矿井瞬变电磁法的时域矢量有限元三维正演  

3D forward modeling of mine transient electromagnetic by time-domain vector finite element

作　　者：张永超 李宏杰[1,2,3] 邱浩 廉玉广[1,2,3] 李文 ZHANG Yongchao;LI Hongjie;QIU Hao;LIAN Yuguang;LI Wen(Mine Safety Technology Branch,China Coal Research Institute,Beijing 100013,China;State Key Laboratory of Coal Mining and Clean Utilization,China Coal Research Institute,Beijing 100013,China;Beijing Coal Mine Safety Engineering Technology Research Center,Beijing 100013,China)

机构地区：[1]煤炭科学技术研究院有限公司安全分院,北京100013 [2]煤炭科学研究总院煤炭资源高效开采与洁净利用国家重点实验室,北京100013 [3]北京市煤矿安全工程技术研究中心,北京100013

出　　处：《煤炭学报》2019年第8期2361-2368,共8页Journal of China Coal Society

基　　金：煤炭科学技术研究院科技发展基金资助项目(2018CX06);国家自然科学基金青年科学基金资助项目(51704162);国家科技重大专项资助项目(2016ZX05045001-004)

摘　　要：为拓展矿井瞬变电磁正演对复杂地质模型的适用性,开展了基于时域矢量有限元的三维正演研究。首先,基于时间域麦克斯韦方程组和库仑规范推导了磁矢量势的赫姆霍兹方程,在此基础上结合理想导体边界条件采用Galerkin加权余量法推导了相应的弱形式方程,采用模型适用性强的一阶四面体矢量单元对弱形式方程进行了单元分析,并在单元分析时将回线源视为多个电流元克服了源的奇异性,时间离散则采用步长逐渐增大的向后差分法进行,由此实现了复杂地质模型的矿井瞬变电磁法全波形响应计算。对于均匀全空间模型,有限元数值解和解析解的均方相对误差为0.84%,验证了上述算法的正确性。其次,正演了关断效应的影响,结果表明关断效应会使感应电压升高,关断时间相同时,线性关断波形的影响大于指数关断波形,关断波形相同时,关断时间越长,关断效应的影响越向晚期延伸;线性关断时,电流完全关断之前的感应电压主要由发射回线中的电流变化引起。然后,正演了巷道的影响,结果表明关断时间为0时巷道会使早期的感应电压降低,但对晚期的数据影响很小,且发射回线位于巷道中心时的影响大于回线位于掘进工作面时,回线朝向顶底板或侧帮时的影响程度要大于朝向掘进工作面时,但考虑到实际仪器的关断时间,巷道的影响基本可以忽略。最后,对长方体状积水采空区的水平剖面和垂直剖面响应进行了正演,结果表明积水采空区会使感应电压升高,在水平剖面上最强的低阻异常响应出现在发射回线指向采空区中心时,但在垂直剖面上却出现在发射回线指向顶底板时。In order to expand the applicability of mine transient electromagnetic (MTEM) forward modeling to complex geological models,a 3D forward modeling method based on time-domain vector finite element was developed.Firstly,the Helmholtz equation of magnetic vector potential based on Coulomb’s gauge was derived from Maxwell’s equations in time domain.On this basis,combining the perfect conductor boundary conditions,the corresponding weak form equation was derived by Galerkin method.The first order tetrahedral vector element that has extensive applicability was used to analyze the weak form equation,and the loop source was regarded as many current elements to overcome the singularity of the source.The backward differentiation with increasing step size was used for time discretization.Thus the full waveform MTEM response of any complex geological model could be calculated.Secondly,the root mean square percentage error between FEM solution of homogeneous whole space and analytical solution was 0.84%,which validates the proposed algorithm.Thirdly,the influence of ramp current was calculated.The results show that the ramp current will increase the induced voltage,the influence of linear ramp current will be stronger than exponential one when their turn-off time are same,and under the same turn-off waveform,the longer turn-off time the influence extends later.Under the linear ramp current,the induced voltage before the turn-off time is mainly caused by the change of current in the transmitting loop.Fourthly,the influence of tunnel was calculated,the results show that when the turn-off time is zero,the tunnel will reduce the induced voltage in early time,but has barely influence in late time,and the influence is stronger when the transmitting loop is in the center of tunnel comparing to that when the loop is at the heading face,when the loop is toward roof/floor or side comparing to that when the loop is toward heading face,but considering the practical turn-off time the influence can be ignored.Finally,the responses in t

关 键 词：瞬变电磁 三维正演 矢量有限元 积水采空区 关断电流 

分 类 号：P631.3[天文地球—地质矿产勘探]