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.     

THE INTERPRETATION OF INDUCED-POLARIZATION SOUNDING CURVES IN THE FREQUENCY DOMAIN *

Two-layer type curves of apparent frequency effect for the Wenner configuration are presented. The formulation is based on the normal definition of frequency effect in terms of resistivities measured at different frequencies plus the definition of apparent resistivity over two horizontal layers as a function of first and second layer resistivities. The use of these type curves in the interpretation of multilayer apparent frequency-effect curves is described and some field examples are given.     

MT方法中Basokur视电阻率定义的研究

电法勘探中不同的视电阻率定义可以带来不同的反演效果,好的视电阻率定义可以提高反演分辨率。传统的Cagniar视电阻率(1953)只是利用了波阻抗的模值,而Basokur 1994年提出的视电阻率利用波阻抗的实部和虚部。本文做了4个不同模型的Basokur视电阻率响应及反演,结果显示新的视电阻率对薄层有很好的反应,对常规模型也有不错的表现。     

The use of laboratory measurements of electric resistivity of rocks for evaluating the magnetotelluric method

Summary A profile model of electric resistivity as a function of depth was compiled, the initial parameters being the values of the electric resistivity determined experimentally for basaltic and eclogitic rocks from the Bohemian Massif. The curves of the apparent resistivity were computed for this model and the measure of information evaluated for the various model layers. The dominant influence of the subsurface layer was proved.     

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．      

A new method for geoelectrical investigations underwater1

A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.     

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％.     

用双侧向测井响应求取地层参数的Newton－SVD反演方法

针对测井中经常遇到的完全非均匀的地层模型，利用深、浅双侧向测井的视电阻率曲线作为约束条件，给出了反演侵入半径ｒ_ｉ、原状地层电阻率Ｒ_ｔ、上（下）围岩电阻率Ｒ_{ｓｕ（Ｒｓｄ）的Ｎｅｗｔｏｎ－ＳＶＤ反演方法．数值模拟表明这一方法是可行的，经实际资料处理．说明该方法实用．}     

实际井眼条件下过套管电阻率测井响应的传输线方程正演算法

过套管电阻率测井通过测量套管壁电势实现测量地层视电阻率,不同的地层模型对过套管电阻率测井会有不同的测井响应. 在传输线方程系数中本文考虑了径向含多个界面地层的影响,对轴向（井轴方向）呈层状、径向阶跃变化地层模型,给出了电势分布递推公式,计算了过套管电阻率测井响应,绘出了测井响应曲线. 算例表明,该方法有较强的轴向地层界面分辨能力;对径向均匀地层计算结果非常接近地层模型电导率,能较好地反映实际地层特征;对高电导地层,低电导水泥环有明显的测井响应;当径向存在多个地层界面时计算结果则为径向各层电导率的综合反映,不是某一径向层的电导率;算例显示该方法有较快（算例运行时间在1s内）的计算速度.     

RESISTIVITY SOUNDING ON A LAYERED TRANSITIONAL EARTH*

Master curves are presented for three-layer earth-sections, the electrical resistivity in the intermediate layer of which has a linear variation with depth. A new approach is proposed to interpret the sounding data with the help of RMS difference in apparent resistivity values.     

SIMPLE DATA PROCESSING OF TRIPOTENTIAL APPARENT RESISTIVITY MEASUREMENTS AS AN AID TO THE INTERPRETATION OF SUBSURFACE STRUCTURE*

The advantages of the Wenner tripotential method (Carpenter 1955) for apparent resistivity profiling are described and two new data processing techniques introduced as an aid to the interpretation of apparent resistivity sections (pseudo-sections). These techniques were developed from model data computed using a two-dimensional finite difference method. Oscillatory components present in anomalies on tripotential profiles and related to electrode spacing are shown to be effectively removed by linear filtering that also simplifies their form and aids recognition. Furthermore, it is shown that the ratio of the beta- and gamma-apparent resistivities is a good indicator of resistivity variation, and is particularly sensitive to lateral change. Model data indicates that, over a wide range of conditions, enough subsurface information can be obtained by inspection of tripotential resistivity and ratio profiles, and from space sections to make possible a useful—and sometimes semi-quantitative—interpretation. A rationale for the general interpretation of tripotential data is developed. Field data are described from an area of weathered granite basement in Nigeria. A model of the subsurface is developed using parameters derived from the processed observations. The observed and calculated apparent resistivity space sections are very similar.     

电阻率测深的数字解释

本文主要介绍了应用积分变换的方法和采样定理将视电阻率ρ_s曲线作线性滤波,得出一新的电阻率转换函数T′曲线,然后,以层参数（各层的电阻率和厚度）算得的T用最优化数值方法在DJS-6型电子计算机上与其进行自动拟合,以达到解释电测深曲线的目的。 文中简述了戈什（Ghosh）提出的对ρ_s作线性滤波的原理,介绍了与国外不同的取样间距和滤波系数的确定以及阻尼最小二乘法和变尺度最优化法的计算框图和应用,最后附有实例和简要的讨论。     

视电阻率法的地形改正

文本提出用理论计算来消除复杂地形对视电阻率影响的方法。借助数学公式解析单元地形的线源畸变电场和点源畸变电场,计算并编制出量板,再将单元地形的视电阻率畸变曲线组合迭加,就能近似地取得复杂地形的改正曲线。文中举出实例,阐明了这种地形改正方法的应用和效果。     

CSAMT单分量数据解释方法

可控源音频大地电磁法(CSAMT)一直沿用大地电磁法(MT)的办法,通过计算电场分量与磁场分量的比值,求取卡尼亚视电阻率.而CSAMT场源已知,电场分量和磁场分量都与地下电阻率存在一定的关系,可以单独采用CSAMT电场分量或者磁场分量提取地下介质的视电阻率.本文通过分析电场分量与磁场分量的数据特性,提出利用CSAMT电场单分量数据进行视电阻率的计算,用改进的广义逆矩阵反演方法,使初始模型中的地电层数等于频道个数,克服了以往反演计算中层数较少的问题;实现全场区电场分量视电阻率曲线的拟合反演.同时对单分量视相位计算方法进行分析,结合山西大同地区积水采空区探测及数据解释结果,论证本文提出的单分量解释方法的有效性.     

Increased resolution of subsurface parameters from 1D magnetotelluric modeling

In electric and electromagnetic techniques, it is well known that the principle of equivalence poses a problem in the interpretation of subsurface layers. This means the inversion problem can provide the conductivity-thickness product more confidently than the individual parameters — conductivity and thickness — separately. The principle of equivalence corresponds to the middle layer in a three-layer earth structure. In order to resolve this problem, we have touched upon the different formulae of apparent resistivity proposed by earlier workers considering the real and imaginary parts of the impedance tensor and designed a new formula to compute apparent resistivity for different models. We observed that the application of our new formula for apparent resistivity using the combination of real and imaginary parts of the impedance has a better resolution as compared to earlier conventional formulae of apparent resistivity. These results have been demonstrated through both forward and inverse modeling schemes.     

FINITE-DIFFERENCE EVALUATION OF APPARENT RESISTIVITY CURVES*

The problem of numerical evaluation of apparent resistivity curves is treated by finite difference modeling. The models proposed are set up in cylindrical coordinates and yield the potential field due to a point source located in a radially symmetric environment. The Schlumberger configuration, widely used for surface measurements, is emphasized. However, the treatment is equally applicable to other similar situations such as the computation of synthetic electric logs when the resistivity of the borehole fluid is different from that of the surrounding uniform or stratified medium. Moreover, the individual layers may not necessarily be isotropic. The medium under investigation is discretized by using a very coarse system of horizontal and vertical grid lines whose distance from the source increases logarithmically; consequently, the physical dimensions of the medium can be made “infinite” without affecting the numerical size of the model. Finer features such as a thin but anomalously resistive or conductive bed which would ordinarily be missed in coarse discretization are accurately taken into account, since the calculations are done in terms of the Dar Zarrouk parameters derived from the exact resistivity distribution of the model. This enables one to compute the potential field by inverting a small sparse matrix. When the medium comprises only a few layers, the efficiency of the finite-difference model is comparable to that of the known analytical methods; for more complicated structures, however, the finite-difference model becomes more efficient. The accuracy of finite-difference results is demonstrated by comparing them with the corresponding analytically obtained data.     

THE USE OF TWO-ELECTRODE AND SCHLUMBERGER FILTERS FOR COMPUTING RESISTIVITY AND EM SOUNDING CURVES*

Different sets of filter coefficients for the linear filter technique for the computations of resistivity and EM sounding curves are evaluated for several electrode and coil configurations. Instead of this procedure, the two-electrode filter can be used for computations of Wenner, Schlumberger, and dipole—dipole apparent resistivity model curves by defining convolutional expressions which contain the new input functions in terms of the resistivity transform function. Similarly, the Schlumberger filter performs the computations of dipole—dipole apparent resistivity model curves. The Wenner, Schlumberger, and dipole—dipole filter functions are defined in terms of the two-electrode filter using the new convolutional expressions. A relationship between the Schlumberger and dipole—dipole filter functions is given. The above arguments are adopted for the computations of EM sounding curves. It is shown that the EM filter for the horizontal coplanar loop system (which is identical to the two-electrode filter) performs the computations of the mutual coupling ratios for perpendicular, vertical coplanar, and vertical coaxial loop systems. In the same way, the Schlumberger filter can be used to compute vertical coaxial sounding curves. The corresponding input functions are defined in terms of the EM kernel for all convolutional expressions presented. After these considerations, integral expressions of the mutual coupling ratios involving zero-order Bessel function are derived. The mutual coupling ratio for the vertical coaxial loop system is given in the same form as the mutual coupling ratio for the vertical coplanar loop system.     

An apparent-resistivity concept for low-frequency electromagnetic sounding techniques

Apparent resistivity is a useful concept for initial quickscan interpretation and quality checks in the field, because it represents the resistivity properties of the subsurface better than the raw data. For frequency‐domain soundings several apparent‐resistivity definitions exist. One definition uses an asymptote for the field of a magnetic dipole in a homogeneous half‐space and is useful only for low induction numbers. Another definition uses only the amplitude information of the total magnetic field, although this results in a non‐unique apparent resistivity. To overcome this non‐uniqueness, a complex derivation using two different source–receiver configurations and several magnetic field values for different frequencies or different offsets is derived in another definition. Using the latter theory, in practice, this means that a wide range of measurements have to be carried out, while commercial systems are not able to measure this wide range. In this paper, an apparent‐resistivity concept is applied beyond the low‐induction zone, for which the use of different source–receiver configurations is not needed. This apparent‐resistivity concept was formerly used to interpret the electromagnetic transients that are associated with the turn‐off of the transmitter current. The concept uses both amplitude and phase information and can be applied for a wide range of frequencies and offsets, resulting in a unique apparent resistivity for each individual (offset, frequency) combination. It is based on the projection of the electromagnetic field data on to the curve of the field of a magnetic dipole on a homogeneous half‐space and implemented using a non‐linear optimization scheme. This results in a fast and efficient estimation of apparent resistivity versus frequency or offset for electromagnetic sounding, and also gives a new perspective on electromagnetic profiling. Numerical results and two case studies are presented. In each case study the results are found to be comparable with those from other existing exploration systems, such as EM31 and EM34. They are obtained with a slight increase of effort in the field but contain more information, especially about the vertical resistivity distribution of the subsurface.     

The perturbation of geomagnetic fields by two-dimensional and three-dimensional conductivity inhomogeneities

Summary A numerical method is used to calculate the geomagnetic fields associated with a three-dimensional conductivity anomaly. Fields associated with a two-dimensional model are also studied numerically for a range of frequencies and apparent resistivity curves for the two models are compared with that calculated for a layered earth. The apparent resistivity curves for both the three-dimensional model and the two-dimensional model differ considerably from the layered case, and it is evident that if a layered model is used for interpretation the results may be very misleading.