本文選題：可控源音頻大地電磁法 + 交錯(cuò)網(wǎng)格有限差分法��； 參考：《東華理工大學(xué)》2015年碩士論文

【摘要】：可控源音頻大地電磁法(CSAMT)是地球物理勘探的重要手段之一,在礦產(chǎn)資源勘查和地質(zhì)調(diào)查等多個(gè)領(lǐng)域得到了廣泛的應(yīng)用。由于傳統(tǒng)的CSAMT一維和二維反演方法難以真實(shí)地反映復(fù)雜變化的介質(zhì)結(jié)構(gòu),CSAMT三維反演技術(shù)的實(shí)用化問題迫在眉睫,而尋求一種高效、穩(wěn)定的正演計(jì)算方法是推進(jìn)CSAMT三維反演實(shí)用化進(jìn)程的關(guān)鍵因素之一。因此本文開展基于聚集代數(shù)多重網(wǎng)格法的CSAMT三維數(shù)值模擬研究。本文從CSAMT滿足的麥克斯韋方程出發(fā),將總場(chǎng)分解為一次場(chǎng)和二次場(chǎng),利用電磁場(chǎng)邊界條件和傅里葉變換推導(dǎo)有限長(zhǎng)電偶源激發(fā)的電磁場(chǎng)公式,并通過快速漢克爾變換實(shí)現(xiàn)快速計(jì)算。然后利用三維交錯(cuò)采樣有限差分法推導(dǎo)出二次場(chǎng)中電、磁場(chǎng)分量滿足的關(guān)系式,并通過變換消去磁場(chǎng)分量,將CSAMT三維數(shù)值模擬的二次場(chǎng)計(jì)算問題轉(zhuǎn)換成僅關(guān)于電場(chǎng)分量的大型線性方程組的求解問題。為提高CSAMT數(shù)值模擬中迭代求解的速度,引入具有高速收斂性的聚集代數(shù)多重網(wǎng)格法(AGMG),重點(diǎn)研究AGMG的聚集粗化策略及求解過程的算法實(shí)現(xiàn)。針對(duì)CSAMT三維有限差分模擬中線性方程組的大型稀疏特性,采用AGMG法作為廣義最小殘差法(GCR)預(yù)處理算子實(shí)現(xiàn)線性方程組求解,開發(fā)了CSAMT三維正演軟件。論文通過二維LAPLACE方程求解比較了算法的優(yōu)越性,表明聚集代數(shù)多重網(wǎng)格-廣義最小殘差法(AGMG-GCR)相比傳統(tǒng)的Krylov子空間迭代法(BCGSTAB,CG,BCG,GCR,DQGMRES,ILU-GCR)既有GCR算法的強(qiáng)穩(wěn)定性,也有線性快速衰減和隨網(wǎng)格剖分?jǐn)?shù)增加迭代次數(shù)基本保存不變的特征。通過水平層狀模型三維正演驗(yàn)證算法的正確性和穩(wěn)定性,并對(duì)典型地電模型(低阻模型、高阻模型和組合模型)進(jìn)行數(shù)值模擬,分析和總結(jié)其CSAMT三維響應(yīng)特征,為野外數(shù)據(jù)采集和資料解釋提供參考。
[Abstract]:Controlled source audio magnetotelluric (CSAMT) is one of the important means of geophysical exploration. It has been widely used in many fields, such as mineral resources exploration and geological investigation. Because the traditional CSAMT one and two dimensional inversion method is difficult to reflect the complex medium structure, the practical problem of CSAMT 3D inversion is forced to An efficient, stable forward calculation method is one of the key factors to promote the practical process of CSAMT 3D inversion. Therefore, this paper develops a three-dimensional numerical simulation of CSAMT based on the multigrid method of aggregation algebra. This paper, based on the Maxwell equation satisfied by CSAMT, decomposes the total field into one field and two fields. The electromagnetic field boundary condition and the Fu Liye transform are used to derive the electromagnetic field formula excited by a finite long couple source, and the Fast Hankel transform is used to calculate the electromagnetic field. Then the three dimensional staggered sampling finite difference method is used to deduce the relationship between the two fields and the magnetic field components, and the three-dimensional numerical simulation of CSAMT is simulated by changing the magnetic field components. The two field computation problem is converted to the solution of a large linear equation group with only an electric field component. In order to improve the speed of iterative solution in the CSAMT numerical simulation, a high speed convergent aggregation algebraic multigrid method (AGMG) is introduced, focusing on the aggregation and coarsening strategy of AGMG and the algorithm implementation of the solution process. The large sparse characteristic of the linear equation group in the finite difference simulation, the AGMG method is used as the generalized minimum residual method (GCR) to solve the linear equations, and the CSAMT 3D forward software is developed. The superiority of the algorithm is compared with the two-dimensional LAPLACE equation, and the multigrid generalized minimum residual method (AGMG-) of the aggregation algebra is shown. (AGMG- GCR) compared with the traditional Krylov subspace iterative method (BCGSTAB, CG, BCG, GCR, DQGMRES, ILU-GCR), it has both the strong stability of the GCR algorithm, the linear fast attenuation and the constant preservation of the number of iterations with the grid fraction. The low resistance model, the high resistance model and the combined model are used to carry out numerical simulation, analyze and summarize the three dimensional response characteristics of CSAMT, and provide reference for field data collection and data interpretation.

【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P631.325

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 陳書浩;代數(shù)多重網(wǎng)格法研究及其在預(yù)處理Krylov子空間方法中的應(yīng)用[D];浙江大學(xué);2008年

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本文編號(hào)：1804801