线性方程组的正则化解法及其应用

NORMALIZED SOLUTION OF LINEAR EQUATION SYSTEM WITH APPLICATIONS

地质矿产部第一海洋地质调查大队

The 1st party of Marine Geological surrey Team, Ministry of Geology and Mineral Resources

在重力资料反演解释中,正则化法解线性方程组是一个行之有效的方法。这种方法的特点是引入正则化因子,求泛函极小和构组一族正则化近似并从中寻求最佳解。在求解过程中,要求对所求的解答预先有一个初步的推断解释。为此,要求对所解释的问题先进行一番研究,并对综合利用各种方法和手段所获得的先验资料进行对比,提出比较合适的基望值。 本文给出了一个参数为已知的理论模型体的横剖面,与正则化法和其它线性方程解法的结果作对比,说明正则化法的有效性。文章也给出了利用正则化法对中国南黄海海域内一地球物理调查剖面进行反演解释应用的效果。

In gravity data inversion and interpretation,the normalized solution for linear equation system is,in fact,effectual. The quintessence of this technique is,to introduce the normalized factor,to extract the functional minimal,to construct afamily of normalized approximation and to find out the optimal solution from within. In the process of solution extraction,it is required to make a preliminary interpretation and to have a basic understanding for the possible solution. Hence,one must hunt through the target being studied and make some cotnparison between the priori information obtained from different means and ways and thus work out the "DESIRED VALUE".In this paper,a transversal section from the theoretical model with known parameters was given. The effectiveness of the normalized technique has already been proved by comparising the result thus obtained with those obtained from other means. The application of the technique to the inversion and interpretation of a section from geophysical investigation in China’s South Yellow Sea was given as an example in this paper.