地震波传播的褶积微分算子法数值模拟

Numerical Simulation of Seismic Wave Propagation Using Convolutional Differentiator

为了解决地震波场数值模拟中的速度与精度的匹配及局部信息与全局信息的耦合等问题,该文借助新推出的基于Forsyte广义正交多项式的褶积微分算子,将计算数学中的Forsyte多项式褶积微分算子应用到地震波传播的数值模拟中.复杂非均匀介质模型数值模拟结果说明了该方法的可行性和优越性.该方法同时具有广义正交多项式褶积微分算子的高精度和有限差分短算子算法的高速度.通过对算子长度的调节及算子系数的优化,可同时兼顾波场解的全局信息与局部信息.

To improve the accuracy and the efficiency of seismic wave simulation and to couple the local and global information better, this paper develops a novel modeling approach referring to the convolutional differentiator based on generalized Forsyte orthogonal polynomial, which applies optimal convolutional operators for spatial differentiation in wave equation. The numerical experiment of complex heterogeneous model demonstrates that the algorithm can bring reliable results with high precision and can be extended to seismic wave simulation in anisotropic media. This method is highly precise in generalized orthogonal polynomial convolutional differentiator and also highly efficient in finite difference short operator method. The local and global information can be considered at the same time by optimizing the coefficients of the operator and adjusting the operator length.