the reflected wave from truncated boundary,we solve the second-order perfectly matched layer(PML)absorbing boundary condition that is constructed at the boundary of the computational domain.The validity and efficiency of the EBE-SEM are demonstrated by two numerical examples.