电导率各向异性频率域可控源电磁法有限元数值模拟

发布时间：2018-05-14 18:19

本文选题：可控源电磁法 + 电导率各向异性　；参考：《中国科学技术大学》2017年博士论文

【摘要】：地球介质电导率各向异性是客观存在的,并且随着可控源电磁法高精度仪器装备的发展以及资料处理精细化的要求,忽略电导率各向异性影响对可控源电磁数据的解释可能会带来较大的偏差,甚至会得到错误的地下地质体信息。正演是反演和资料解释的基础,而现有的频率域电磁法正演计算大多基于电导率各向同性介质理论,不能模拟地球介质电导率各向异性的实际情况。本文在前人研究的基础上,以电导率各向异性模型为前提,系统地开展既适用于地面可控源音频大地电磁测深法又可以应用于海洋可控源电磁测深法的一维正演计算、2.5维有限元数值模拟计算和三维矢量有限元数值模拟计算方法研宄,并对不同电导率各向异性的理论地电模型进行计算,分析电导率各向异性对可控源电磁法电磁响应的影响。首先,实现了电导率垂直各向异性水平地层频率域电偶源CSEM全空间电磁响应计算方法。从麦克斯韦方程组出发,引入磁矢量位和标量位,获得电导率垂直各向异性水平地层频率域电偶源CSEM磁矢量位边值问题;利用傅里叶变换将空间域中的磁矢量位转换到波数域中,利用边界条件层层递推获得每一层的波数域电磁场值,再经过傅里叶逆变换获得空间域中任意位置的电磁场值,为基于二次场CSEM三维有限元数值模拟算法过程中所需任意空间位置一次电磁场值提供计算工具;最后分析了覆盖层、中间层电导率各向异性对可控源电磁数据的影响。然后,考虑起伏地形的影响,研究了电导率正交各向异性2.5维CSEM等参有限元数值模拟方法。利用傅里叶变换导出了电导率正交各向异性2.5维CSEM波数域电磁场耦合方程,采用伽里金加权余量法推导了相应的有限元方程;采用任意四边形单元对研究区域进行网格剖分,并在单元中进行双二次插值,将有限元方程转换为线性代数方程组;求解线性方程组并进行反傅里叶变换获得空间域电磁场值;最后,分析不同各向异性系数对MCSEM电磁响应的影响,分析电导率各向异性对起伏地形条件下MCSEM电磁数据的影响。其次,考虑到实际介质电导率连续变化的情况,实现了基于二次场电导率分块连续变化的三维CSEM节点有限元数值模拟方法。从电偶源三维地电断面可控源电磁法二次电场边值问题出发,引入广义变分原理推导了电偶源三维CSEM二次电场边值问题的变分问题,采用任意六面体单元对研究区域进行剖分,并且在单元分析中同时对电导率及二次电场进行三线性插值,实现电导率分块连续变化情况下,基于二次场的可控源电磁三维有限元数值模拟。通过对比本文计算结果与层状模型解析解结果检验了算法的有效性,其三维异常体组合模型以及倾斜异常体等复杂模型的有限元计算结果有效地反映了异常形态。最后,实现了电导率任意各向异性CSEM三维矢量有限元数值模拟方法。从电导率各向异性三维介质电性源CSEM二次电场的边值问题以及相应的变分问题出发,采用长方体单元对研究区域剖分,将场分量定义在剖分单元的边上,利用矢量有限单元法求解变分问题,实现了电导率任意各向异性可控源电磁三维矢量有限元数值模拟。一维电导率各向异性模型电磁场数值解与解析解吻合得相当好,无论在源附近还是远离源处相对误差均不超过1%;电导率各向异性二维模型的计算结果与已有文献采用的非结构有限元模拟结果十分吻合;三维地电模型数值模拟结果显示,电导率各向异性张量电导率主轴分量和欧拉角对不同装置海洋可控源电磁响应均有着明显的影响。
[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.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：P631.325

【参考文献】