基于谱元法三维航空电磁电各向异性模拟及识别研究（英文）

发布时间：2018-04-11 12:01

本文选题：谱元法 + 各向异性　；参考：《Applied Geophysics》2017年03期

【摘要】：航空电磁法具有高采样率探测特征,传统数值模拟方法为保证航电响应计算精度,特别是针对复杂地质体(如电各向异性),需要对模拟域进行精细剖分,导致计算工作量庞大。因此本文采用谱元法对航空电磁各向异性响应进行三维正演模拟,该方法结合谱方法和有限元法双重优势,它与谱方法类似采样高阶基函数代替有限元中的线性插值,同时具有有限元拟合边界的灵活性。因此该方法能改善离散网格内部的数值模拟精度,减弱数值模拟结果对网格的依赖性,实现航空电磁各向异性响应的高精度计算。首先,本文将旋转张量的各向异性电导率引入Maxwell方程,并给出GLL谱元基函数给出电场表示形式,采用伽辽金加权余量法形成基于谱元法大型线性方程组获得电磁响应,以VMD发射源为例进行航空电磁响应模拟。其次,本文采用粗物理网格四阶谱元法对任意各向异性半空间的航空电磁响应进行计算,通过与一维半解析解对比验证了该算法的高精度性。再次,本文采用不同物理网格和谱元阶数讨论不同各向异性条件下三维异常体的航空电磁响应,得出了不同各向异性异常体的电磁响应的收敛条件。最后,本文首次基于谱元算法,采用Hr/Hz方式给出了三维各向异性异常体,各向异性围岩以及围岩和异常体同时存在各向异性时航空电磁各向异性的识别方式,这航空电磁各向异性的三维反演和各向异性地质区域测量具有指导意义。
[Abstract]:Airborne electromagnetic method (AEM) has the characteristics of high sampling rate detection. In order to ensure the accuracy of avionics response, the traditional numerical simulation method, especially for complex geological bodies (such as electrical anisotropy), needs to be subdivided into the simulation domain, which results in a huge amount of computational work.In this paper, spectral element method is used to simulate the anisotropic response of aeronautical electromagnetic field. This method combines the advantages of spectral method and finite element method. It is similar to the spectral method by sampling high order basis function instead of linear interpolation in finite element method.At the same time, it has the flexibility of finite element fitting boundary.Therefore, this method can improve the accuracy of numerical simulation in discrete meshes, reduce the dependence of numerical simulation results on the grid, and realize the high accuracy calculation of aeronautical electromagnetic anisotropic response.Firstly, the anisotropic conductivity of rotating Zhang Liang is introduced into the Maxwell equation, and the basic function of GLL spectral element is given to express the electric field. The Galerkin weighted residual method is used to form a large linear system of equations based on spectral element method to obtain the electromagnetic response.The VMD emitter is taken as an example to simulate the aero-electromagnetic response.Secondly, the fourth order spectral element method of rough physical grid is used to calculate the aero-electromagnetic response of any anisotropic half-space. The high accuracy of the algorithm is verified by comparison with the one-dimensional semi-analytical solution.Thirdly, the aero-electromagnetic responses of three-dimensional anomalous bodies under different anisotropic conditions are discussed by using different physical meshes and spectral element orders, and the convergence conditions of electromagnetic responses of different anisotropic anomalous bodies are obtained.Finally, based on the spectral element algorithm for the first time, Hr/Hz method is used to identify the three-dimensional anisotropic anomaly body, the anisotropic surrounding rock and the anisotropy of the surrounding rock and the abnormal body at the same time.The three-dimensional inversion of aero-electromagnetic anisotropy and the measurement of anisotropic geological regions are of guiding significance.
【作者单位】：吉林大学地球探测科学与技术学院;
【基金】：financially supported by the Key Program of National Natural Science Foundation of China(No.41530320) China Natural Science Foundation for Young Scientists(No.41404093) Key National Research Project of China(Nos2016YFC0303100 and 2017YFC0601900) China Natural Science Foundation(No.41774125)
【分类号】：P631.325

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