ON SOME RESISTIVITY LOG INTERPRETATION CHARTS*

The paper relates primarily to the borehole and the side bed correction charts for Latero-logs 3 and 7. Versions of some of these charts published by different companies—or even by the same company in different years—exhibit significant variations. Usually, such publications do not contain adequate information on how the charts were constructed and do not explain why discrepancies occur. Because of these reasons, an attempt has been made in this paper to reconstruct the borehole correction chart for Laterolog 7 and the shoulder bed correction charts for Latero-logs 3 and 7. For the latter two, the results found differ substantially from those published earlier. The paper demonstrates how departure (response) curves and correction charts for the lateral and the Laterolog 7 sondes can be computed from those for the normal sonde. An apparent resistivity formula is suggested for Laterolog 7 in which all currents that exist in the ground at the time of measurement and that produce the signal are monitored and used. Response curves and correction charts for Laterolog 7, based on such a formula, are presented as illustrations.     

NEW RESULTS IN RESISTIVITY WELL LOGGING*

Two independent theoretical analyses show that, spacing for spacing, the two-electrode normal device investigates deeper than the seven-electrode focused Laterolog 7. The first analysis, published earlier, compares the radii of investigation of the different sondes from the portion of the ground that contributes maximum to, or fifty percent of, the measured signal. The second relates to the nature of the departure curves for the two sondes for an infinitely thick resistive formation pierced by a bore hole. With increasing spacing, the apparent resistivity for the normal device rises much faster and asymptotically approaches the true resistivity much earlier than that for Laterolog 7. These two analyses also prove that, in a Laterolog 7, the radius of investigation increases as O₁O₂ decreases relatively to A₁A₂. Since any complex point electrode system is equivalent to a superposition of elementary dipoles or two-electrode devices, it follows that no resistivity sonde of discrete point electrodes can have a radius of investigation larger than that for the normal device of the same spacing. Laboratory measurements in a model tank confirm these theoretical results. For thin highly resistive formations we find from theoretical and model studies that the normal device is markedly superior to Laterolog 7 as it gives apparent resistivity values much closer to the true. It has other advantages as well. Thus, our results on the comparative performances of the normal and Laterolog 7 devices are at variance with those published so far since the introduction of Laterolog 7 in 1951. For reasons given in the text, the chief characteristic of Laterolog 7—namely, focusing the current from the central electrode in a thin horizontal sheet into the target formation—does not endow it with any special advantage. The main reason is that the measured potential in a Laterolog 7 is caused not only by the current focused into the target formation but also by the currents from the outer two electrodes which flow, due to the same focusing process, entirely through the adjacent formations and the mud column. Indeed, the contribution to the measured signal by the outer two power electrodes is considerably larger than that from the central.     

LABORATORY RESULTS IN RESISTIVITY LOGGING*

This paper is an experimental extension of the theoretical investigations by Roy (1975) on the relative performances of the Laterolog 7, normal and some other sondes in logging of resistive formations. Only infinitely resistive formations have been simulated and placed in a tank containing tap water (true resistivity 27 Ωm) as electrolyte—representing both the mud column and the adjacent formations. Two sets of laboratory results (Doll 1951, NN 1958, 1969), have been repeated and we find that, for both these sets, the performance of the normal device is by far the superior of the two. In addition, we have studied the effect of varying the spacings A₁A₂, O₁O₂ and AM of Laterolog 7, normal, and two new sondes—Laterolog 4 and modified unipole—for two bore hole diameters in each case. For formation thicknesses less than A₁A₂ or AM, the Laterolog 7 is unsuitable because its response is flat and close to the base-line value. The normal device is more diagnostic, although, in such a case, it registers a trough or a resistivity low even against a resistive formation. For bed thicknesses clearly greater than A₁A₂ or AM, the normal sonde is decidedly superior to Laterolog 7, since its anomalies are sharper and larger. When the formation thickness is equal to or only slightly larger than A₁A₂ or AM, Laterolog 7 is somewhat better as it records a readable positive deflection while the normal does not. However, one must remember that a single run of the conventional resistivity log includes two normals and a lateral at different spacings. Laterolog 4 and modified unipole can in many instances produce better logs than normal, other considerations apart. The results are consistent with our own theoretical predictions and experience in surface resistivity profiling. They do not, however, agree with the prevalent concepts on Laterolog 7 vis-a-vis normal sonde.     

新型贴井壁式阵列方位侧向测井数值模拟与响应特性

在现有侧向测井仪器基础上,提出了一种新型贴井壁式阵列方位侧向测井电极系,该仪器能提供径向和周向方位电阻率测量.该电极系采用贴井壁测量方式,提供5种径向探测深度.利用三维有限元方法模拟了阵列方位侧向测井电极系的井眼影响特性、径向探测特性、纵向分层能力、方位分辨能力,并模拟其对井周地层、水平井非对称泥浆侵入和倾斜地层的响应.在导电泥浆中最大探测深度为1.23m,纵向分辨率为0.3m,可以识别出0.1m薄层,方位分辨率为20°.贴井壁测量时,纵向分辨率不受泥浆和围岩电阻率的影响,能够准确测量井周方位电阻率,较不贴井壁测量具有很大优势,同时利用12条方位电阻率曲线能够反映出水平井泥浆非对称侵入特性,倾斜地层倾角和倾斜方向.     

3D laterolog array sonde design and response simulation

A new three-dimensional laterolog array sonde (3D-LS) is presented. The 3DLS is based on existing high-resolution laterolog array and azimuthal resistivity imaging sondes with radial, longitudinal, and circumferential detection abilities. Six investigation modes are designed using the 3D finite-element method and different investigation depths are simulated based on the pseudo-geometrical factor of the six modes. The invasion profile is described using multi-array radial logs. From the analysis of the pseudo-geometrical factor, the investigation depth of the 3D-LS is about 1.5 m for conductive invasion, which is close to that of the dual laterolog tool but greater than that of the highly integrated azimuthal laterolog sonde. The vertical and azimuthal resolution is also analyzed with the same method. The 3DLS can detect low-resistivity anomalies of 0.5 m thickness and 15° around the borehole for infinitely thick formations. This study lays the foundation for more work on 3D laterolog array sonde for evaluating low-resistivity anomalies.     

THE CONCEPT OF APPARENT RESISTIVITY IN LATEROLOG 7*

It appears that Doll (1951) and N. N. (1958, 1969, 1972) on the one hand, and Roy (1975) and Roy and Apparao (1976) on the other, used different formulas for computing the apparent resistivity for the Laterolog 7 sonde. This would partly explain the contra-dictory nature of LL7 results from these two groups of workers. The first group use a formula that relates the measured potential to a system of currents that are largely fictitious and non-existent in the ground at the time of measurement. The second group, on the other hand, employ a formula that combines the observed signal with the currents that actually exist in the ground and produce that signal. We believe that the second procedure is the right one.     

On the classification of surface geoelectric arrays

We collected approximately one hundred independent geoelectric arrays from published geophysical literature. We have presented them in a systematic way and with a unified notation. The classification of arrays is based on three divalent parameters: “superposition” of measurements, “focusing” of currents and “colinearity” of the array, creating 8 classes of geoelectric arrays. Among the 102 independent arrays we found in the geophysical literature, we managed to classify 92 arrays in the aforementioned way. Ten further techniques fell beyond the proposed classification. The classification we propose may open the way to new geoelectric arrays, hopefully providing improving responses to the infinite variety of field problems we may face. It may bring to daylight, exclusively in a logical way, currently unused arrays. In searching new geoelectric arrays this paper helps to avoid rediscovering the discovered. Although it might be thought that the modern multielectrode systems will supersede all former arrays, such systematization is not only for historical and tutorial interests: some of the “old” arrays can be perhaps built into new multielectode systems, further enhancing their effectivity in the future. Finally, this collection of arrays establishes the possibility of systematic intercomparisons of arrays on the basis of various theoretical or practical aspects.     

FOCUSSED ELECTRICAL RESISTIVITY ARRAYS: SOME THEORETICAL AND PRACTICAL EXPERIMENTS*

The “Laterolog 7′’and the “Microlaterolog’ have been studied theoretically for the case of a conducting halfspace containing a single overburden, using a technique based on the method of images. The results have shown these focussed arrays to be more sensitive to the lower medium (i.e., having greater depth of investigation) than unfocussed ones of the same dimensions, when the “correct’ geometric factor is used. The geometric factor of a focussed electrode array is somewhat involved, and is explained with reference to an ideal focussed array; such an array would pass a measuring current of constant intensity into a fixed geometrical shape of conducting material, irrespective of any layering or any other heterogenities that may be present, using auxiliary current sources of variable magnitude. This concept of a constant amount of current flowing in a beam of fixed geometry and current density, is the basis of focussed arrays, and it is shown that the geometric factor, used to calculate the apparent resistivity, is the one derived when considering the homogeneous case. The value of the constant measuring current, alone, is used to convert the measured potential difference into a resistance, the ratio between this value and the combined intensities of the auxiliary current sources, for the homogeneous case, being incorporated into the geometric factor. Surprisingly good agreement was found between the theoretical models and practical experiments using a focussing seabed resistivity probe which is a substantial modification of the “Microlaterolog”. Both show similar deviations from the ideal case which are explained in terms of refraction at the overburden interface. All experiments indicated that focussed arrays have a greater depth of investigation than similar unfocussed ones for a single overburden, whether it be resistive or conductive.     

Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration

In this paper, we discuss the effects of anomalous out‐of‐plane bodies in two‐dimensional (2D) borehole‐to‐surface electrical resistivity tomography with numerical resistivity modelling and synthetic inversion tests. The results of the two groups of synthetic resistivity model tests illustrate that anomalous bodies out of the plane of interest have an effect on two‐dimensional inversion and that the degree of influence of out‐of‐plane body on inverted images varies. The different influences are derived from two cases. One case is different resistivity models with the same electrode array, and the other case is the same resistivity model with different electrode arrays. Qualitative interpretation based on the inversion tests shows that we cannot find a reasonable electrode array to determine the best inverse solution and reveal the subsurface resistivity distribution for all types of geoelectrical models. Because of the three‐dimensional effect arising from neighbouring anomalous bodies, the qualitative interpretation of inverted images from the two‐dimensional inversion of electrical resistivity tomography data without prior information can be misleading. Two‐dimensional inversion with drilling data can decrease the three‐dimensional effect. We employed two‐ and three‐dimensional borehole‐to‐surface electrical resistivity tomography methods with a pole–pole array and a bipole–bipole array for mineral exploration at Abag Banner and Hexigten Banner in Inner Mongolia, China. Different inverse schemes were carried out for different cases. The subsurface resistivity distribution obtained from the two‐dimensional inversion of the field electrical resistivity tomography data with sufficient prior information, such as drilling data and other non‐electrical data, can better describe the actual geological situation. When there is not enough prior information to carry out constrained two‐dimensional inversion, the three‐dimensional electrical resistivity tomography survey is the better choice.     

ARRAYS AND NOMOGRAMS FOR ELECTRICAL RESISTIVITY EXPLORATION*

A number of electrical resistivity arrays are available to the exploration geophysicist in the conduct of vertical or horizontal profiling. The advantage of using central-type arrays which produce large potential drops, such as the Wenner or the Schlumberger, must be weighed against the ease of acentral arrays such as the polar and equatorial arrays. A series of nomograms has been designed to provide a means of rapid calculation of the potential drop to be obtained by any of the various central and acentral arrays, as a function of apparent resistivity, electrode spacings and available transmitter power. The same nomograms may also be used for approximate computation of the apparent resistivities in routine surveys. However, the accuracy of resistivity calculation is directly related to the accuracy of drawing lines between the scales and hence is rather limited in reduced-size nomograms in this paper.     

Field test to compare 3D imaging capabilities of three arrays in a site with high resistivity contrast regions

The applicability of three kinds of electrode configurations used to delineate a buried horizontal pipe was studied. A 3D resistivity imaging survey was carried out along eight parallel lines using pole-pole, pole-dipole, and dipole-dipole arrays with 1m minimum electrode spacings. Roll-along measurements were carried out to cover a rectangular grid. The 2D and 3D least squares algorithms based on the robust inversion method were used in the inversion of the apparent resistivity data sets. The 2D inversion of data sets could not delineate the orientation and dimension of the subsurface anomalies clearly. To obtain more accurate results, a 3D joint inversion of the pole-pole and pole-dipole data sets was performed, as well as of pole-pole and dipole-dipole data sets. In this case, both horizontal and vertical dimensions of subsurface structures were resolved. The resulting model obtained from each array was compared to those of joint inversion method. The result showed that the horizontal resolution does not improve so much as that in the vertical direction when joint inversion is applied.     

2D电阻率正反演成像在水平和垂直模型上的异常响应研究

2D电阻率成像技术近年来被广泛应用于工程、水文、环境和矿产等领域,在实际应用中它具有多种的装置类型,不同的装置类型对特定的地质情况有不同的应用效果.本文通过采用Wenner、Wenner-Schlumberger和dipole-dipole三种排列装置在一个水平和一个垂直模型上正演模拟和块反演,揭示了不同的排列装置在水平结构和垂直结构的异常响应,并对高阻体和低阻体进行了模拟.结果显示当采用Wenner,Wenner-Schlumberger和dipole-dipole数据采集技术时,不同的模型结构异常响应有明显的不同,三种排列类型对地下低阻体的分辨能力均高于高阻体,Wenner装置和dipole-dipole装置分别对水平层状结构和垂直结构有较好的分辨力,wenner-Schlumberger装置对水平层状结构有好的分辨力,对垂直结构有中等的分辨能力.     

Optimized arrays for 2D cross‐borehole electrical tomography surveys

The use of optimized arrays generated using the ‘Compare R’ method for cross‐borehole resistivity measurements is examined in this paper. We compare the performances of two array optimization algorithms, one that maximizes the model resolution and another that minimizes the point spread value. Although both algorithms give similar results, the model resolution maximization algorithm is several times faster. A study of the point spread function plots for a cross‐borehole survey shows that the model resolution within the central zone surrounded by the borehole electrodes is much higher than near the bottom end of the boreholes. Tests with synthetic and experimental data show that the optimized arrays generated by the ‘Compare R’ method have significantly better resolution than a ‘standard’ measurement sequence used in previous surveys. The resolution of the optimized arrays is less if arrays with both current (or both potential) electrodes in the same borehole are excluded. However, they are still better than the ‘standard’ arrays.     

ON THE IMPROVEMENT IN PENETRATIO ACHIEVED BY USING EXTENDED MARINE SOURCE ARRAYS*

In dealing with the problem of large amplitude multiple reflections arising from a hard water-bottom, it has been found that the use of extended source array techniques resulted in a considerably better penetration than that obtained using either computer simulated long arrays or the conventional air-gun array systems. The purpose of this paper is to use the concept of the array directivity factor in discussing the reason for the improvement in penetration achieved by using extended marine source arrays. Examples are given showing that the low frequency power radiated within the so called “penetration window” can be increased by a factor of two by choosing the correct spacing of the point sources forming the extended array. It is concluded that to ensure that most of the low frequency energy is concentrated within the penetration window to achieve deep penetration, a source array with spacing comparable with the wavelength is required.     

Near surface geophysical surveys with a high frequency mutual impedance measuring system

Relationships for the mutual impedance of horizontal coplanar, vertical coplanar, perpendicular and vertical coaxial loop antenna arrays operating at a high frequency, located over a layered conducting medium, have been derived. The relationships take into account the occurrence of displacement currents in both the free space and the conducting medium. The relations can be used for calculating the earth parameters in geophysical prospecting. The use of high frequency antenna array makes it possible to determine distributions of apparent resistivity as well as apparent electrical permittivity. The potential application of the measurements of mutual impedance of loop antennas operating at a high frequency to the geophysical examinations is presented. The measuring system developed for this purpose is described. A simple method of interpreting the mutual impedance measurements to obtain the traces of apparent resistivity and apparent permittivity of the investigated earth is given.     

THE USE OF A SQUARE CONFIGURATION IN RESISTIVITY PROSPECTING *

Consideration is given to the use of a configuration of four electrodes set in a square array for resistivity measurements. It is found that, by passing current successively between different pairs of electrodes, an apparent resistivity can be determined which is both more sensitive to the position of the array centre and less dependent on orientation than the measures usually obtained with colinear arrays of electrodes. At the same time the observations made enable the degree of the departure of local conditions from conditions of lateral homogeneity to be assessed. Theoretical and practical examples of the use of this electrode system are given and the use of the system both as a tool in mapping and in depth investigations is considered. It is shown that provided electrode spacings are suitably arranged the results of a probe carried out using the square array can be interpreted by conventional methods. The system is shown to have particular advantages in the investigation of lateral resistivity variations and the reduced dependence on orientation makes possible the recasting of interpretation data in an orientationally invariant form with a consequent drastic reduction in the number of type curves required for a particular problem.     

方位梯度电极系的正反演

针对环井周的非均质地层模型,利用三维有限元方法模拟了方位梯度电极系的测井响应．结果表明,在非均质程度比较小的情况下,各个方位上的响应之间差别不大,与真实的电阻率分布差别也不大;反之,则差别很大．其特点是所测得的响应远远低于较高的真电阻率值,而接近较低的真电阻率值．因此,有必要对测井响应进行校正．考虑到传统的校正方法的弊端,本文利用非线性反演方法求取真实的电阻率分布,数值模拟的结果表明了此方法的可行性．     

INDUCED POLARIZATION RESPONSE OF A HORIZONTALLY MULTILAYERED EARTH WITH NO RESISTIVITY CONTRAST*

The induced polarization response of a horizontally multilayered earth with no resistivity contrast can rapidly be calculated on a desk calculator or minicomputer for any electrode array. The formulation is a simple series summation of the products of weighting coefficients and the true induced polarization responses for each of the layers. The coefficients are directly derivable from the corresponding resistivity model. This series approach to IP formulation was originally described by Seigel but has not been treated extensively in the present-day geophysical literature. This method can be applied to either time or frequency domain induced polarization measurements. Once the coefficients are known, apparent induced polarization response can readily be obtained by judicious substitution of known, suspected, or assumed values of the true induced polarization of each layer. Basic formulation is presented for the IP potential coefficients (pole-pole or two array) with no resistivity contrast between the layers. From these coefficients, response of any number of layers for any electrode array can be obtained by suitable differentiation. Some examples of Wenner array for a three-layered earth and dipole-dipole array for a four-layered earth are used to illustrate the application. The results of this technique are valid for many natural situations of modest resistivity contrast. However, they definitely cannot be used if there are highly contrasting resistivity layers present. Such an approach is conceptually simple and is useful for survey planning, checking or setting the “depth-of-penetration”of a given array. For field induced polarization data that fits reasonably well to the no-resistivity-contrast model, this simple approach facilitates quantitative interpretation.     

RESISTIVITY AND IP MODELING OF THE THREE-ARRAY DOWN-HOLE PROSPECTING TECHNIQUE*

The resistivity and induced polarization responses due to a number of IP targets for a down-hole three-array have been calculated numerically. The IP targets are approximated by triangle-faceted polyhedra; number and size of the facets are limited by the numerical procedure. Despite this limitation a number of profiles have been obtained for a sphere, lens, prolate spheroid and thin dipping slab. The profiles obtained do not differentiate between the shapes of the IP targets, but depend upon the vertical extent of the target within the search-radius of the borehole. The type curves produced could be of use for preliminary interpretation and in the field for planning the next stages of a geophysical survey. The lateral and vertical search radii of the borehole are increased by the use of such an array. For the bodies used it is estimated that the search radii are extended by 2.0 dipole units.     

基于电阻率敏感性函数的随钻电磁波测井探测特性研究

为研究地层电性变化时不同区域对电磁波测井响应的贡献分布,从响应信号对地层参数求偏导的角度,给出一种新的电阻率敏感性函数定义,引入模式匹配法对纵向成层、径向非均匀介质敏感性分布进行快速模拟;通过对敏感性函数纵、横向积分给出了单发双收线圈系纵、横向探测范围,研究了井眼、频率、背景地层电阻率等对探测特性的影响.结果表明:敏感性函数能够定量表征响应对地层纵向与径向微观与宏观敏感性,幅度比与相位差敏感性分布形态类似,幅度比较广较深,而相位差分辨率高,敏感范围小;敏感性函数进行径向积分后可表征仪器的探测深度,与伪几何因子对比达到了同样的效果;背景地层电阻率在1~100Ωm变化时,工作频率2 MHz下幅度比探测深度约为0.6~2.3m,相位差为0.3~0.8m,幅度比50%纵向积分敏感性层厚约为0.3~1.6m,相位差约为0.2~0.6m;异常体与背景地层电阻率对比度在1~50变化时,引起的探测深度与敏感性层厚差异约为0.1~0.2m,远小于地层电阻率的影响.