伪谱法弹性波场数值模拟中的边界条件

边界条件问题长期以来一直是困扰地震波数值模拟研究者的一个难题,许多人都提出了有效的方法,但是该问题仍然需要研究.本文针对伪谱法地震波场数值模拟的特殊要求,即所有网格点相互耦合,且傅立叶变换的周期性使得方程在网格边界上很难得到一个吸收的替代方程,研究衰减边界条件中衰减系数的变化对边界反射波衰减效果的影响.数值实验结果说明,随着衰减系数的增大,振幅衰减加快,用很少的过渡带网格就可以使边界上的反射波能量很小.但是如果衰减率过大,就会在传播区和过渡带产生干扰波场.因此,在衰减系数的选择上应采取折中办法,即在取某一较小的衰减系数的前提下,设置较少的过渡带网格数使边界的能量反射最少.

Boundary condition for pseudospectral numerical simulation of seismic wave propagation

For a long time one of the nagging problems which arises in numerical simulations of wave-propagation using pseudospectal method is the presence of side reflections from the boundaries of the numerical meshes.Though many researchers put forward several efficient methods,yet there is not a perfectly method to overcome this problem sufficiently.In this paper we aim at the special demands of pseudospectral method,that is all the mesh grids are coupling and it is hard for us to find an alternative equation on the boundary of the numerical meshes for the reason of the periodicity of Fourier transform,to investigate the effect of the reduction coefficient to the attenuation of the side reflections on using the nonreflecting boundary conditions.Numerical results demonstrate that the larger the reduction coefficient is the quicker the amplitude reduction will be,thus the energy of the side reflections is small with a narrow strip of nodes surrounding the numerical meshes.However,the undesired events will be produced between the numerical meshes and the strip if the reduction coefficient is too large.So in the application we musu have a tradeoff between the reduction coefficient and the strip nodes.