声波方程有限差分数值模拟的变网格步长算法

地震波场正演模拟是研究地震波在介质中传播特点的重要手段。常规的傅立叶变换法和有限差分方法在对含低速/高速介质、薄层/厚层介质的模型进行波场模拟时通常采用均匀网格,因此,这两种方法往往缺乏稳定性。本文对解决上述问题有较高优越性的变网格算法进行了介绍,对传统的有限差分法与变网格差分算法在内存需求、计算速率等方面的差别进行了比较,并对变网格算法中的边界条件、时间积分的快速展开算法进行了阐述,总结了变网格算法的优点。

Acoustic Equation Numerical Modeling on a Grid of Varying Spacing

It is an important method to study the feature of seismic wave propagates in the medium by the forward modeling of seismic wave field. Traditional Fourier spectral method and finite difference use uniform grids in numerical simulation of low-speed/high-speed medium,thin layer/thick layer. So the two methods are all lack of flexibility. In this paper, an algorithm of moving grid is recommended, which has solved the problem described above. The difference of storage requirement and computational efficiency between traditional finite difference and the algorithm of moving grid is discussed. And the boundary condition, rapid expansion method (REM) for the time integration of the algorithm of moving grid are introduced and the advantages of this algorithm are summarized.