瞬变电磁法三分量正演
首发时间:2009-07-13
摘要:瞬变电磁法的资料解释通常多采用垂直磁场对时间的导数这一单一物理量,然而,在复杂地质构造勘探中,传统解释技术已经越来越不能满足野外实际生产的需求,为了提高瞬变电磁法的综合解释精度,增强其探测复杂地质构造的能力,开展该方法的多分量数据正反演问题研究已经日益紧迫。基于此,本文作者开展了一种建立在电场磁场分离基础上的瞬变电磁法多分量数据的2.5维有限单元法正演研究。借助矢量的旋度和散度运算规则,文中首先由拉普拉斯域三维电磁场分离出沿地质构造走向的电场和磁场分量;然后对其进行走向方向(电导率在该方向没有变化)的傅立叶变换,得到二维地电断面中拉氏傅氏域独立电磁场所满足的边值问题;尔后通过Galerkin方法获得大型有限元方程组;进而运用有限单元法求解拉氏傅氏域电磁场分量的数值近似解。较之于传统算法而言,文中提出的算法优势主要在于待求解的稀疏线性方程组规模被大幅度削减,仅为传统方法的四分之一。为了验证该方法的可行性和有效性,文后对中心回线激发源条件下几例典型地电模型进行了模拟计算。结果表明,该方法计算速度较之传统耦合电磁场的有明显提高;同单分量解释技术相比较,瞬变电磁法三分量数据解释可充分利用采集到的多分量信息,从而对异常体的空间特性进行更为全面的分析和解释。
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Three-Component Forward of TEM
Abstract:In general, the time derivative of vertical magnetic field is considered only in the data interpretation of transient electromagnetic method (TEM). However, to survey in the complex geology structures, this conventional technique has begun to be unsatisfied with the demand of field exploration gradually. In order to improve the integrated interpretation precision of TEM and its detection capacity for the complex structures, it is necessary to study the three-components forward and inversion. In this paper, a three-component forward algorithm for 2.5-D transient electromagnetic method (TEM) based on the independent electric and magnetic field has been developed. By dint of the operation rule of curl and divergence, the present modeling method transforms the governing Maxwell equations into Laplace domain and then expands them in component format. Applying the Fourier transform to the components in the invariant conductivity direction (or strike direction), we obtain 2.5-D TEM boundary value problem in the Laplace and along-strike spatial Fourier domain. The Galerkin method is used to derive the finite-element equations subsequently, thus we get the EM components numerical solutions in Laplace and Fourier domains by the finite element method. Compared with the conventional algorithm, the main advantage of the new scheme can reduce the size of the global system matrix to the utmost extent, that is to say, the present is only one fourth of the former. In order to illustrate the feasibility and usefulness of the present algorithm, several typical geoelectric models of the transient electromagnetic responses produced by loop sources at air-earth interface are presented. The results of the numerical experiments show that the computation speed of the present scheme is increased obviously and three-component interpretation can get the most out of the collected data, from which we can analyze or interpret the space characteristic of the abnormity object more comprehensively.
Keywords: Transient electromagnetic method Three-component Independent EM field 2.5-D forward
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