大地电磁自适应正则化反演算法

An adaptive regularized inversion algorithm for magnetotelluric data

针对大地电磁正则化反演中正则化因子的选取困难问题提出了自适应正则化反演算法(AdaptiveRegularizedInversionAlgorithm,ARIA).在该算法中,①提出了一种新的数据方差处理方法:数据方差规范化,使得数据方差的大小只对数据的拟合发生影响,不对数据目标函数和模型约束目标函数的权重产生影响,从而减少了正则化因子取值的影响因素;②提出了粗糙度核矩阵的概念,并给出了由基本结构插值基函数计算粗糙度核矩阵的公式,使得模型目标函数的构建更为简便、直接;③根据数据目标函数、模型约束目标函数和正则化因子之间的关系,提出了两种正则化因子自适应调节方法.本文详细阐述了最平缓模型约束下的大地电磁一维连续介质反演的ARIA实现,以几个算例的分析比较来说明ARIA的有效性.

In this paper, a new inversion method, Adaptive Regularized Inversion Algorithm (ARIA), is presented to overcome the difficulty in determination of regularized factors for magnetotelluric (MT) inversion. In ARIA, first a new data variance disposing method, data variance normalization method, is put forward. This method uses a new way to calculate the influence matrix of data variance in inversion. Thus, the data variance only influences data fitting, and has no influence on the weight between the data object function and the model constraint object function. So the influence factors in determination of the regularized factor are reduced. Second, the definition of roughness kernel matrix is presented in the course of constructing the model constraint object function, and a concise equation of it is derived. Thus the construction of the model object function becomes very simple and direct. Third two adaptive methods of regularized factors are put forward based on the relations of data object function, model constraint object function, and regularized factor. ARIA is used to solve the one_dimensional inversion by MT data by the constraint of the flattest model. Several examples are given to illustrate the effectiveness of ARIA.