基于不等式约束的井地电阻率法三维非线性共轭梯度反演研究  

3-D hole-to-surface resistivity inversion with nonlinear conjugate gradients method under the constraint of inequality

作　　者：王智[1,2] 潘和平[2] 骆玉虎 李刚[1,2] 方思南 杨怀杰[2] 

机构地区：[1]长江大学电子信息学院,荆州434023 [2]中国地质大学(武汉)地球物理与空间信息学院,武汉430074 [3]中海石油(中国)有限公司湛江分公司,湛江524057

出　　处：《地球物理学进展》2016年第1期360-370,共11页Progress in Geophysics

基　　金：国家自然科学基金资助项目(41074086)资助

摘　　要：基于共轭梯度的最小构造反演方法是三维电阻率反演的主要方法,是基于线性系统的线性反演,而反问题的不适定性很大程度上与非线性问题的线性化有关,且存在着多解性较强的问题.为了改善以上问题,本文利用目前较为主流的非线性共轭梯度法(NLCG)实现了三维井地电阻率法的反演,将表征模型参数变化范围的不等式约束作为先验信息以惩罚函数法的方式引入到NLCG反演方法中.通过对多种理论模型的反演结果比较,有效的改善了反演结果的精度,在一定程度上降低了反演的多解性.在目标函数中加入构造位置的先验信息作为局部不等式约束的反演算例表明,给出的范围越精确,反演结果就越准确.Inversion for minimum structure based on Conjugate Gradient is the main method of three-dimensional resistivity inversion. This is a kind of linear inversion relying on linear systems. However, ill-posed problems of inversion are largely related to linearization of nonlinear questions,and the ambiguity is strong in some cases. In order to alleviate the problems above,a prevailing method,Non Linear Conjugate Gradient（ NLCG）,was adopted to achieve three-dimensional hole-to-surface resistivity inversion. Also penalty function which represented the range of model parameters was introduced into inversion of NLCG as priori information. After comparing the inversion results from a variety of theoretical models, we found that this method can effectively improve the accuracy of the inversion results, and reduce the ambiguity of inversion. Meanwhile,the inversion instances which took structural position as a local inequality constraints when setting the priori information indicated that the more precise the location of structure was,the more accurate the inversion results were.

关 键 词：井地电阻率法 反演 非线性共轭梯度法 不等式约束 惩罚函数法 

分 类 号：P631[天文地球—地质矿产勘探]