大地电磁双二次插值FEM正演及最小二乘正则化联合反演

冯德山^{1, 2}，王 珣^{1, 2}

(1. 中南大学 地球科学与信息物理学院, 长沙 410083；
2. 中南大学 有色金属成矿预测教育部重点实验室，长沙 410083)

摘 要：从大地电磁(MT) 二维正演所满足的偏微分方程边值问题出发，应用矩形网格剖分和单元内双二次插值推导有限单元法求解大地电磁TE与TM两种极化模式正问题详细算法。应用反演理论将病态问题求解的正则化方法应用到最小二乘优化方法中，获得最光滑约束最小二乘正则化反演目标函数，并利用Matlab编制了大地电磁二维正反演计算程序。应用该程序对高低阻地电模型和Sasaki模型开展了正反演计算，并绘制TE模式和TM模式、TE&TM联合反演模式的反演成果剖面图。将所得的反演剖面与初始模型对比可知，TE模式反演剖面纵向分辨率较高，TM模式横向分辨率较高，TE&TM联合反演优于单一极化模式的反演，并证明双二次插值有限元法MT正演及最小二乘正则化反演算法的有效性与可行性。

关键词：大地电磁；有限单元法；正演模拟；最小二乘正则化；联合反演

Magnetotelluric finite element method forward based on biquadratic interpolation and least squares regularization joint inversion

FENG De-shan^{1, 2}, WANG Xun^{1, 2}

(1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education,
Central South University, Changsha 410083, China)

Abstract:Based on the boundary value problem of partial differential equation of the two-dimensional magnetotelluric (MT) forward modeling meet, the detail algorithm of finite element method deduced by the rectangular grid subdivision and cell biquadratic interpolation method were used to solve the electromagnetic problems both in TE and TM polarization mode. By using the basic theory of inversion, the solving ill-posed problem regularization method was applied to the least-square optimization approach, and the most smoothness constrained least square regularization inversion objective function was gotten, then a completed two-dimensional magnetotelluric forward computational program was written by Matlab. This program was applied on high/low resistance geoelectric model and Sasaki model, the inversion cross-sectional profiles of TE mode, TM mode and TE&TM joint inversion model separately were plotted. Compared the inversion results with the original models, TE mode inversion profile has higher vertical resolution, TM mode has higher lateral resolution, TE&TM joint inversion is superior to the single inversion of polarization mode. At the same time, MT biquadratic interpolation finite element forward modeling and least-square regularization inversion algorithm are proved to be effective and feasible.

Key words:magnetotelluric; finite element method; forward simulation; least-squares regularization joint; joint inversion