(1. 中南大學(xué) 地球科學(xué)與信息物理學(xué)院, 長沙 410083；
2. 中南大學(xué) 有色金屬成礦預(yù)測教育部重點(diǎn)實(shí)驗(yàn)室，長沙 410083)
摘 要: 從大地電磁(MT) 二維正演所滿足的偏微分方程邊值問題出發(fā)，應(yīng)用矩形網(wǎng)格剖分和單元內(nèi)雙二次插值推導(dǎo)有限單元法求解大地電磁TE與TM兩種極化模式正問題詳細(xì)算法。應(yīng)用反演理論將病態(tài)問題求解的正則化方法應(yīng)用到最小二乘優(yōu)化方法中，獲得最光滑約束最小二乘正則化反演目標(biāo)函數(shù)，并利用Matlab編制了大地電磁二維正反演計(jì)算程序。應(yīng)用該程序?qū)Ω叩妥璧仉娔Ｐ秃蚐asaki模型開展了正反演計(jì)算，并繪制TE模式和TM模式、TE&TM聯(lián)合反演模式的反演成果剖面圖。將所得的反演剖面與初始模型對比可知，TE模式反演剖面縱向分辨率較高，TM模式橫向分辨率較高，TE&TM聯(lián)合反演優(yōu)于單一極化模式的反演，并證明雙二次插值有限元法MT正演及最小二乘正則化反演算法的有效性與可行性。
關(guān)鍵字: 大地電磁；有限單元法；正演模擬；最小二乘正則化；聯(lián)合反演
（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
