【摘要】：大地電磁正演領(lǐng)域,目前流行的數(shù)值計(jì)算方法包括有限差分法和有限元法,該類數(shù)值計(jì)算方法都是基于網(wǎng)格插值求解計(jì)算域物理場(chǎng),對(duì)復(fù)雜地電模型的網(wǎng)格剖分比較繁瑣,計(jì)算精度嚴(yán)重依賴于單元剖分的形狀和大小。為克服這些困難,無網(wǎng)格法作為有網(wǎng)格法的一種重要補(bǔ)充和發(fā)展具有重要的研究意義和實(shí)用價(jià)值。本文重點(diǎn)研究基于全局弱式無網(wǎng)格法的大地電磁二維正演問題。首先從大地電磁場(chǎng)二維問題所滿足的Maxwell方程組出發(fā),利用變分問題與邊值問題的等價(jià)性,對(duì)大地電磁二維問題滿足的微分方程進(jìn)行推導(dǎo)并得到其相應(yīng)的變分形式。利用一系列離散場(chǎng)節(jié)點(diǎn)對(duì)求解域進(jìn)行離散,采用移動(dòng)最小二乘法(MLS)構(gòu)造積分點(diǎn)支持域形函數(shù)。根據(jù)Galerkin法原理,推導(dǎo)出與大地電磁法二維邊值問題對(duì)應(yīng)的無網(wǎng)格全局弱式矩陣表達(dá)式。采用含背景網(wǎng)格的高斯積分將計(jì)算域離散化,求得最終總體矩陣的離散表達(dá)式。后續(xù)通過多個(gè)一維層狀模型數(shù)值模擬計(jì)算,研究了相關(guān)重要參數(shù),如高斯點(diǎn)數(shù)目,無量綱支持域尺寸等對(duì)計(jì)算精度及計(jì)算效率的影響,并確定其參數(shù)最優(yōu)值,選取高斯點(diǎn)數(shù)量為2~3、無量綱支持域尺寸a為1.1~1.3。確定最優(yōu)參數(shù)值后,分別用有限元法和全局弱式無網(wǎng)格法計(jì)算幾個(gè)典型一維模型和二維模型,通過對(duì)比計(jì)算結(jié)果及計(jì)算精度,驗(yàn)證本文中提出的全局弱式無網(wǎng)格法的有效性及在處理復(fù)雜模型上的優(yōu)越性。最后,根據(jù)冬瓜山銅礦實(shí)際情況設(shè)計(jì)了二維地質(zhì)模型,并用本文提出的全局弱式無網(wǎng)格法對(duì)其進(jìn)行數(shù)值模擬計(jì)算,其計(jì)算結(jié)果對(duì)低阻礦體實(shí)際形態(tài)反應(yīng)較好,進(jìn)一步證明了無網(wǎng)格算法在地球物理電磁波數(shù)值模擬中具有重要的意義。
[Abstract]:In the field of magnetotelluric forward modeling, the popular numerical methods include finite difference method and finite element method. These numerical methods are based on grid interpolation to solve the physical field in computational domain. The accuracy of calculation depends heavily on the shape and size of the unit. In order to overcome these difficulties, meshless method as an important supplement and development of grid method has important significance and practical value. This paper focuses on the magnetotelluric two-dimensional forward modeling based on the global weak meshless method. Starting from the Maxwell equations satisfied by the two-dimensional magnetotelluric problem and using the equivalence between the variational problem and the boundary value problem, the differential equations of the two-dimensional magnetotelluric problem are derived and the corresponding variational forms are obtained. A series of discrete field nodes are used to discretize the solution domain, and the moving least square method (MLS) is used to construct the integral points to support the domain shape function. According to the principle of Galerkin method, the meshless global weak matrix expression corresponding to the two-dimensional boundary value problem of magnetotelluric method is derived. The computation domain is discretized by Gao Si integral with background mesh, and the discrete expression of the final total matrix is obtained. Through numerical simulation of several one-dimensional layered models, the effects of some important parameters, such as Gao Si number and dimensionless support domain size, on the calculation accuracy and efficiency are studied, and the optimum values of the parameters are determined. The number of Gao Si points is 2 ~ 3 and the dimension of dimensionless support domain a is 1.1 ~ (1.3). After determining the optimal parameter value, the finite element method and the global weak meshless method are used to calculate several typical one-dimensional and two-dimensional models respectively. The effectiveness of the global weak meshless method proposed in this paper and its superiority in dealing with complex models are verified. Finally, according to the actual situation of Dongguashan Copper Mine, a two-dimensional geological model is designed, and the global weak meshless method proposed in this paper is used to numerically simulate the orebody. The calculated results have a good response to the actual shape of the low resistivity orebody. It is further proved that the meshless algorithm is of great significance in the numerical simulation of geophysical electromagnetic waves.
【學(xué)位授予單位】：長(zhǎng)安大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P631.325

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