用于褶积型线性反演问题的伪广义逆方法

PSEUDO GENERALIZED INVERSE METHOD FOR CONVOLUTION-TYPE LINEAR INVERSION

地矿部石油物探研究所,南京210007

1. Research Institute of Geophysical Prospecting for Petroleum, MGMR, Nanjing 210014;2. The 6th Geophysical Prospecting Party, MGMR, Nangjing 210007

本文以褶积型线性反演问题的傅氏变换形式为基础,把傅氏变换矩阵的性质与求解反演问题的广义逆方法结合起来,提出了一种原理简明,算法简便的求解褶积型线性反演问题的反演方法—伪广义逆方法,将这种方法应用于位场的向下延拓问题(一种典型的不适定“褶积型”问题),获得了良好的结果。

BASED on the convolution-type linear inversion problem formulated in the form of Fourier Transformation, a so-called pseudo generalized inverse method which proved concise in principle and easy to operation for solving such an inversion problem is put forward in this paper by making use of the properties of Fourier transform matrices. The method has resulted in satisfactory results while applied to the downward continuation of potential fields which is considered to be a typical ill-posed deconvolution-type problem.