One-dimensional magnetotelluric inversion using an adaptation of Zohdy's resistivity method

An iterative refinement method for determining a layered resistivity model from a Schlumberger or Wenner sounding curve is adapted to determine a layered resistivity model by using apparent resistivity and phase derived from the magnetotelluric impedance. Magnetotelluric observations presented as a function of period are first converted to an approximate resistivity–depth profile using Schmucker's transformation and this is used to construct an initial guess (starting) model. A two-stage procedure is then invoked. Keeping resistivities constant, layer boundaries are first adjusted to give a minimum misfit between measured data and responses and this is followed by resistivity adjustments with fixed layer boundaries to reduce the misfit further. The method is illustrated by application to some synthetic data both exact and with added noise, to a real field data set and to some magnetotelluric profile data obtained in a survey over the Carnmenellis granites in south Cornwall. The method is validated by recovering conductivity models from the exact and noisy 1D synthetic data. For complicated three-dimensional data at a single site and along a profile of stations, the method is shown to produce acceptable solutions which may be used as starting models in further two- or three-dimensional studies.     

水平分层大地的交流视电阻率

本文给出了水平分层大地视电阻率的一种改进的定义,在这种改进了的视电阻率的远区曲线中,假极值效应有所压低,曲线的起伏度变得比原来的大,视电阻率的值也较接近于地层的真实电阻率.这些特性对于作出正确的判断都是有利的.     

three-dimensional sensitivity coefficients of apparent resistivity and preliminary application

We calculate three-dimensional sensitivity coefficients distribution of apparent resistivity observation when Schlumberger array is used by using finite element method. Analysis results suggest that for the situation of one-dimensional positive or minus coefficient of surface medium, three-dimensional sensitivity coefficients distribution at surface shows similar patterns, and sensitivity coefficients distributions of different layered electric structures are also similar. There are two approximate ellipses at the two-dimensional surface plane between current electrodes and potential electrodes, where sensitivity coefficients are minus, and sensitivity coefficients at other areas are positive. Sensitivity coefficients at two approximate ellipses between current electrodes and potential electrodes are minus at the vertical section along monitoring line, while others are positive. From the three-dimensional view, minus sensitivity coefficients are at the two approximate half ellipsoids between current electrodes and potential electrodes when arrays are applied at surface. And coefficients near the electrodes are much greater than other areas. When resistivity of local areas at surface changes, we can qualitatively analyze the disturbing effects caused by the areas using three dimensional sensitivity coefficients distribution, and the analysis result can serve as reference for further experiment and numerical model quantitative analysis.     

二维频率测深边界单元法正演计算

在二维层状介质中含有横向非均匀体的地电断面情况下，对电偶源的偶极长度作了延长，并选取了适当的基本解及无穷远边界条件，因而将相应的含源谐变电磁场的边值问题转化为较简单的边界积分方程．用边界单元法求出了相应的电磁场分量，进而计算阻抗视电阻率，并对这一算法作了相应的检验．     

Apparent resistivity of azimuthal anisotropy layered media

Introduction The method of apparent resistivity with direct current (DC) measurement, adopted from geophysical exploration, is one of the most important precursory approaches in earthquake prediction, in which the geo-electric constitutive model is illustrated by the scalar theory Archies law and correspondingly a set of calculation methods for apparent resistivity of layered media has been established (QIAN, et al, 1985; YAO, 1989). But this is not consistent with the fact that in earthqu…     

层状方位各向异性介质的视电阻率计算

从电性各向异性的欧姆定律出发，推导了直流电法层状方位各向异性介质中的电位分布、边界条件及视电阻率计算公式．以四极对称装置系统为例，对具有相同各向异性系数的4层模型采用核函数递推法作了理论数值模拟，得到了不同方向的电阻率测深曲线及其等值线形态．结果表明理论公式是正确的，测深曲线既反映了分层介质的电阻率差异，又反映了各层中电阻率的各向异性特征．      

多辐射场源地空瞬变电磁法多分量全域视电阻率定义

本文针对多辐射场源地空瞬变电磁法理论,建立了相应的多分量全域视电阻率定义方法.分析了利用磁场强度进行多辐射场源地空系统全域视电阻率定义的优点,针对磁场强度的各个分量,提出了各自的全域视电阻率算法,实现了多分量、全时域、全空域视电阻率计算,并分析了偏移距对全域视电阻率的影响.通过调整源的相对位置及电流方向等参数,多辐射源瞬变电磁地空系统不仅可以加强不同分量信号强度,削弱随机干扰,还可更好地分辨地下异常体的位置.通过对所设计模型的处理,证实了多辐射场源地空系统多分量全域视电阻率算法的有效性,也验证了多辐射场源地空系统的优势.     

大地电磁局部畸变异常特征三维数值模拟研究

局部畸变问题曾经困扰大地电磁资料反演解释几十年,大地电磁三维数值模拟技术的发展为剖析局部畸变特点和得到可靠的反演成像结果提供了技术基础。本文采用三维数值模拟成像方法对典型三维局部畸变模型进行模拟分析。三维数值模拟结果显示:电场分量垂直电性分界面的极化模式视电阻率曲线(对应二维情况下TM模式)在穿越低阻异常体界面时,曲线会先上移后下移,而在穿越高阻异常体界面时,曲线会先下移后上移,这与电性分界面处积累面电荷产生的二次电场有关。三维模型中XY模式、YX模式视电阻率和相位在三维异常体附近的水平变化是呈现近似垂向对称的,该现象与电场垂直跨越电性界面时视电阻率的变化规律是吻合的,当测线分别沿X方向和Y方向展布时,三维情况下的XY和YX模式分别对应二维情况下的TM模式。低阻小异常体对区域构造响应的畸变影响比高阻小异常体要严重。低阻小异常体对二维区域响应的两种极化模式视电阻率和相位都有非常明显的畸变影响,相比较而言对TE模式的畸变要大于TM模式,因此我们在做二维反演解释时,可优先考虑拟合TM模式数据。位于小异常体中心上方测点的三维畸变响应虽然与对应真实二维区域响应的差异比较大,但可以等效于某种二维模型响应,这种由局部畸变造成的假二维响应在实际野外数据的解释中是需要注意的。      

A SIMPLE METHOD OF INTERPRETATION OF RESISTIVITY SOUNDING DATA USING EXPONENTIAL APPROXIMATION OF THE KERNEL FUNCTION*

A simple unified equation of apparent resistivity for a general four-electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge-regression estimation method is used in the identification of layer parameters from the kernel function.     

DC resistivity methods for determining resistivity in the earth's crust

The use of Schlumberger and dipole arrays for crustal-scale resistivity soundings is considered. Advantages and disadvantages of the two methods are described. The depth to which resistivity may be determined from field measurements is discussed as well as the determination from the sounding curves of various parameters associated with layered structure. The interpretation of experimental data using reference curves as well as two approaches used in computer assisted interpretation are discussed.     

Definitions of apparent resistivity for the presentation of magnetotelluric sounding data1

A new definition of apparent resistivity for the presentation of magnetotelluric sounding data is proposed. The new definition is based on the frequency-normalized impedance function. Both the existing and proposed definitions of apparent resistivity are analysed theoretically and are compared using model curves computed for a 1D earth model. Apparent resistivity curves computed using the proposed definition are a better approximation to the true resistivity values of the subsurface layers. In addition, the layers are more noticeable on the apparent resistivity curves, which is an advantage, especially for the ascending and descending type of apparent resistivity curve.     

铁轨干扰浚县地震台地电阻率观测的有限元分析

2016年5月浚县地震台地电阻率EW向测值出现明显变化,为正确评价该变化,依据浚县地震台地质资料、岩层电性资料和EW向电测深曲线,将该台地下介质电性分布简化为二维电性结构,建立三维有限元模型。通过数值模拟,计算测区内地表铁轨干扰对地电阻率观测的影响形态和幅度。结果表明,由数值模拟所得干扰幅度、形态与实际测值的异常变化较吻合,因此从数值分析的角度确定了铁轨对浚县地震台地电阻率观测的干扰。     

Theoretical study of slope effects in resistivity surveys and applications

When electric soundings are made over an irregular terrain, topographic effects can influence the values of apparent resistivity and lead to erroneous 1D interpretation. A 3D finite-element method has been applied to study the topographical effect of a slope on Schlumberger soundings parallel to the strike. When the resistivity survey is performed at the top of the slope, the apparent resistivity values can be two times higher than in the flat-earth case, depending on the angle (α) and height (H) of the slope, and on the distance (X) between the sounding and the slope top. The results are presented as nondimensional curves which can be used for evaluating topographic anomalies for any value of the parameters α, H and X. It is numerically shown that the topographic effects can be removed from measurements on horizontally layered structures with an irregular earth surface. Real measurements were performed in different geological conditions over an irregular terrain. The correction method based on the nondimensional curves has been applied to the data and has enabled the determination of the correct layered ground configuration using 1D interpretation.     

有限元直接迭代算法及其在线源频率域电磁响应计算中的应用

采用有限元直接迭代算法实现了线源频率域测深电磁响应的二维正演计算. 首先给出了线源正演问题的有限元直接迭代格式,然后由迭代法进行求解. 在处理奇异源问题上,采用向内递推的组合网格技巧,在源点附近可进行局部加密,并实现粗细网格的对接,从而较好地解决了奇异源附近的计算问题. 还提出一种迭代求取全区视电阻率的方法,避免了远近区的划分. 通过对均匀半空间、层状介质和二维模型电磁响应的计算,获得了与大地电磁测深相似的视电阻率曲线,验证了算法的正确性;通过对计算结果的分析,在理论上说明了线源频率域近区测深的可行性.     

大地电磁全张量响应的一维各向异性反演

目前大地电磁(MT)测深资料反演主要基于各向同性介质,但随着MT实际应用的需要,各向异性研究已逐渐引起关注.我们采用广泛应用的广义逆法对一维MT水平层状各向异性介质模型反演进行了探索性研究,并实现了MT全张量响应(即所有的阻抗张量的视电阻率和相位)的一维各向异性反演.理论模型试验表明,无论理论观测值中是否含有噪声,这种方法都能够较好地恢复真实模型,验证了其正确性和有效性.将此方法用于MT实测资料时,能够同时拟合4对视电阻率和阻抗相位曲线,说明本方法可以用于实测资料的处理解释,具有一定的实用价值.     

复电阻率法二维有限元数值模拟

伴随着复电阻率法的广泛应用,发展精确和快速的正演和反演算法成为复电阻率法研究的重点.本文采用基于三角单元剖分的有限单元法进行了复电阻率二维数值模拟研究.为了提高计算速度,对无穷远边界进行了近似处理.整个正演计算过程分为两步,首先采用有限单元法计算四个不同频率的视复电阻率数据,然后对前一步得到的视复电阻率数据采用递推算法计算视Cole-Cole参数.采用这种正演算法与一维正演的结果进行了对比,验证了本文方法的正确性.设计了两个二维极化模型,数值模拟结果表明视复电阻率和Cole-Cole视参数等值线断面图对于异常目标体都有比较明显的反映.     

Modeling Electrical Field Distribution in Layered Geological Rock Formations with a Borehole Using the Coulomb Charges Method

The Coulomb charges method is used to model apparent resistivity measurements carried out in layered geological formations with a borehole using various devices. It is characterized by a high level of effectiveness and accuracy. The results are compared with the theoretical solutions for a homogenous medium with the borehole and invaded zone for point current source lateral devices. The relative error was less than 2% for different values of the range of the invaded zone and resistivity of invaded and true resistivity of formation.     

基于最高频相位法和空间滤波法的二维模型的大地电磁静态校正

静态效应一直是影响大地电磁测深法精确性的主要原因之一.在相位校正法的基础上提出了一种更适用于电性变化较为平缓的地质情况的静态校正方法—最高频相位法,其核心是用需要校正测点两侧受静态效应影响较小测点的最高频视电阻率的算术平均值代替相位法递推公式中每个频点前一个频点的视电阻率值,以消除相位法中的误差积累.以二维模型的正反演...     

GEOELECTRICAL MODEL CALCULATIONS FOR TWO-DIMENSIONAL RESISTIVITY DISTRIBUTIONS*

For the calculation of geoelectrical model curves for a two-dimensional resistivity distribution, the potential equation is transformed by means of a Fourier cosine transform into a two-dimensional Helmholtz equation containing the separation parameter λ. The numerical solution of this equation for different values of λ for an irregular grid is obtained using the method of finite differences combined with the method of overrelaxation. The method by which derivatives are replaced by finite differences turned out to be very important, especially for high resistivity contrasts. After testing several methods designed to deal with any type of resistivity distribution, a method of discretization similar to that used by Brewitt—Taylor and Weaver (1976) for magnetotelluric modeling for H polarization was found the best. Examples are given of model curves for Schlumberger soundings over a vertical fault covered by overburden. The incorrect use of horizontal-layer models leads to erroneous interpretations that are more complex than the real subsurface situations.     

电阻率反演及其应用

针对大部分沉积岩具有层理结构,从其电性上来看,它们是由各种不同电阻率的地层组成的,这样的地层其电阻率呈现出各向异性。在对电阻率断面进行观测时,要在层状介质背景剖面的基础上,利用二维电阻率扰动反演方法,将背景场环境中的电性层结构进行掌控,并对敏感矩阵进行计算,通过实验得到良好的效果。