模拟地震波传播的三维逐元并行谱元法

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.