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．      

地震前后祁连山中段深部电性变化的跟踪研究

利用在青藏高原北缘第一个长约４００ｋｍ的ＭＴ重复监测剖面上所获得的地震前后最新的地表视电阻率资料，用一维ＭＴ反演方法得到了剖面古方电性结构随时间的变化。着重分析相当于大陆多震层深度范围内介质电阻率参数在地震前后的变化。结果表明，地下电阻率的变化呈现分区特征，并与剖面附近地震的强度及位置有关。     

层状介质中膨胀球模拟力源的应力——应变场与视电阻率的关系

本文研究了三层介质中膨胀球模拟震源的应力、应变场以及由这个应力、应变场产生的电阻率变化量和地表视电阻率变化的关系。结果表明,对于一定强度的“震源”,在地电装置探测范围内的应力场随具有不同弹性参数的层位有显著的变化;而应变场却看不出有明显的突变;由地表视电阻率变化量的计算结果揭示了地电异常受台站介质电性结构与力学结构的综合影响。因此作为预报地震的地电阻率法一方面要寻找具有高电阻率——应变灵敏度岩层的台址,另一方面台址的视电阻率变化对各层真电阻率变化要具有好的响应。     

岩石电阻率的实验研究

本文首先概述岩石在室内各种受载条件下电阻率的实验研究工作,这对于认识和理解电阻率变化特征、规律以及探索其机理起着重要的作用。但是在实验中主要采用4个固定电极的测量系统,它只能获得从某个深度到岩样表面的整个深度层的视电阻率变化的综合信息,而无法获得不同深度层的视电阻率变化特征,不利于进一步研究电阻率及其各向异性变化的机理。我们利用电阻率层析成像方法获得了多个方向的电阻率数据,据此可以获得随深度变化的电阻率及其各向异性曲线以及随应力变化的电阻率图像,可能为深入理解和研究电阻率变化机理起到积极的帮助。      

地电阻率的数值模拟和多极距观测系统

本文利用高精度的多层水平层状介质视电阻率计算公式,模拟了不同结构剖面、不同装置极距、不同规律的真电阻率变化,以及这种变化在介质中所处不同部位条件下地表视电阻率变化的计算结果;讨论了发生于介质中的真电阻率随时间变化在上述各种不同条件下,与在地表观测到的地电阻率(即视电阻率)变化两者之间的关系;指出为了解次异常变化与干扰变化的识别问题,应当将现行单一极距观测改造为多极距观测,并研究和发展相应的地电阻率随时间变化的反演技术和方法,以促进地电阻率法预报地震从看图识字的被动状态向物理预报方向转化。      

强地震附近电阻率对称四极观测的探测深度

针对我国地震监测预报中固定地点和固定观测装置及参数的视电阻率观测,给出了半空间倾斜各向异性介质中电阻率对称四极观测的理论探测深度,研究了地震前兆信息的检测深度问题,得到：(1)在强地震、孕震晚期阶段,在震中区及附近可检测到地壳近地表较深部介质的电阻率变化,其深度大于或远大于均匀介质之;(2)震级、震中距、观测方向不同或在不同的孕震阶段,探测深度存在差异,甚至存在大的差异,且是动态变化的.并依据理论探测深度讨论了地震视电阻率前兆变化的复杂性、地电台址电性条件等问题.     

航空瞬变电磁法的全时域视电阻率计算方法

鉴于ATEM数据量大质低的特点,视电阻率仍是最有效而直观的参数.本文给出了适用于ATEM多种观测条件下(包括各种装置类型,发送波形,关断电流等情况)的全时域视电阻率的计算方法,并对典型层状大地模型的理论瞬变电磁响应作了全时域视电阻率及其对应等效深度的计算.结果表明,全时域视电阻率随等效深度变化的曲线可定性反映地下介质电性特征,并可近似估计低阻或高阻层上界面深度.对于非单调下降的瞬变电磁曲线,该方法也能取得较好的计算结果.     

滇西地区几个测点的大地电磁视电阻率影响系数分析

采用水平分层均匀的地电阻率结构模型,研究了滇西地区3个测点的MT视电阻率影响系数随频率变化的特征。结果表明:①各地层视电阻率影响系数都随周期变化,为了更好地获得地震多发层内地电阻率变化信息,可以通过影响系数值选择合适的电磁场频段;②在某一特定周期内的短周期段,视电阻率主要反映易受干扰的第一层的变化,对于地震观测而言,应避开该周期段,该周期值可以通过影响系数分析确定;③各地层影响系数之和并非常数,而是随周期变化,在不同频段观测的视电阻率反映地层电阻率变化的能力不同。影响系数分析对MT地震观测频段和测点的选择具有一定的指导意义。     

含裂隙介质中的视电阻率各向异性变化

我国50多年的视电阻率连续观测结果表明,大地震前近震中区域的视电阻率呈现出与主压应力方位有关的各向异性变化,即:垂直于主压应力方向观测的变化幅度最大,平行方向最小或不明显,斜交方向介于二者之间.目前我国定点台站视电阻率观测的探测范围主要在浅层沉积层以内,通常含有较多的含水裂隙.本文将地下岩土介质简化为由固体基质和含流体/气体裂隙组成的固液气三相介质,且基质、流体和气体具有标量形式的电阻率,推导出了包含基质和流体电阻率、裂隙率、饱和度和裂隙面积率因子的电阻率张量表达式.以裂隙的扩展/闭合表示应力作用下裂隙的变化,得到了电阻率随裂隙变化的微分形式,电阻率变化对裂隙体积变化放大系数的表达式和裂隙横向变化对纵向电阻率影响的横向权系数的表达式.在此基础上得到了介质电阻率和视电阻率的各向异性变化特征:对于含水裂隙介质,无论裂隙如何变化,均是最小主轴方向电阻率的变化幅度大于其他方向;对于含水孔隙介质,沿孔隙主要变化方向的主轴电阻率变化幅度大于其他方向.对于各向异性变化,视电阻率和介质电阻率存在π/2的方向差异.相较于含水岩石,无水岩石介质电阻率的各向异性变化不显著.本文提出的电阻率表达式可以对实验室和野外实际观测的许多结果做出合理的解释.     

水平多层大地上垂直磁偶极频率测深的全波视电阻率

本文根据视电阻率定义的原则,以及用不同的场量定义的视电阻率效果不同这一事实,提出一种新的全波视电阻率定义.在全区同时用均匀大地上电磁场的三个分量来分区定义祝电阻率.在远区视电阻率由磁场的水平分量求出,在近区由磁场的垂直分量或其实分量定义,而在过渡区则由电场的水平分量确定.用这种方法定义的视电阻率为电磁响应的单值函数,它随频率变化的曲线显著改善,能直观地反映地层电阻率随深度的变化,数值比较接近地层的真电阻率值,假极值效应明显压低.在计算中用切比雪夫多项式分段拟合均匀大地电磁响应的反函数,并给出一套系数,由此算出的视电阻率误差小于1％.     

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.     

A STUDY ON THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDING DATA MEASURED BY WENNER ELECTRODE CONFIGURATION*

This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation where K₁(λ) is the kernel and B₁(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least-squares method. The least-squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions.     

THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*

In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression. As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.     

NUMERICAL INTERPRETATION OF RESISTIVITY SOUNDINGS OVER HORIZONTAL BEDS*

The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth.     

DIRECT INTERPRETATION OF TWO-ELECTRODE RESISTIVITY SOUNDINGS *

This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940).     

RESISTIVITY SOUNDING ON A MULTI-LAYERED EARTH WITH TRANSITIONAL LAYERS. PART I: THEORY*

The electrical potential generated by a point source of current on the ground surface is studied for a multi-layered earth formed by layers alternatively characterized by a constant conductivity value and by conductivity varying linearly with depth. The problem is accounted for by solving a Laplace's differential equation for the uniform layers and a Poisson's differential equation for the transitional layers. Then, by a simple algorithm and by the introduction of a suitable kernel function, the general expression of the apparent resistivity for a Schlumberger array placed on the surface is obtained. Moreover some details are given for the solution of particular cases as 1) the presence of a infinitely resistive basement, 2) the absence of any one or more uniform layers, and 3) the absence of any one or more transitional layers. The new theory proves to be rather general, as it includes that for uniform layers with sharp boundaries as a particular case. Some mathematical properties of the kernel function are studied in view of the application of a direct system of quantitative interpretation. Two steps are considered for the solution of the direct problem: (i) The determination of the kernel function from the field measurements of the apparent resistivity. Owing to the identical mathematical formalism of the old with this new resistivity theory, the procedures there developed for the execution of the first step are here as well applicable without any change. Thus, some graphical and numerical procedures, already published, are recalled. (ii) The determination of the layer distribution from the kernel function. A recurrent procedure is proposed and studied in detail. This recurrent procedure follows the principle of the reduction to a lower boundary plane, as originally suggested by Koefoed for the old geoelectrical theory. Here the method differs mainly for the presence of reduction coefficients, which must be calculated each time when passing to a reduced earth section.     

MATRIX METHOD FOR THE TRANSFORMATION OF RESISTIVITY SOUNDING DATA OF ONE ELECTRODE CONFIGURATION TO THAT OF ANOTHER CONFIGURATION1

Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions. Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable interpretation.     

On the automatic interpretation of direct current resistivity soundings

A method for the automatic inversion of resistivity soundings is presented. The procedure consists of two main stages. First, application of linear filters which transforms the apparent resistivity curve into the kernel function, and vice versa. In the second stage the first and second derivatives of the kernel function are calculated and used in a second-order modified Newton-Raphson iterative fitting procedure. The model obtained is optimal in the least squares sense. The method has been tried on some field examples and produced resistivity models which show a good agreement with the geological well logs.     

THE APPLICATION OF LINEAR FILTER THEORY TO THE DIRECT INTERPRETATION OF GEOELECTRICAL RESISTIVITY SOUNDING MEASUREMENTS*

Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy. In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%.     

GEOELECTRICAL SURVEYS OF DIPPING STRUCTURES1

Among resistivity methods, models containing two dipping discontinuity surfaces with a conductive medium between them have been considered in this study. The theoretical apparent resistivity curves obtained for such models were calculated using Alfano's integral equation for various dip angles of planes at different array distances from the contacts. The results obtained showed that it is possible to achieve the dip values of the discontinuities under particular conditions, but ambiguities cannot be ruled out.