基于模糊C均值聚类的二维直流电阻率与射频大地电磁联合反演

Joint Inversion of Two-Dimensional Direct Current Resistivity and Radio- Magnetotelluric Data Based on Fuzzy C-Means Clustering Model Constraint

摘要:

为结合直流电阻率（direct current resistivity， DCR）与射频大地电磁（radio-magnetotelluric， RMT）法反演优势，开展了二维DCR与RMT数据联合反演研究。在经典最小结构模型正则化的基础上，采用平衡算子调节两个数据间的权重，引入模糊C均值（fuzzy C-means， FCM）聚类对电阻率模型进行约束，根据数据均方根误差自动调整FCM聚类项的权重，提高了联合反演效果。通过单独反演与联合反演结果的对比，分析了两种方法的反演能力，总结了联合反演的优势。模型试算表明，DCR与RMT数据联合反演得到的电阻率模型较单独反演更接近实际模型，FCM聚类约束的应用可进一步提高联合反演的效果。

Abstract:

In combination with the advantages of the direct current resistivity （DCR） and radio-magnetotelluric （RMT） methods， a joint inversion of two-dimensional DCR and RMT data was performed in this paper. A balancing operator was proposed to adjust the weightings of the two types of data in the joint inversion. To obtain a reliable inverted resistivity model， a fuzzy C-means （FCM） clustering was added to the regularization objective function based on classical minimum structure constraint. In the inversion， a strategy of increasing the weight of the FCM part with the inversion iteration based on root-mean-square error calculation was applied. The single inversion and joint inversion of the DCR and RMT data were compared， and the advantage of joint inversion was summarized. The synthetic tests show that the recovered resistivity model with joint inversion is closer to the true subsurface structure than that with single inversion. Moreover， the FCM clustering constraint improves the accuracy of the inverted model.