断层效应反演问题的数值算法

The Numerical Method for an Inverse Problem of Faultage Effect

考虑一类垂直断层效应反演问题,其数学模型是具有解析核的第一类积分方程.因其不适定性,获得它的稳定解非常困难.为获得其数值解,通过积分变换和变量代换,将其转化为一维Hausdorff矩问题进行求解,获得了近似解的误差估计.数值算例显示了算法的有效性.

A class of inverse problems of perpendicular Faultage effect are discussed, which are modeled by a first kind integral equation with an analytic kernel. It is very difficult to recover its stabihzed solution due to its ill-posedness. By the techniques in integral transforms and variable transform, we transform it 1-D Hausdoff moment problem to solve it numerically, and obtain the error estimates for its approximate solution. Some examples verify the numerical method＇s availability.