基于復(fù)雜結(jié)構(gòu)雙二次插值的有限元大地電磁二維正反演研究
發(fā)布時間：2019-01-13 08:09
【摘要】：大地電磁測深法(MT)是基于巖礦石電性差異,利用天然交變電磁場研究地球電性結(jié)構(gòu)的有效方法。針對此方法開展的正反演數(shù)值模擬問題,國內(nèi)外學(xué)者已經(jīng)提出多種方法并取得較好效果。本文結(jié)合當(dāng)前MT二維正反演問題存在的一些問題,并在正反演過程中同時考慮電阻率和磁導(dǎo)率異常影響,開展了基于二次場算法的MT數(shù)值模擬的算法探討。本文從麥克斯韋方程組出發(fā),導(dǎo)出了同時考慮電阻率與磁導(dǎo)率異常的大地電磁法二次場方程;為了提高計算精度與效率、簡化計算節(jié)點生成,采用了格林定理處理二次場方程源項,并利用二次場算法進行了模型試算,采用了基于二叉樹結(jié)構(gòu)的三角單元剖分的有限單元法,推導(dǎo)出了雙線性與雙二次插值的單元剛度矩陣表達式;分別對電阻率異常及磁導(dǎo)率異常模型進行了試算。數(shù)值計算結(jié)果表明,二次場算法無需對場源區(qū)域剖分,可有效的減小計算區(qū)間,提高了計算效率;與總場算法相比二次場算法邊界處理簡單;二次場算法有利用提高計算精度,解決了低頻計算不穩(wěn)定問題;試算表明,較小的磁導(dǎo)率變化就可對可控源視電阻率產(chǎn)生明顯影響,使電阻率增大。本文基于Tikhonov提出的正則化反演理論,針對目標(biāo)函數(shù)的最優(yōu)化求解及正則化因子的確定問題,分析了幾種常用的的最優(yōu)化方法,并選取擬牛頓法作為目標(biāo)函數(shù)進行最優(yōu)化求解;其次,采用修正的“L-Curve”方法求解正則化因子,改善了正則化因子的選取精度,提高了反演精度和速率,并在算例中得到了驗證。
[Abstract]:Magnetotelluric sounding (MT) is an effective method to study the electrical structure of the earth by using natural alternating electromagnetic field based on the difference of electrical properties of rock and ore. For the forward inversion numerical simulation problem developed by this method, many methods have been proposed by domestic and foreign scholars and good results have been obtained. In this paper, considering some problems existing in MT 2-D forward and inverse modeling, and considering the influence of resistivity and permeability anomalies in the process of forward and inverse modeling, the algorithm of MT numerical simulation based on quadratic field algorithm is discussed in this paper. Based on Maxwell's equations, a magnetotelluric quadratic field equation considering both resistivity and permeability anomalies is derived. In order to improve the accuracy and efficiency of calculation and simplify the generation of calculation nodes, Green's theorem is used to deal with the source term of quadratic field equation, and the model trial calculation is carried out by using quadratic field algorithm. The element stiffness matrix expressions of bilinear and bi-quadratic interpolation are derived by using the finite element method of triangulation based on binary tree structure. The models of resistivity anomaly and permeability anomaly are calculated respectively. The numerical results show that the quadratic field algorithm can effectively reduce the calculation interval and improve the computational efficiency without dividing the field source region, and the boundary processing of the quadratic field algorithm is simpler than that of the total field algorithm. The quadratic field algorithm can improve the accuracy of calculation and solve the unstable problem of low frequency calculation. It is shown from the trial calculation that the apparent resistivity of controllable source can be obviously affected by the change of magnetic permeability and the resistivity increases. In this paper, based on the regularization inversion theory proposed by Tikhonov, aiming at the optimization of objective function and the determination of regularization factor, several common optimization methods are analyzed, and the quasi Newton method is selected as the objective function to solve the optimization problem. Secondly, the modified "L-Curve" method is used to solve the regularization factor, which improves the accuracy of the regularization factor selection, improves the inversion accuracy and rate, and is verified by an example.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：P631.325
[Abstract]:Magnetotelluric sounding (MT) is an effective method to study the electrical structure of the earth by using natural alternating electromagnetic field based on the difference of electrical properties of rock and ore. For the forward inversion numerical simulation problem developed by this method, many methods have been proposed by domestic and foreign scholars and good results have been obtained. In this paper, considering some problems existing in MT 2-D forward and inverse modeling, and considering the influence of resistivity and permeability anomalies in the process of forward and inverse modeling, the algorithm of MT numerical simulation based on quadratic field algorithm is discussed in this paper. Based on Maxwell's equations, a magnetotelluric quadratic field equation considering both resistivity and permeability anomalies is derived. In order to improve the accuracy and efficiency of calculation and simplify the generation of calculation nodes, Green's theorem is used to deal with the source term of quadratic field equation, and the model trial calculation is carried out by using quadratic field algorithm. The element stiffness matrix expressions of bilinear and bi-quadratic interpolation are derived by using the finite element method of triangulation based on binary tree structure. The models of resistivity anomaly and permeability anomaly are calculated respectively. The numerical results show that the quadratic field algorithm can effectively reduce the calculation interval and improve the computational efficiency without dividing the field source region, and the boundary processing of the quadratic field algorithm is simpler than that of the total field algorithm. The quadratic field algorithm can improve the accuracy of calculation and solve the unstable problem of low frequency calculation. It is shown from the trial calculation that the apparent resistivity of controllable source can be obviously affected by the change of magnetic permeability and the resistivity increases. In this paper, based on the regularization inversion theory proposed by Tikhonov, aiming at the optimization of objective function and the determination of regularization factor, several common optimization methods are analyzed, and the quasi Newton method is selected as the objective function to solve the optimization problem. Secondly, the modified "L-Curve" method is used to solve the regularization factor, which improves the accuracy of the regularization factor selection, improves the inversion accuracy and rate, and is verified by an example.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：P631.325
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