本文選題：頻率域電磁法 + 三維正反演��； 參考：《吉林大學(xué)》2017年博士論文

【摘要】：地面頻率域電磁法方法種類(lèi)繁多,在深部地球結(jié)構(gòu)探測(cè)、地?zé)峥碧�、礦產(chǎn)勘查、油氣勘查及環(huán)境與工程勘探等各個(gè)領(lǐng)域起到關(guān)鍵作用。隨著電磁勘探技術(shù)的逐步發(fā)展以及“精細(xì)化”和“透明化”地質(zhì)勘探的需求,實(shí)施地面頻率域電磁法三維勘探與解釋逐步成為常態(tài)。因而,頻率域電磁法三維正反演成為大規(guī)模電磁數(shù)據(jù)精細(xì)化和定量解釋的關(guān)鍵,然而受到多場(chǎng)源、正演模擬速度和精度、三維反演的適用性以及計(jì)算效率等問(wèn)題的困擾,仍難于在實(shí)際勘探中獲得應(yīng)用。為此,本論文采用有限體積法求解Lorenz規(guī)范條件下耦合勢(shì)對(duì)稱(chēng)方程實(shí)現(xiàn)任意場(chǎng)源頻率域電磁法三維正演,并引入聚集多重網(wǎng)格求解技術(shù)實(shí)現(xiàn)大規(guī)模問(wèn)題的線(xiàn)性代數(shù)方程組高精度快速求解;同時(shí),提出一種“全局”優(yōu)化算法—截?cái)嗯ｎD法及多種經(jīng)典反演方法實(shí)現(xiàn)了地面頻率域電磁法三維反演,并以大地電磁為例探討該三維反演方法的適用性及其影響因素,期望以此建立地面頻率域電磁三維正反演平臺(tái),為提高地面電磁勘探的三維精細(xì)化解釋提供技術(shù)支撐。為了克服空氣層和地表耦合以及不同場(chǎng)源類(lèi)型、不同觀測(cè)數(shù)據(jù)的頻率域電磁法三維正演,本文首先從Maxwell方程出發(fā),推導(dǎo)基于Lorenz規(guī)范條件的磁矢勢(shì)和標(biāo)勢(shì)耦合對(duì)稱(chēng)方程,并采用有限體積技術(shù)對(duì)方程進(jìn)行離散,得到大型對(duì)稱(chēng)稀疏線(xiàn)性代數(shù)方程組;然后利用一系列短導(dǎo)線(xiàn)(電性)源組合模擬各種不同類(lèi)型場(chǎng)源,并采用預(yù)處理擬最小殘差法(QMR)以及PARDISO、MUMPS等求解庫(kù)進(jìn)行求解,成功實(shí)現(xiàn)不同場(chǎng)源類(lèi)型的地面頻率域電磁法三維正演模擬。通過(guò)層狀介質(zhì)模型不同場(chǎng)源類(lèi)型的三維正演模擬,并與一維解析解對(duì)比驗(yàn)證本文算法的準(zhǔn)確性和有效性;進(jìn)而,對(duì)典型地電模型在不同場(chǎng)源激發(fā)下頻率域電磁法響應(yīng)特征進(jìn)行對(duì)比分析。為了加快地面頻率域電磁三維正演的求解速度,將一種新型的代數(shù)多重網(wǎng)格算法—聚集多重網(wǎng)格算法(AGMG)引入到三維正演模擬中。本文從AGMG算法的粗化策略和套迭代技術(shù)出發(fā),將AGMG和傳統(tǒng)Krylov子空間(GCR、FCG)迭代算法進(jìn)行耦合,提出五種不同AGMG求解算法。以大地電磁法為例,通過(guò)對(duì)典型復(fù)雜地電模型進(jìn)行正演模擬,并與已有的大地電磁三維正反演程序(Mod EM)結(jié)果進(jìn)行對(duì)比,驗(yàn)證本文算法的準(zhǔn)確性。另外,將不同剖分網(wǎng)格和不同極化方式的正演模擬結(jié)果與QMR迭代算法進(jìn)行對(duì)比表明,K-AGMG-GCR算法不僅能夠改善AGMG算法的穩(wěn)定性,同時(shí)還具有收斂精度高、速度快、計(jì)算效率高等優(yōu)點(diǎn)。相對(duì)于現(xiàn)有Mod EM程序,K-AGMG-GCR算法能夠提高計(jì)算速度數(shù)十倍,因此特別適合大規(guī)模地面頻率域電磁三維正演問(wèn)題。針對(duì)地面頻率域電磁三維反演,本文引入一種全局優(yōu)化信賴(lài)域算法和牛頓法結(jié)合的截?cái)嗯ｎD法(TRN)。首先,從最優(yōu)化和正則化反演理論出發(fā),建立頻率域電磁法三維反演的目標(biāo)函數(shù)、模型協(xié)方差矩陣及數(shù)據(jù)協(xié)方差表達(dá)式;并詳細(xì)推導(dǎo)了不同類(lèi)型頻率域電磁法梯度、Hessian矩陣和Jacobi矩陣統(tǒng)一表達(dá)式;進(jìn)而詳細(xì)闡述了截?cái)嗯ｎD法的基本原理及關(guān)鍵技術(shù)(比如步長(zhǎng)全局搜索、自適應(yīng)截?cái)嗾`差算法以及正則化因子冷卻法等);同時(shí)介紹了經(jīng)典最優(yōu)化反演算法-最速下降法(STD)、非線(xiàn)性共軛梯度法(NLCG)、高斯牛頓-共軛梯度法(GNCG)和有限內(nèi)存擬牛頓法(L-BFGS)。最后,采用模塊化設(shè)計(jì)思想及利用消息傳遞接口(MPI)實(shí)現(xiàn)并行加速,實(shí)現(xiàn)了不同算法地面頻率域電磁法三維反演。本文以大地電磁三維反演為例,首先通過(guò)對(duì)比兩個(gè)理論模型(高低組合模型、“拱橋”低阻模型)不同反演算法的結(jié)果,表明本文實(shí)現(xiàn)的反演算法(TRN、STD、NLCG、L-BFGS和GNCG)均能取得良好效果,與國(guó)際著名的大地電磁開(kāi)源程序Mod EM效果相當(dāng);而本文所提出的TRN算法是一種收斂速度快、迭代次數(shù)少的全局優(yōu)化算法,其反演效果與GNCG算法相當(dāng),優(yōu)于梯度類(lèi)反演算法(STD、NLCG、L-BFGS),并且改善了GNCG計(jì)算效率及局部?jī)?yōu)化的缺點(diǎn)。然后,本文以低阻隱伏礦體模型為例,探討TRN反演算法的反演參數(shù)(正則化因子,初始截?cái)嗾`差、初始模型和網(wǎng)格剖分)以及觀測(cè)數(shù)據(jù)(噪聲水平、數(shù)據(jù)集、頻點(diǎn)數(shù)和測(cè)點(diǎn)數(shù))對(duì)反演結(jié)果的影響,表明TRN算法對(duì)初始模型依賴(lài)較小,同時(shí)具有較強(qiáng)的抗干擾能力。最后,將該算法應(yīng)用于內(nèi)蒙某地區(qū)的大地電磁實(shí)測(cè)數(shù)據(jù)處理中。通過(guò)與二維反演及地震解釋地質(zhì)剖面對(duì)比發(fā)現(xiàn),TRN三維反演結(jié)果能夠準(zhǔn)確反演基底起伏情況,同時(shí)能夠有效解決二維反演受三維異常體引起的畸變,進(jìn)一步驗(yàn)證了TRN算法的可靠性。
[Abstract]:There are many kinds of electromagnetic methods in the ground frequency domain. It plays a key role in various fields, such as deep earth structure exploration, geothermal exploration, mineral exploration, oil and gas exploration, environment and engineering exploration. With the gradual development of electromagnetic exploration technology and the demand of "fine" and "transparent" geological exploration, ground frequency domain electromagnetic method is implemented. Three dimensional exploration and interpretation have gradually become normal. Therefore, the three-dimensional positive and inverse performance of the frequency domain electromagnetic method has become the key to the refinement and quantitative interpretation of large-scale electromagnetic data. However, it is still difficult to be applied in practical exploration by many sources, the speed and precision of the forward modeling, the applicability of the three-dimensional inversion and the efficiency of calculation. In this paper, the finite volume method is used to solve the coupling potential symmetric equation under the Lorenz standard to realize the three-dimensional forward modeling of the electromagnetic method in the frequency domain of any field source, and a high precision and rapid solution for the linear algebraic equations of large-scale problems is realized by the aggregation multigrid solving technique. At the same time, a "global" optimization algorithm, truncated Newton method, is proposed. The three-dimensional inversion of ground frequency domain electromagnetic method is realized by a variety of classical inversion methods. The applicability and influence factors of the three dimensional inversion method are discussed with magnetotelluric as an example. It is expected to establish the ground frequency domain electromagnetic three-dimensional positive and inverse platform to provide technical support for improving the three-dimensional fine interpretation of ground electromagnetic exploration. In this paper, the magnetic vector potential and the coupled symmetric equation of the magnetic vector potential based on the Lorenz standard conditions are derived from the Maxwell equation, and the finite volume technique is used to discrete the equations, and the large symmetric sparse linear algebraic equations are obtained. Then a series of short wire (Electrical) sources are used to simulate various types of field sources, and the pre processed quasi minimum residual method (QMR) and PARDISO, MUMPS and other solutions are used to solve them. The three-dimensional forward simulation of the ground frequency domain of different source types is successfully realized. The accuracy and effectiveness of the proposed algorithm are compared with one dimensional analytical solution. Then, the characteristics of the electromagnetic response of the typical geoelectric model in the frequency domain under different source excitation are compared and analyzed. In order to speed up the solving speed of the three dimensional forward electromagnetic field in the ground frequency domain, a new algebraic multigrid algorithm - aggregated multigrid is put forward. The algorithm (AGMG) is introduced into the 3D forward modeling. This paper, starting from the roughing strategy of AGMG algorithm and the set of iterative techniques, combines AGMG and the traditional Krylov subspace (GCR, FCG) iterative algorithm to propose five different AGMG algorithms. The results of Mod EM are compared to verify the accuracy of the proposed algorithm. In addition, the comparison between the forward modeling results of different mesh and different polarization modes and the QMR iterative algorithm shows that the K-AGMG-GCR algorithm can not only improve the stability of the AGMG algorithm, but also have high convergence precision, fast speed, and calculation. Compared with the existing Mod EM program, the K-AGMG-GCR algorithm can improve the computing speed dozens of times, so it is especially suitable for the large-scale ground frequency domain electromagnetic three dimensional forward problem. In view of the ground frequency domain electromagnetic 3D inversion, this paper introduces a global optimization trust region algorithm and Newton method combined truncated Newton method (TRN). First, Starting from the optimization and regularization inversion theory, the objective function, the model covariance matrix and the data covariance expression of the three dimensional inversion of the frequency domain electromagnetic method are established, and the unified expressions of the electromagnetic gradient, Hessian matrix and Jacobi matrix in different frequency domains are derived in detail, and then the basic principle of the truncated Newton method is described in detail and the basic principles of the truncated Newton method are elaborated. Key technologies (such as global search for step size, adaptive truncation error algorithm and regularization factor cooling method), and the classical optimal inversion algorithms - STD, nonlinear conjugate gradient (NLCG), Gauss Newton conjugate gradient (GNCG) and finite memory quasi Newton (L-BFGS). Finally, the modular design idea is adopted. And using the message transfer interface (MPI) to achieve parallel acceleration, the three dimensional inversion of electromagnetic method in the ground frequency domain of different algorithms is realized. This paper, taking the three dimensional magnetotelluric inversion as an example, first compares the results of two theoretical models (high and low combination model, arch bridge "low resistance model), and shows the inverse algorithm (TRN, STD) realized in this paper. NLCG, L-BFGS and GNCG can achieve good results, which are equivalent to the famous international magnetotelluric open source program Mod EM, and the TRN algorithm proposed in this paper is a global optimization algorithm with fast convergence speed and less iterative times. The inversion effect is equivalent to the GNCG algorithm, which is superior to the gradient inversion algorithm (STD, NLCG, L-BFGS), and improves GNCG. In this paper, the effect of the inversion parameters (regularization factor, initial truncation error, initial model and grid subdivision) and the effect of observation data (noise level, data set, frequency number and number of points) on the inversion results of the TRN inversion algorithm are discussed in this paper. The results show that the TRN algorithm is insidious to the initial results. The model is less dependent and has strong anti-interference ability. Finally, the algorithm is applied to the magnetotelluric data processing in a certain area of Inner Mongolia. By comparing with two-dimensional inversion and seismic interpretation, it is found that the TRN three-dimensional inversion results can accurately inverse the condition of the base undulation, and can effectively solve the two-dimensional inversion by three. The distortion caused by the dimension abnormal body further verifies the reliability of the TRN algorithm.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：P631.325

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