关键词: 声波散射, 数值模拟, 波场分裂, 拟解析近似

Abstract: 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.

Key words: acoustic scattering, numerical modeling, wavefield splitting, quasi-analytical approximation