摘要
电磁场解析方法是用于研究电磁勘探仪器快速正\反演的重要方法,其中均匀介质精确解的代数表达式具有函数关系清晰,计算结果高效稳定等特点,被大量用于勘探方法原理分析、仪器结构设计及响应特征分析等研究;也常作为层状介质与复杂三维介质模型的背景场,用于加速数值计算速度、提高数值结果精度以及提升计算方法的稳定性.本文针对磁导率、电导率和介电常数全参数单轴各向异性均匀介质,从麦克斯韦方程组出发,首先引入矢量势和标量势,推导得到笛卡尔坐标系矢量势分量偏微分方程组;其次根据矢量势分量耦合关系分别求出对应偏微分方程的标量Green函数精确解,进而利用矢量势和标量势与电磁场表达关系,明确给出由三轴磁/电偶极子源激发的全张量电磁场精确解的代数表达式.此外,本文针对电磁波测井问题的垂直井和水平井模型分别给出其仪器响应的简化表达式.最后,通过与有限元数值方法模拟结果对比,验证了本文给出的电磁场精确解代数表达式的正确性.数值结果显示,受电导率各向异性影响,磁场主分量Hxx和Hyy不相等,交叉分量Hzx和Hxz相等且不为零;受磁导率各向异性影响,交叉分量Hzx和Hxz不再相等.
The analytical method of Electromagnetic(EM)field is an important method to study the rapid forward and inverse modeling of EM exploration instruments.The algebraic expression for exact solutions in homogeneous medium has the characteristics of clear functional relationship,high efficiency and stability of calculation results,and is widely used in the research of exploration method principle analysis,instrument structure design and response characteristic analysis.It is also used as the background field of layered media and complex three-dimensional(3D)media models to accelerate the speed of numerical calculation,improve the accuracy of numerical results and improve the stability of calculation methods.In this paper,based on Maxwell equations,vector potential and scalar potential are introduced to obtain the Partial Differential Equations(PDEs)of vector potential components in Cartesian coordinate system.Secondly,the exact solutions of the scalar Green function of the corresponding PDE are obtained according to the coupling relation of the vector potential components,and then the algebraic expressions of the exact solution of the full tensor EM fields excited by the triaxial magnetic/electric dipole source are given by using the expression relation between the vector potential and the scalar potential of the EM field.In addition,the simplified expressions of instrument response for the vertical and horizontal well models of EM wave logging problems are given.Finally,the correctness of the algebraic expressions for the exact solution of EM fields are verified by comparing with the numerical simulation results of Finite Element Method(FEM).Numerical results demonstrate that,influenced by conductivity anisotropy,the primary magnetic field components Hxx and Hyy are unequal,whereas the cross-components Hzx and Hxz are equivalent yet non-zero.Furthermore,under the additional influence of permeability anisotropy,the equality between the cross-components Hzx and Hxz is no longer maintained.
作者
武圣哲
赵凯
洪德成
WU ShengZhe;ZHAO Kai;HONG DeCheng(Key Laboratory of Material Simulation Methods and Software,Ministry of Education,College of Physics,Jilin University,Changchun 130012,China)
出处
《地球物理学报》
北大核心
2025年第9期3634-3650,共17页
Chinese Journal of Geophysics
基金
国家自然基金项目(42474164,41874132)
吉林省自然基金项目(20230101101JC)资助.
关键词
全参数各向异性
均匀介质
偶极子源
解析解
并矢格林函数
Full parameter anisotropy
Homogeneous medium
Dipole source
Analytical solution
Dyadic Green′s function
