【作者】 李建慧；

【导师】 朱自强；

【作者基本信息】 中南大学 ， 地球探测与信息技术， 2011， 博士

【摘要】 大回线源瞬变电磁法是一种常用的电磁法野外工作方法。发射回线铺好以后,可采用多个探头在发射回线中心区域同时测量；主要优点是工作效率高、勘探深度大。然而其资料处理、反演水平并不高,主要停留在一维阶段；而正演是反演和资料处理解释的基础,因此有必要先进行正演研究。为了反映瞬变电磁场真实的传播规律、校正地形起伏对瞬变电磁场的影响、提高瞬变电磁法资料处理解释水平、改善瞬变电磁法的应用效果,本文采用了矢量有限单元法对大回线源激发的瞬变电磁场进行了三维数值模拟。主要研究内容如下：(1)推导了大回线源激发的电磁场一维表达式。根据垂直磁偶源激发的频率域电场,对其磁偶极矩按发射回线面积进行积分得到大回线源激发的频率域电场面积分表达式；根据0阶和1阶Bessel函数与空间位置水平坐标的微分关系,把电场表达式由面积分转化为线积分。利用Gaver-Stehfest算法将大回线源激发的电场从频率域转换至时间域,然后利用法拉第电磁感应定律求得大回线源激发的磁场脉冲响应,进而得到感应电动势。大回线源激发的电磁场一维表达式主要用于定义全期视电阻率、验证矢量有限单元法数值解精度和正演模拟中局部异常体区域背景场的计算。(2)确定了Gaver-Stehfest算法滤波系数最佳数目和适用范围。研究Gaver-Stehfest算法滤波系数的最佳数目和适用范围的意义在于提高计算感应电动势的精度,特别是晚期的精度,从而能够计算更晚期时刻的感应电动势。由于Gaver-Stehfest算法要求双精度计算,因此其精度与计算机字长密切相关。本文在32位Windows操作系统试验Gaver-Stehfest算法,确定了Gaver-Stehfest算法滤波系数的最佳数目是14；当所求感应电动势小于5×10-13V时,利用Gaver-Stehfest算法已不适用。(3)利用矢量有限单元法对大回线源激发的瞬变电磁场进行了三维数值模拟。利用拉普拉斯变换将时间域Maxwell’s方程组转换至拉普拉斯域,并推导出拉普拉斯域的电磁场Helmholtz方程。从电场Helmholtz方程出发,由伽辽金法进行有限单元法分析。本文网格剖分采用矩形块单元,基函数采用Whitney型矢量基函数,求解大型线性稀疏方程组采用对称超松弛预处理的双共轭梯度稳定法(SSOR-BICGSTAB)。利用有限元法求解出电场值后,应用Gaver-Stehfest算法将其转换至时间域,然后通过法拉第电磁感应定律获得磁场脉冲响应。通过与层状介质地电模型的准解析解和低阻块状体的积分方程法、时域有限差分法数值解对比,验证了矢量有限单元法解的正确性。最后,我们对直立低阻板状体等模型进行了数值模拟。(4)定义了含有测点位置信息的全期视电阻率。首先计算某个测点各个时刻的晚期电阻率,将其作为计算各个时刻全期视电阻率的初始值,利用快速模拟退火法(VFSA)拟合大回线源在均匀半空间表面激发的该点感应电动势与野外实测值,求得带测点位置信息的全期视电阻率。最后,将该算法应用于内蒙古自治区那仁宝力格煤田勘探区,划分出了碎屑岩与玄武岩的界限。更多还原

【Abstract】 Large source loop transient electromagnetic method is one of common electromagnetic methods. Once transmitting loop laid later, several receivers can measure simultaneously within the central area of the transmitting loop. The method’s advantages are high efficiency and large exploration depth. However, the level of data processing and inversion stays in one-dimensional stage. The forward is the basis for inversion and data processing, so it is necessary to conduct research forward firstly. To reflect the real propagation of transient electromagnetic field, correct terrain on the impact of transient electromagnetic fields, improve the interpretation of transient electromagnetic data processing level, improve the application of transient electromagnetic effects, we use the vector finite element method for simulating3D transient electromagnetic field excited by large source loop. The main contents are as follows:(1) We deduced transient electromagnetic field expressions excited by large source loop. According to the electric field excited by vertical magnetic dipole in frequency domain, the electric field excited by large source loop could be got using loop area integral for magnetic moment. Using differential expressions between0and1orders Bessel function and spatial location cooridinates, the electric field expressions were transformed from area integral to line integral. Using Gaver-Stehfest algorithm, the electric field excited by large source loop in time domain was converted from in frequency domain. Based on Faraday law of electromagnetic induction, impulse responses of magnetic induction were deduced from electric field strength step responses, and then we could obtain EMF.1D transient electromagnetic field excited by large source loop is mainly used for defining all-time apparent resistivity, validating vector finite element method numerical solutions and calculating background electromagnetic field for forward. (2) We determined the optimal number of coefficients and the application scope of Gaver-Stehfest algorithm. Researching the coefficient’s optimal number and the application scope of Gaver-Stehfest algorithm is to improve the accuracy of EMF, in particular at late times. Because the Gaver-Stehfest algorithm requires double precision calculation, the accuracy is closely related with the computer word length. We test Gaver-Stehfest algorithm in32-bit Windows operating systems. We found the optimal number of coefficients is14. If the value needs to be calculated is less than5×10-13V, Gaver-Stehfest algorithm doesn’t validate.(3) We simulated3D transient electromagnetic field excited by large source loop using vector finite element method. By Laplace transform, Maxwell’s equations were transformed from time domain to Laplace domain, and then Helmholtz equations for electromagnetic field were deduced. We made electric field Helmholtz equation as governing equation, and derived the corresponding system of vector finite element method equations using the Galerkin method. For solving the governing equation using vector finite element, we divided the computing domain into homogenous brick elements, and used Whitney type vector basis functions. To solve linear system of equations, we used Bicgstab method with a SSOR preconditioner. After obtaining the electric field values by vector finite element method, we used Gaver-Stehfest algorithm to transform these values to the time domain, and obtained the magnetic field impulse response through Faraday law of electromagnetic induction. By comparing quasi-analytic solutions of layered model and integral equation method and FDTD solutions of low resistiviy block, we verified vector finite element method solutions. Finally, we simulated transient electromagnetic field of different models, such as upright low resitivity sheet model.(4) The all-time apparent resistivity including measuring point position information is obtained. Firstly, we take late time apparent resistivity of transient electromagnetic method as the priori information for VFSA. Then, utilizing VFSA to fit theoretical EMF and measured EMF obtains the all-time apparent resistivity of the measuring points in rectangular transmitting loop. At last, we applied this algorithm to carve out of the boundaries of clastic rocks and basalt at Narenbalige in Inner Mongolia Autonomous Region.更多还原