声波散射数值模拟的两种新方案

Two New Schemes for Numerical Modeling of Acoustic Scattering

声波散射的数值模拟问题一般用网格法或积分方程法解决。当模型的尺度很大时,两种方法都会遇到计算机资源不足所造成的困难。另外,在网格法中,场源的位置和场源附近的波场奇异性逼近精度都受网格点的控制,因此难以满足实际问题所提出的要求。针对这些问题,提出了两种处理声波散射问题的新方案。一种主要针对网格法,另外一种针对积分方程法。在针对网格法的方案中,通过模型分解和波场分裂,将原始的总场计算问题转化为散射场计算问题。由于背景场是由解析公式给出的,所以可以将场源放置在数值网格的任意位置,不一定非得在网格点上。基于同样的原因,场源附近的波场奇异性可以精确地算出。在针对积分方程法的方案中,通过引入拟线性近似,使得散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。所建立的数值计算方案具有普遍的适用性,其基本思想可以直接用于解决弹性波散射的数值模拟问题并用于反演密度和速度。

Two types of methods are usually used for solving problems of numerical modeling of acoustic scattering. One consists of the methods based on grids, and the other on integral equations. When the model has a large scale, both types of the methods become difficult to be implemented because of the shortage of the computer storage. Furthermore, in the methods based on grids, near the source point both the source position and the computation accuracy are limited by the grid used, and thus cannot meet the demands of practical applications. To solve these problems, this paper presents two new schemes for numerically treating acoustic scattering problems. In these two schemes, one is for grid methods and the other for integral equation methods. In the scheme for grid methods, the original modeling problem of total field is transformed into the one for scattered field, by means of splitting the total wavefield into the background and the scattered wavefield. Since the background field can be computed analytically, the source can be located at any point that does not need to be a grid point. Because of the same reason, the singular property of the wavefield near the source point can be treated analytically. In the scheme for integral equation methods, by means of introducing the quasi--linear approximation, the field computation needs no longer to be realized by solving large linear equation systems. A numerical integration is enough. The schemes presented in the present paper can be used for solving general problems, and their basic ideas can be directly used for treating elastic scattering problems as well as for establishing schemes for velocity and density inversion.