基于最小支持的2.5维直流电阻率正则化反演研究

地球物理反问题存在多解性和不稳定性,正则化是得到稳定解的重要手段之一,正则化方法中稳定因子的设计与正则化因子的选择是两项重要研究内容。稳定因子的主要功能是对模型的解空间进行限制,以减少多解性,求得稳定解;为更好的定位地下目标体,研究工作采用了最小支持稳定因子,并给出了统一表达形式。正则化因子在模型误差与数据误差之间起到平衡作用,研究工作在＂L曲线法＂自动选取正则化因子的基础上,提出一种修正的计算正则化因子算法。以2.5维直流电阻率为例,运用非线性共轭梯度法,进行了试算研究,结果表明了修正的＂L曲线法＂算法快速、稳定,最小支持稳定因子具有较好的聚焦特性,有利于实现陡变边界反演。

The Study of Regularization Inversion for 2. 5 Dimension DC Resistivity Based on Minimum Support Stabilizing Factor

Multiple solutions and instability are existed in geophysical reverse problems; regularization is an important method to obtain a stabilizing solution. The design for stabilizing factor and the choice of regularization factor are two important research contents in the regularization method. The main function of the stabilizing factor is to limit the model space,for this we can reduce the multiple solutions and obtained the stabilizing solution. We adopt the minimum support stabilizing factor for locate the target underground,and give a unity expression of the stabilizing factor. Regularization factors play a balance between model error and data error,give a modified autoselecting algorithm based on the L-curve criterion. It is taken 2. 5D DC resistivity method for instance,using the nonlinear conjugate gradient method,the result of the trial proved the modified L-curve criterion fast and stable,the minimum support stabilizing factor has good focusing and can identify the inversion of the abrupt change boundary.