本文選題：大地電磁 + 二維數(shù)值模擬�。� 參考：《成都理工大學(xué)》2015年碩士論文

【摘要】：大地電磁測深法(MT)屬于電磁法勘探中的頻率域方法,利用天然交變場源對地球深部巖石的電性參數(shù)進(jìn)行研究。大地電磁法已廣泛應(yīng)用于油氣勘探、海洋及地球深部等探測,現(xiàn)已成為深部地球物理探測的一種重要方法和必不可少的手段。開展大地電磁測深工作時(shí),往往并不是在平坦的地表處,而是在山區(qū)復(fù)雜地形條件下進(jìn)行。復(fù)雜地形條件對野外實(shí)測數(shù)據(jù)影響非常大,給資料的處理和解釋帶來了很大困難。因此,對帶地形的大地電磁數(shù)據(jù)進(jìn)行數(shù)值模擬是非常必要的。在復(fù)雜的地形條件下提高資料處理精度和解釋準(zhǔn)確性仍是當(dāng)今的難點(diǎn)問題之一,實(shí)現(xiàn)帶地形的二維大地電磁正演是提高資料處理解釋水平的重要途徑,受到工作者們和研究者們的重視。因此,研究在起伏地形條件下的大地電磁數(shù)值模擬是一個(gè)很有意義的課題。目前,大地電磁法的二維正演問題已基本解決,在使用有限單元法,有限差分法和積分方程法等數(shù)值模擬方法解決二維大地電磁正演問題方面有廣泛的研究結(jié)果;但在網(wǎng)格剖分方式、電性參數(shù)設(shè)定、輔助場定義和起伏地形模擬等方面,仍有改進(jìn)之處。本文研究的就是起伏地形條件下大地電磁的數(shù)值模擬方法,并將有限單元法用于起伏地形條件下二維大地電磁場的正演計(jì)算。首先,由麥克斯韋方程組(Maxwell Equations)得出大地電磁場的基本方程亥姆霍茲方程(Helmholtz Equation)的有限元格式和大地電磁場所應(yīng)該滿足的邊界條件。然后,以電磁場所滿足的微分方程、邊界條件和變分問題為出發(fā)點(diǎn),推導(dǎo)出起伏地形下二維MT正演的有限元算法。在有限單元法網(wǎng)格剖分方式上,采用矩形網(wǎng)格內(nèi)剖分三角形網(wǎng)格的方案,這種剖分方式便于對起伏地形的模擬,以適應(yīng)各種水平或起伏地形情況�？紤]到實(shí)際地層中的巖石,礦物體等在水平方向和垂直方向上電性參數(shù)是連續(xù)變化的,而在一些反演方法中,反演結(jié)果的電性參數(shù)也是連續(xù)變化,故將網(wǎng)格單元內(nèi)的電性參數(shù)設(shè)定為線性變化。根據(jù)單元節(jié)點(diǎn)主場值和線性插值形函數(shù)間的關(guān)系,計(jì)算出單元節(jié)點(diǎn)輔助場值。在方程組的求解方面,采用變帶寬存儲解決含有大量零元素的大型稀疏矩陣的存儲和方程組的求解問題,以節(jié)約內(nèi)存使用量和提高計(jì)算速度。根據(jù)起伏地形情況下實(shí)測電磁場分量的特征,定義TE和TM兩種模式下的視電阻率和阻抗相位計(jì)算公式。根據(jù)以上原理和結(jié)論編制一套實(shí)用的大地電磁正演程序,并設(shè)計(jì)了均勻?qū)訝钅Ｐ汀⒕鶆虬肟臻g中含有電性異常體模型、有地表起伏的均勻半空間模型,以此驗(yàn)證程序的正確性。利用一維正演程序?qū)Ξ?dāng)下比較熱點(diǎn)的“低阻薄層效應(yīng)”進(jìn)行了簡單的分析,正演結(jié)果基本正確,總結(jié)出的規(guī)律與前人吻合;對于二維正演,通過對多種模型的驗(yàn)證,得出不同地電斷面的水平地形和起伏地形的正演模擬結(jié)果與前人模擬結(jié)果一致,模型參數(shù)基本吻合。結(jié)合兩種極化模式的視電阻率和相位信息的橫向和縱向分辨率特點(diǎn),對地下異常體的深度定位、規(guī)模大小和方位判定表現(xiàn)出良好的效果。非水平地形情況下的正演響應(yīng)結(jié)果也與正演模型基本符合,驗(yàn)證了本文方法的正確性和有效性。
[Abstract]:Magnetotelluric sounding (MT) is a frequency domain method in the exploration of electromagnetic method, using natural alternating field sources to study the electrical parameters of rock in the deep earth. Magnetotelluric method has been widely used in oil and gas exploration, ocean and earth deep exploration, and has now become an important method and indispensable means for deep earth physical exploration. When the magnetotelluric sounding work is carried out, it is often not at the flat surface, but in the complex terrain conditions of the mountain area. The complex terrain conditions have great influence on the field measured data, which brings great difficulties to the processing and interpretation of the data. Therefore, it is very necessary to simulate the magnetotelluric data with the terrain. It is still one of the difficult problems to improve the accuracy and interpretation accuracy of data processing under complex terrain conditions. The realization of two-dimensional magnetotelluric forward modeling with terrain is an important way to improve the level of data processing and interpretation, which is paid attention to by workers and researchers. Therefore, the magnetotelluric numerical simulation under the undulating terrain conditions is studied. At present, the two dimensional forward problem of magnetotelluric method has been basically solved. There are extensive research results in the use of finite element method, finite difference method and integral equation method to solve the two-dimensional magnetotelluric forward problems. However, the method of grid division, the setting of electrical parameters, the definition of auxiliary field and the definition of auxiliary field The numerical simulation method of magnetotelluric in undulating terrain is studied in this paper, and the finite element method is applied to the forward calculation of the two-dimensional magnetotelluric field under the undulating terrain conditions. First, the basic equation of the magnetotelluric field is obtained by the Maxwell equation group (Maxwell Equations). The finite element format of the Helmholtz Equation equation and the boundary condition that the magnetotelluric place should satisfy. Then, based on the differential equations, boundary conditions and variational problems which are satisfied by the electromagnetic field, the finite element algorithm for the two-dimensional MT forward modeling under the undulating terrain is derived. A scheme of triangulating triangular meshes, which facilitates the simulation of undulating terrain to adapt to a variety of horizontally or undulating topographic conditions. Considering the continuous variation of the electrical parameters in the horizontal and vertical directions, the rock in the actual stratum and the mineral body are continuously changed, and the electrical parameters of the inversion results are also in some inversion methods. It is a continuous change, so the electrical parameters in the grid unit are set as linear changes. According to the relationship between the home value of the node and the linear interpolation function, the auxiliary field values of the unit nodes are calculated. In the solution of the equations, the storage of large sparse matrices with a large number of zero elements and the solution of the equations are solved by the variable bandwidth storage. In order to save the amount of memory use and improve the speed of calculation, according to the characteristics of the measured electromagnetic field components in the fluctuating terrain, the formulas of the apparent resistivity and impedance phase in the two modes of TE and TM are defined. A set of practical magnetotelluric forward sequence is developed based on the above principles and conclusions, and a homogeneous layered model is designed, and the uniform half space is designed. There is an electrical anomaly body model and a uniform half space model with surface undulation to verify the correctness of the program. By using one dimensional forward program, the "low resistance thin layer effect" is simply analyzed. The forward results are basically correct and the rules are in agreement with the predecessors. The simulation results of horizontal and undulating terrain of different geoelectric sections are consistent with the previous simulation results, and the model parameters are basically consistent. Combining the transverse and longitudinal resolution characteristics of the apparent resistivity and phase information of the two polarization modes, the depth location, size and azimuth of the underground anomaly body are determined. Good results. The forward response results of non horizontal terrain are also consistent with the forward modeling, which verifies the correctness and effectiveness of the method.
【學(xué)位授予單位】：成都理工大學(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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本文編號：1963353