利用广义逆矩阵的窗口系数法反演重磁界面

INVERSION FOR THE BOUNDARY SURFACE OF GRAVITA-TION AND MAGNETISM BY THE WINDOW COEFFICIENT METHOD OF THE GENERALIZED INVERSE MATRIX

本文讨论了直接法(矩阵法)求解二维三维重磁界面反演问题时常常遇到的方程病态问题;利用广义逆矩阵方法获得病态问题的稳定解;通过设置流动窗口和预先求出反演系数的方法,解决了直接法反演未知参数多、占用机器内存大、计算效率低的问题,使重磁界面的反演过程也能象圆滑、二次导数一类圆环系数法一样地易于实现。

In the paper, the ill-conditioned matrix is discussed, established by the direct method,which is often encountered in the inverse solusion of two or three-dimensional boundary surface of gravitation and magnetism. The stable solusion for the ill-conditioned matrix can be obtained by the generalized inverse matrix method. By establishing movable window and previously solving out inverse coefficients, the drawbacks of the direct method such as large storage and low speed as well as unknown multiple coefficients can be overcome. This leads to that the inverse process of the boundary surface of gravitation and magnetism can be realized as easy as a kind of the circle coefficient method such as the smoothing or the second deriving.