本文選題：可控源電磁法 + 電導率各向異性�。� 參考：《中國科學技術大學》2017年博士論文

【摘要】：地球介質電導率各向異性是客觀存在的,并且隨著可控源電磁法高精度儀器裝備的發(fā)展以及資料處理精細化的要求,忽略電導率各向異性影響對可控源電磁數(shù)據(jù)的解釋可能會帶來較大的偏差,甚至會得到錯誤的地下地質體信息。正演是反演和資料解釋的基礎,而現(xiàn)有的頻率域電磁法正演計算大多基于電導率各向同性介質理論,不能模擬地球介質電導率各向異性的實際情況。本文在前人研究的基礎上,以電導率各向異性模型為前提,系統(tǒng)地開展既適用于地面可控源音頻大地電磁測深法又可以應用于海洋可控源電磁測深法的一維正演計算、2.5維有限元數(shù)值模擬計算和三維矢量有限元數(shù)值模擬計算方法研宄,并對不同電導率各向異性的理論地電模型進行計算,分析電導率各向異性對可控源電磁法電磁響應的影響。首先,實現(xiàn)了電導率垂直各向異性水平地層頻率域電偶源CSEM全空間電磁響應計算方法。從麥克斯韋方程組出發(fā),引入磁矢量位和標量位,獲得電導率垂直各向異性水平地層頻率域電偶源CSEM磁矢量位邊值問題;利用傅里葉變換將空間域中的磁矢量位轉換到波數(shù)域中,利用邊界條件層層遞推獲得每一層的波數(shù)域電磁場值,再經(jīng)過傅里葉逆變換獲得空間域中任意位置的電磁場值,為基于二次場CSEM三維有限元數(shù)值模擬算法過程中所需任意空間位置一次電磁場值提供計算工具;最后分析了覆蓋層、中間層電導率各向異性對可控源電磁數(shù)據(jù)的影響。然后,考慮起伏地形的影響,研究了電導率正交各向異性2.5維CSEM等參有限元數(shù)值模擬方法。利用傅里葉變換導出了電導率正交各向異性2.5維CSEM波數(shù)域電磁場耦合方程,采用伽里金加權余量法推導了相應的有限元方程;采用任意四邊形單元對研究區(qū)域進行網(wǎng)格剖分,并在單元中進行雙二次插值,將有限元方程轉換為線性代數(shù)方程組;求解線性方程組并進行反傅里葉變換獲得空間域電磁場值;最后,分析不同各向異性系數(shù)對MCSEM電磁響應的影響,分析電導率各向異性對起伏地形條件下MCSEM電磁數(shù)據(jù)的影響。其次,考慮到實際介質電導率連續(xù)變化的情況,實現(xiàn)了基于二次場電導率分塊連續(xù)變化的三維CSEM節(jié)點有限元數(shù)值模擬方法。從電偶源三維地電斷面可控源電磁法二次電場邊值問題出發(fā),引入廣義變分原理推導了電偶源三維CSEM二次電場邊值問題的變分問題,采用任意六面體單元對研究區(qū)域進行剖分,并且在單元分析中同時對電導率及二次電場進行三線性插值,實現(xiàn)電導率分塊連續(xù)變化情況下,基于二次場的可控源電磁三維有限元數(shù)值模擬。通過對比本文計算結果與層狀模型解析解結果檢驗了算法的有效性,其三維異常體組合模型以及傾斜異常體等復雜模型的有限元計算結果有效地反映了異常形態(tài)。最后,實現(xiàn)了電導率任意各向異性CSEM三維矢量有限元數(shù)值模擬方法。從電導率各向異性三維介質電性源CSEM二次電場的邊值問題以及相應的變分問題出發(fā),采用長方體單元對研究區(qū)域剖分,將場分量定義在剖分單元的邊上,利用矢量有限單元法求解變分問題,實現(xiàn)了電導率任意各向異性可控源電磁三維矢量有限元數(shù)值模擬。一維電導率各向異性模型電磁場數(shù)值解與解析解吻合得相當好,無論在源附近還是遠離源處相對誤差均不超過1%;電導率各向異性二維模型的計算結果與已有文獻采用的非結構有限元模擬結果十分吻合;三維地電模型數(shù)值模擬結果顯示,電導率各向異性張量電導率主軸分量和歐拉角對不同裝置海洋可控源電磁響應均有著明顯的影響。
[Abstract]:The anisotropy of earth dielectric conductivity is objective, and with the development of high precision instrument and equipment of controllable source electromagnetic method and the requirement of fine data processing, neglecting the influence of conductivity anisotropy may bring great deviation to the interpretation of controllable source electromagnetic data, and will get the wrong underground geological information. It is the basis of inversion and data interpretation, and the existing frequency domain forward electromagnetic method is mostly based on the conductivity isotropic medium theory, and can not simulate the actual situation of the anisotropy of the conductivity of the earth medium. Based on the previous research, this paper applies the conductivity anisotropy model as the premise, which is applied to the ground controllable source. The audio magnetotelluric sounding method can be applied to one dimensional forward calculation, 2.5 dimensional finite element numerical simulation and three-dimensional vector finite element numerical simulation, and the theoretical geoelectric model of different conductivity anisotropy is calculated, and the anisotropy of electrical conductivity to controllable source electromagnetic field is analyzed. First, the method of calculating the full space electromagnetic response of CSEM in the vertical anisotropy horizontal stratigraphic frequency domain is realized. From the Maxwell equation, the magnetic vector potential and the scalar position are introduced to obtain the boundary value of the CSEM magnetic vector potential in the vertical anisotropy horizontal stratigraphic frequency domain. The magnetic vector bits in the space domain are converted into the wave number domain by the Fourier transform, and the electromagnetic field values of each layer are obtained by the boundary condition. Then the electromagnetic field value of any position in the space domain is obtained by inverse Fourier transform, which is the position of any space required in the algorithm process based on the two field CSEM three-dimensional finite element value simulation. The secondary electromagnetic field value provides a computing tool. Finally, the influence of the covering layer and the conductivity anisotropy of the middle layer on the controllable source electromagnetic data is analyzed. Then, considering the influence of the undulating topography, the orthogonal anisotropic 2.5 dimension CSEM isoparametric finite element numerical simulation method is studied. The conductivity orthogonal anisotropy 2.5 is derived by Fourier transform. The coupling equation of electromagnetic field in CSEM wavenumber domain is derived, and the corresponding finite element equation is derived by the galilkin weighted residual method. The finite element equation is interpolated in the element with arbitrary quadrilateral element, and the finite element equation is converted into a linear algebraic equation, and the linear equations are solved and the inverse Fourier transform is carried out. The electromagnetic field value of the space domain is obtained. Finally, the influence of the different anisotropy coefficient on the MCSEM electromagnetic response is analyzed, and the influence of the conductivity anisotropy on the MCSEM electromagnetic data under the undulating terrain condition is analyzed. Secondly, the continuous change of the conductivity of the actual medium is taken into account, and the three dimensional CSEM node based on the continuous change of the two field conductivity block is realized. Starting from the two electric field boundary value problem of the three dimensional controlled source electromagnetic method of the electric couple source, the generalized variational principle is introduced to deduce the variational problem of the boundary value problem of the three dimensional CSEM two electric field of the galvanic source, which is divided by any hexahedral element to the study area and the electrical conductivity is simultaneously carried out in the element analysis. With the three linear interpolation of the two electric field, the three-dimensional finite element numerical simulation of the controllable source based on the two order field is realized under the continuous change of the conductivity block. The validity of the algorithm is tested by comparing the results of this paper with the analytic solution of the layered model, and the complex model of the three-dimensional anomalous body and the inclined abnormal body. The results of the finite element calculation effectively reflect the abnormal shape. Finally, a three-dimensional vector finite element numerical simulation method for the conductivity of an arbitrary anisotropic CSEM is realized. From the boundary value problem of the two electric field of the electrical conductivity of the anisotropic three-dimensional dielectric source CSEM and the corresponding variational problem, the field division is used for the study of the field. The component is defined on the edge of the division unit and the vector finite element method is used to solve the variational problem. The three-dimensional vector finite element numerical simulation of the electrical conductivity arbitrary anisotropic controllable source is realized. The numerical solution of the electromagnetic field in the one-dimensional conductivity anisotropic model is in good agreement with the analytical solution, and the relative error near the source or away from the source is in good agreement. It is not more than 1%, and the calculation results of the anisotropic two-dimensional conductivity model are in good agreement with the unstructured finite element simulation results used in the literature. The three-dimensional electrical model numerical simulation results show that the principal component of the conductivity and the Euler angle of the conductivity anisotropy tensor have obvious influence on the electromagnetic response of different marine controllable sources.

【學位授予單位】：中國科學技術大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：P631.325

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本文編號：1888968