大地电磁反演中改进的自适应正则化因子选取研究

An improved adaptive regularized parameter selection method in MT inversion

摘要:

正则化方法目前已广泛应用于地球物理反演研究中，以改善反问题的不适定性。正则化因子的选取对于正则化反演至关重要，然而目前多数研究往往只选择单一方式如定值的正则化因子，对如何合理选取正则化因子研究不充分。本文通过建立大地电磁(MT)层状地电模型，在OCCAM反演的框架下利用共轭梯度法求解反问题，在给定不同初始模型的条件下对多种正则化因子选取方法进行了计算比较，并以此为基础深入分析了各种方法的特点和使用条件。结果表明，自适应正则化算法的效果可与传统的定值方法如L曲线法，并且在反演中具有传统方法无法比拟的便捷。为了解决反演依赖于初始模型的局限并增强解的稳定性，基于多种自适应正则化方案的对比分析，提出了改进的自适应正则化方案，选取数据拟合泛函与模型稳定泛函较大的比值为正则化因子的初始值，并提出相应的调整方案自动控制正则化因子衰减。模型试验表明该方法对初始模型的依赖性大大低于其他几种自适应的算法，反演结果的稳定性较强并可以进一步提高正则化反演的效率。

Abstract:

The regularized methods are widely used in geophysical inversion to improve the ill-posedness of inverse problem. The selection of the regularization parameter is very important to the results of regularized inversion, most of the recent researches usually concern about a single way such as a fixed value of regularization parameter. The research on how to choose the optimal regularization parameter is uncertain. In this paper, by establishing layered magnetotelluric (MT) models, the conjugate gradient method is used in Occam’s inversion, we compare the inversion results of many ways to select the optimal regularization parameter with different initial model in order to analysis the characteristic and some conditions of each methods. The results show that the adaptive regularization algorithm can get a similar inversion result compared with some traditional ways such as L-curve method, and it’s faster and easier to use. Moreover, with the purpose to reduce the limit of inversion depending on the initial model and improve the stability of inversion, we put forward an improved adaptive regularization method which selects a large ratio of the misfit functional and stabilizing functional as the initial value of regularization parameter, takes an automatic decay coefficient scheme to reduce the regularization parameter when misfit functional decline slowly. Model test shows that the method is much lower depended on initial model than other adaptive algorithms, the inversion result is stable and it can be further improved the efficiency of regularization inversion.