Research Note: The mean sensitivity depth of the electrical resistivity method

Until now, a simple formula to estimate the depth of investigation of the electrical resistivity method that takes into account the positions of all of the electrodes for a general four‐electrode array has not been available. While the depth sensitivity function of the method for a homogeneous infinite half‐space is well known, previous attempts to use it to characterize the depth of investigation have involved calculating its peak and median, both of which must be determined numerically for a general four‐electrode array. I will show that the mean of the sensitivity function, which has not been considered previously, does admit a very simple mathematical formula. I compare the mean depth with the median and peak sensitivity depths for some common arrays. The mean is always greater than or equal to the median that is always greater than the peak. All three measures give reasonable estimates to the depths of actual structures for most circumstances. I will further show that, for 1D soundings, the use of the mean sensitivity depth as the pseudo‐depth assigns an apparent resistivity to a given pseudo‐depth that is consistent between different arrays. One consequence of this is that smoother depth soundings are obtained as “clutches,” caused by a change in the depth sensitivity due to moving the potential electrodes, are effectively removed. I expect that the mean depth formula will be a useful “rule of thumb” for estimating the depth of investigation before the resistivity structure of the ground is known.     

新城子井下地电阻率观测影响系数分析

以新城子观测站地电阻率为研究对象,结合新城子观测站电测深资料通过影响系数理论用水平层状介质模型对比分析地表、井下地电阻率两种手段的观测效果,对新城子地电阻率观测各层影响系数随深度和极距的变化分析新城子井下地电阻率观测布极的合理性。其结果反应为新城子地电阻率井下观测设计较为合理,减少场地资源的同时对地表和浅层干扰有更好的抑制作用,对深层的映震能力优于地表观测,分析结果可为类似台址电性结构中实施井下地电阻率观测提供参考。     

冻土区天然气水合物各向异性储层的AMT响应特征

陆域天然气水合物通常发育于冻土层下方破碎带和岩层裂隙处,其储层会表现明显电性各向异性特征.音频大地电磁法（AMT）能有效探测陆域水合物储藏范围,且不易受高阻冻土层的压制和干扰,可用于陆域天然气水合物探测研究.本文采用AMT对角各向异性二维正演方法,对多种陆域天然气水合物各向异性储层模型及相关参数进行了模拟试算,分析其视电阻率和相位响应特征.结果表明AMT能清晰显示各向异性储层空间位置和分布情况,并对储层的水合物饱和度变化以及储层数量等特征都有所反映.天然气水合物电性各向异性模拟研究为这一新型潜力能源的勘查工作提供了新的思路.     

低渗透复杂润湿性储层电阻率实验及导电机理研究

低渗透岩性油气藏发育的黏土膜吸附原油造成了储层亲油,电阻率异常高,高阻油水层、水层的存在给储层流体性质识别带来了很大挑战.为了明确不同润湿性储层的电阻率响应特征以及微观导电机理,本文选取了鄂尔多斯盆地西部三叠系延长组长8段的岩心,模拟了油驱水、老化和水驱油过程,并测量了岩心薄片洗油后的接触角.实验结果表明,洗油后异常高阻岩心已表现为不完全亲水,然而,其测量的胶结指数m与正常电阻率岩心相差很小.油驱水至束缚水时,正常电阻率岩心的电阻增大率I_r与含水饱和度Sw的关系在双对数坐标下基本表现为直线的关系,而异常高阻岩心则表现为明显的凸曲线特征.且老化过程前后,异常高阻岩心的电阻率基本不变.结合对异常高阻岩心不同状态下的核磁共振T_2谱的分析,表明在油驱水过程中,岩石的润湿性已经向亲油方向发生转变,老化过程对润湿性的改变影响很小.水驱油至残余油时,异常高阻岩心的I_r-S_w曲线表现为近似直线特征,反映出水驱油过程中岩石的导电结构并未发生改变.基于实验结果的分析与讨论,明确了一种适用于低渗透复杂润湿性储层的成藏模式及其导电机理,说明了高阻水层主要是亲油润湿性条件下的连续导电路径遭到破坏造成的.     

RESISTIVITY SOUNDING ON AN EARTH MODEL CONTAINING TRANSITION LAYERS WITH LINEAR CHANGE OF RESISTIVITY WITH DEPTH*

Mallick and Roy solved the problem of determining the apparent resistivity function for a three-layer stratification in which the central layer is a transition layer with linear change of the conductivity with depth. In the present paper the problem is solved for a transition layer with linear change of the resistivity with depth, a type of change that seems to be more common in nature than the type considered by Mallick and Roy. The solution is extended to layer stratifications involving an arbitrary number of transition layers and of homogeneous layers. The solution is given in the form of a modification of the recurrence relation that was derived by Pekeris for homogeneous layers.     

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.     

Interpretation of VLF Resistivity Data for Ground Water Contamination Surveys

Very low frequency (VLF) military communications systems provide a primary field that can be used for shallow geophysical surveys to locate ground water contamination and vertical geologic contacts. Useful properties that can be easily obtained from the interaction of the earth and the primary field are the magnitude of the vertical secondary magnetic field, the surface impedence, and the phase angle between the electrical and magnetic horizontal components. The variations in the secondary magnetic field can be related to vertical geologic contacts, such as the edges of landfill trenches. The surface impedence yields an apparent terrain conductivity, which can be used to locate low-resistivity anomalies often associated with contaminated ground water. The phase angle gives information on vertical variations in resistivity, phase angles less than 45° indicating increasing resistivity with depth. The depth of penetration of the VLF field is about one skin depth. For a frequency of 20 kHz, the skin depth in meters is approximately equal to 3.67 where p is terrain resistivity in ohmmeters.     

Magnetotelluric sounding results in eastern Tibetan Plateau

The results of Zayü-Qingshuihe MT sounding profile carried out in eastern Tibetan Plateau are presented in this paper. Using 2-D RRI method, the resistivity distribution with depth is obtained along the profile. It is featured by the resistivity zones in the horizontal direction and layers in the vertical direction. The Bangong-Nujiang suture zone and Jinshajiang suture zone are both important electrical conductivity-separating zones in the plateau, and the former is a zone with relatively low resistivity while the latter is an electrical conductivity gradient zone. The highly electrical conductive bodies in the mid and lower crust of northern Qiangtang and Bayan Har Terrain might be caused by regional melting due to shear heating during the process of subduction in tectonic evolution.     

Characterisation of subsurface spatial variability using a cone resistivity penetrometer

The subsurface spatial variation in clay soils, such as thin-layered sand seams, affects the mechanical strength and electrical resistivity. The objective of this study is the development and application of cone resistivity penetrometer (CRP), which measures the cone tip resistance, sleeve friction, and electrical resistivity to evaluate the subsurface spatial variability. The electrical resistivity is measured at the cone tip to increase its resolution. Two outer diameters of the cone resistivity penetrometers (CRPs) are developed: D=10 mm CRP with a projected area of 0.78 cm² and D=15 mm CRP with a projected area of 1.76 cm². The cone tip resistance is effectively separated using a friction sleeve. Strain gauges are used to measure the mechanical strength, and coaxial type electrodes monitor the electrical resistivity. The application tests in the laboratory are conducted using layered soils and saturated sands. In addition, the penetration tests in the field are carried out and compared with the standard piezocone test. The penetration tests show that the soil layers and the density changes are clearly detected by the electrical resistivity and mechanical strength. Field tests show that CRP clearly evaluates the subsurface profile. This study suggests that CRP may be a useful technique for the evaluation of subsurface spatial variability during penetration testing.     

VERTICAL FREQUENCY EFFECT SOUNDING IN INDUCED POLARIZATION AND GALVANIC RESISTIVITY METHODS *

It has been shown that for a polarizable layer as a transmission medium there is an indirect proportionality between the frequency effect (fe) in induced polarization (IP) and the wave number of the electrical induced field. Making use of this relationship for a two layered earth a polarization transform function has been obtained. Since the mathematical expression for the polarization transform function is the same as that of the resistivity transform function, it is possible to make direct interpretation for IP frequency effect field curves. Thus, AA or QQ type resistivity sequences can be interpreted from induced polarization response of a horizontally stratified earth without resistivity extrema. A depth factor has been defined in order to obtain the true depth using the apparent depth. In this way, some electromagnetic effects between horizontal layers with different polarizabilities can partly be eliminated.     

THE AUTOMATIC FITTING OF A RESISTIVITY SOUNDING BY A GEOMETRICAL PROGRESSION OF DEPTHS *

The problem of interpretation of geoelectrical resistivity soundings has been studied and a compromise method of interpretation developed. A simple depth sequence of increasing bed thickness is taken and resistivities assigned to the various layers so that a good fit is obtained to the observed apparent resistivity curve. An initial estimate of the resistivities is made by a direct method but the model is then altered to give an improved fit by the indirect method of curve matching. The whole method is computerized and input data to the computer program consists of spacings and apparent resistivities. The method is extremely rapid, about one third of the computation time is devoted to obtaining the resistivity transform by the method of convolution. A normal type of solution, incorporating additional information if necessary, can also be obtained.     

高密度电阻率法在海底金矿含水构造探测中的应用

海底金矿上覆岩层中含水直接对矿床的开采构成威胁,选择山东三山岛金矿新立矿区海底-135m水平沿脉巷道,采用地球物理高密度电阻率法对该巷道635m测线以下200m深度范围内岩体中的含水构造进行了坑道探测,利用三种装置(温纳装置(Wenner)、偶极装置(Dipole-Dipole)、Schlumberger装置)进行实施,相互验证,取得了很好的探测结果.温纳、偶极和Schlumberger三种装置的视电阻率反演结果反映在测线(-135m沿脉巷道)以下至30m深度为一高阻层,表明自-135~-165m的岩体中已不含水或含少量的水;测线以下30~60m段为低阻层,反映-165~-200m的岩体中含基岩裂隙水;测线以下大于60m的地段为特高阻层,反映-200m以下岩体含水性逐渐变差.该探测结果与矿区水文地质结构调查分析结论具有很好的一致性,表明了坑道高密度电阻率法探测含水构造是可行的.     

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。      

A NUMERICAL DIRECT INTERPRETATION METHOD OF RESISTIVITY SOUNDINGS USING THE PEKERIS MODEL*

A numerical method is presented for direct interpretation of resistivity sounding measurements. The early part of the resistivity transform curve derived from field observations by standard methods is approximated by a two-layer curve. The resistivity of the first layer is determined from the arithmetic mean of the successive computations which are carried on each of three successive discrete values of the resistivity transform curve. Using this mean value of the resistivity, the thickness of the first layer is computed from the sample values in pairs of the resistivity transform curve. After these determinations, the top layer is removed by Pekeris's reduction equation. The parameters of the second layer are obtained from the discrete values of the reduced transform curve (which corresponds to the second part of the resistivity transform curve) by the same procedure as described for the first layer. The same computational scheme is repeated until the parameters of all intermediate layers are obtained. The resistivity of the substratum is determined from the reduction equation.     

Determination of electrical resistivity,its anisotropy and heterogeneity on drill cores: a new method1

This paper presents a new method for the measurement on core samples of their electrical resistivity, its anisotropy and heterogeneity. The equipment used has been developed in the field laboratory of the German Continental Deep Drilling program KTB in the north-east of Bavaria on the western rim of the Bohemian Massif. The apparatus measures the resistivity at a fixed frequency as a function of the drill core azimuth and along the core by moving point electrode configurations. From these azimuth and depth dependences, mean values of resistivity and additional information about its anisotropy and heterogeneity are determined. Geometrical averaging is used, because the resistivity data follows a log normal distribution. The quantitative parameters ‘azimuth factor’, corresponding to horizontal anisotropy, and ‘heterogeneity factor’ are introduced. The depth logs of resistivity, azimuth factor and heterogeneity factor, measured on cores obtained from the KTB main drill hole (gneisses and amphibolites) at depths between 4150 m and 8080 m are presented. The geometrically averaged mean values of resistivity of gneisses and amphibolites are in the same range (? 10³Ωm). The resistivities tend to decrease with depth. The stress release of the drill cores during recovery produces microcracks which may partially account for this effect. Reduced resistivities (down to 150 Ωm) within an amphibolite core correlate with an alteration zone. One sample of this core displays alteration from fresh to completely altered. This sample is also electrically heterogeneous (heterogeneity factor ? 2). Other samples with uniform low alteration are more homogeneous heterogeneity factor ? 1.4). In general, higher anisotropies are observed in gneisses (mean azimuth factor 2.8), lower anisotropies in amphibolites (mean azimuth factor 1.3). Examples of isotropic and homogeneous samples, as well as anisotropic and heterogeneous samples are also presented.     

ELECTRICAL SOUNDING ON THE WATER SURFACE AT KHOR KUNDI EL-BAHARI IN EGYPT*

Electrical resistivity sounding was attempted with success in 1960 on the surface of the Nile water in Khor Kundi El-Bahari, the starting place for the construction of the offset channel of the High Dam. The method was applied to determine the depth to the upper surface of the granite below the alluvium and Nile water. The success of the method conducted at two stations in the Khor is attributed to the favourable geological conditions of the section which consists of nearly homogeneous layers besides the good earthing conditions of electrodes dipped in water. The high resistivity contrast between water and granite facilitates interpretation of sounding curves. Factors interfering with the results of interpretation are mentioned.     

Two-level magnetovariational measurements for the determination of underground resistivity distributions1

We investigate, from a theoretical point of view, the possibility of performing marine two-level magnetovariational measurements. An apparent resistivity function is denned and calculated after solving the differential equation governing the behaviour of the natural magnetic field variations inside a one-dimensional earth. In order to generalize the problem, a frequency-dependent resistivity is assumed to characterize the layers and the distortions caused by the polarization effects are carefully analysed. The computation of three-layer amplitude and phase diagrams for the apparent resistivity function shows that, in the case of an intermediate polarizable layer, sandwiched between a non-dispersive overburden and substratum, the H-type sequence results are the most affected by the dispersion phenomenon as it occurs in magnetotellurics. Finally we consider the problem of the sensitivity of the method, since, in practice, it requires top and bottom sensors separated by a vertical finite distance. It is found that in the higher-frequency range, due to the strong attenuation of the relative components of the field, the depth of the bottom sensor must be small enough to guarantee detectable signals, well above the full-scale resolution of the acquisition system. Conversely, in the lower-frequency range such a depth must be large enough to allow the difference between the top and bottom signals to be above the same recording sensitivity threshold.     

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Electrical resistivity tomography is a non-linear and ill-posed geophysical inverse problem that is usually solved through gradient-descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two-dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high-dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non-linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high-frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un-reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient-based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.     

Laterally constrained inversion of helicopter-borne frequency-domain electromagnetic data

Helicopter-borne frequency-domain electromagnetic (HEM) surveys are used for fast high-resolution, three-dimensional resistivity mapping. Standard interpretation tools are often based on layered earth inversion procedures which, in general, explain the HEM data sufficiently. As a HEM system is moved while measuring, noise on the data is a common problem. Generally, noisy data will be smoothed prior to inversion using appropriate low-pass filters and consequently information may be lost.For the first time the laterally constrained inversion (LCI) technique has been applied to HEM data combined with the automatic generation of dynamic starting models. The latter is important because it takes the penetration depth of the electromagnetic fields, which can heavily vary in survey areas with different geological settings, into account. The LCI technique, which has been applied to diverse airborne and ground geophysical data sets, has proven to be able to improve the HEM inversion results of layered earth structures. Although single-site 1-D inversion is generally faster and — in case of strong lateral resistivity variations — more flexible, LCI produces resistivity — depth sections which are nearly identical to those derived from noise-free data.The LCI results are compared with standard single-site Marquardt–Levenberg inversion procedures on the basis of synthetic data as well as field data. The model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the resolution of deep horizontal conductors in one-dimensional inversion results. The field data example comprises a wide resistivity range in a sedimentary as well as hard-rock environment.If a sufficient resistivity contrast between air and subsurface exists, the LCI technique is also very useful in correcting for incorrect system altitude measurements by using the altitude as a constrained inversion parameter.     

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.