DEPTH OF INVESTIGATION IN RESISTIVITY METHODS USING LINEAR ELECTRODES *

Depths of investigation for normal (bipolar) and focusing (unipolar) linear electrode arrays have been computed following the method given earlier (Roy and Apparao 1971) both in homogeneous and layered earth. The focusing arrangement is found to be superior to normal arrangement both in regard to depth of investigation and zone of uniform depth of investigation. This analysis holds good in layered media too. Further, the depth of investigation increases with the increase in the length (2M) of the electrode and reaches a limit, 0.29L for normal and 0.50L for focusing, when the electrode attains an optimum length to satisfy the infinite condition. This optimum length of the electrode is six times the distance L of the observation point from the electrode for normal and about ten times for focusing. A contour diagram for contributions of individual ground elements to the total signal measured at the centre of focused system is also discussed.     

AIRBORNE RESISTIVITY MAPPING USING A MULTIFREQUENCY ELECTROMAGNETIC SYSTEM*

Airborne electromagnetic methods are most commonly used in mineral exploration. However, new developments, such as multifrequency capability and digital on-board field recording, as well as improvements in instrumentation resulting in high signal-to-noise ratios in recorded data, have made their application in geological mapping possible. A three-frequency airborne EM survey carried out over an area northwest of Timmins, Ontario, was interpreted in terms of thickness and resistivity of the layers of a two-layer earth section. Since both in-phase and quadrature components are measured, this provides six independent parameters at each point in space. Based on prior geological information and a preliminary interpretation of the field records, two two-layer models of the subsurface seemed to be appropriate for most of the survey area. An automatic computerized interpretation procedure was devised to interpret the field data at each point in terms of thickness and resistivity parameters of those two models. When the geology is more complex, the data do not fit the models and no interpretations are made. Two maps illustrating the variation of the resistivity and the thicknesses of the layers were constructed from the interpreted data. These maps agree with the known geological information about the distribution of glacial clay in the area. Areas where the layered models do not fit are known to be areas where the geology is complex with a large number of dykes and other lateral inhomogeneities. The study shows that multifrequency airborne EM surveys can be very useful in geological mapping over inaccessible terrain and can significantly help the mapping geologist where outcrops are scarce.     

MODEL TANK EXPERIMENTS ON RESOLUTION OF RESISTIVITY ANOMALIES OBTAINED OVER BURIED CONDUCTING DYKES — INLINE AND BROADSIDE PROFILING*

Model tank inline resistivity profiles with Wenner and two-electrode systems obtained over two vertical, parallel, infinitely conducting dykes submerged in water show that the two-electrode resistivity anomalies resolve better than the four-electrodes Wenner. anomalies. In contrast, the broadside resistivity anomalies obtained with a Wenner configuration resolve much better than those obtained with two-electrode configuration over an identical ground structure.     

AN APPROXIMATE METHOD OF RESISTIVITY SOUNDING INTERPRETATION*

An approximate method of interpretation of resistivity sounding is presented, which may be described as a very crude manner of application of the exact direct interpretation method. The accuracy of this method is fairly low, the errors being in the order of 25%. The method is very fast in application and well suited for application to multilayer cases. The main advantage of the method is that it is in close and clear relation to the exact theory.     

AN ANALYSIS OF EQUIVALENCE IN RESISTIVITY SOUNDING*

A mathematical analysis is given of the phenomenon of equivalence in resistivity sounding, which is based upon the properties of the raised kernel function. Analysis of this function instead of the apparent resistivity function is justified because, as has been shown in a previous publication, variations in the apparent resistivity function lead to variations in the raised kernel function with relative values of the same order of magnitude The expression for the raised kernel function is expanded into a Mac Laurin series. Equivalence can occur only if the second order term of this series is negligible. The coefficient of the first order term depends on the resistivity and the thickness of the layer under consideration. There is an infinite set of combinations of values for these two quantities, for which the coefficient of the first order term has the same value. All these combinations represent equivalent layer distributions.     

波前重建法折射成像及应用研究

根据实际工作需要对传统的地震折射资料解释方法的适用范围进行了讨论,指出了传统折射资料解释方法所存在的问题。采用重建波前的方法进行折射成像,通过改进震源函数,并在反演过程中使用有限差分技术解程函方程,进行波场外推,从根本上解决了传统折射资料解释方法存在的问题,计算精度高,速度快。通过理论模型和实际资料的对比计算和验证,效果良好。     

EARTH CRUST INVESTIGATION USING CONVERTED WAVES*

The conditions for creating and recording converted waves in the area of the Panonien basin are considered. Comparison between the characteristics of converted waves recorded in the field and characteristics of converted waves calculated for the model which approximately corresponds to lithophysical conditions of the area is made. The comparative interpretation of the crustal structure along the profile, using different types of waves, is given.     

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.     

A SOLUTION OF THE DIPPING INTERFACE PROBLEM USING THE SQUARE ARRAY RESISTIVITY TECHNIQUE*

Apparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array. In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array. Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.     

A BOREHOLE MAGNETOMETRIC RESISTIVITY EXPERIMENT*

A borehole magnetometric resistivity (MMR) experiment is described in which an attempt is made to determine the extent and orientation of zones of fissuring within an otherwise massive sequence of carboniferous limestone. The region under investigation lies beneath a landfill site and the main parameter of interest is the direction of flow of ground water, which will be influenced by the orientation of the faults or fissures within the rock. The MMR method possesses some extremely advantageous features for application to hydro-geological problems of this kind. The method is sensitive to electrical current channelling within an otherwise relatively resistive medium, and the detection of the magnetic field within the borehole does not depend upon electrical contact of the receiver with the ground. Consequently, the method can be used in dry or plastic-cased boreholes. A direction of maximum electrical current flow is deduced from the MMR data which coincides with the predominant direction of jointing within the region. We are most grateful to the Water Research Centre, Medmenham, Berkshire, for supporting this research and particularly to Dr M. Fleet and Mr K. Beesley for their help and advice.     

ETINCELEURS MULTIELECTRODES A HAUTE RESOLUTION*

HIGH RESOLUTION MULTIELECTRODES SPARKERS Multielectrode sparkers can bring a considerable improvement of high resolution seismic. A 2 meter resolution and a penetration of about 150 meters can be obtained with 1000 joule sparker with several hundred electrodes. Several records are shown.     

AN ELECTRICAL RESISTIVITY PROFILE IN HAWAII WITH NOVEL ELEVATION CORRECTION*

In order to locate relatively optimum sites for drilling exploratory holes for fresh water, an electrical resistivity survey was conducted along the new Mahukona-Kawaihae Road on the west flank of the Kohala Mountain. Two resistivity soundings made at the same stations, using the Schlumberger electrode configuration, determined an a spacing of 275 feet for horizontal profiling with the Wenner array. The correlation coefficient of the elevation to profile data was 0.41. A procedure for removing elevation effect from observed apparent resistivity was developed. Based on the reduced resistivity profile, four relatively optimum sites for additional exploration, such as by drilling, are specified. There is no specific interpretation of the data that can definitely indicate the occurrence of large underground reservoirs of fresh water anywhere along the profile. This is because the interpretation of horizontal profiling data is essentially relative and not absolute.     

视电阻率法测矿井岩石应变实验的初步总结

本实验目的是揭示受力岩石中应力与电阻率的关系,以验证形变电阻率法能否用于地震预报工作。 实验在一离地面深100多米、正在开采的矿坑中进行。视电阻率的测量用四极对称装置,干电池供电,最高电压13.5伏,最大观测均方误差为1—2％。五个测点上贴了电阻丝应变片,以测定岩石主应变的大小、方向以与视电阻率极大值进行对比。应变计的读数值最大误差不超过3—4με。实验中考虑了岩石有严重极化现象的影响。 实验的初步结果表明:岩石的视电阻率和应变值的变化,总趋势相当一致,所以用形变电阻率法来测量应变是极有希望的。对1973年在四川省南坪发生的几次地震进行震例分析的结果,得到同样的结论。 文中对实验中存在的问题,也作了一些讨论。     

DEPTH OF INVESTIGATION IN WENNER,THREE-ELECTRODE AND DIPOLE-DIPOLE DC RESISTIVITY METHODS*

Using a method and definition given earlier (Roy and Apparao, 1971), this paper computes the depths of investigation in homogeneous ground for (a) the Wenner α, β and γ configurations, (b) the three electrode system and (c) the dipole-dipole arrangements when the dipole lengths are not infinitesimally small. The results for (a) and (b) have been summarised in a table, while those for (c) are shown as contour diagrams. In all the dipolar arrangements examined in this paper, except the equatorial, the depth of investigation decreases (and the vertical resolution increases) with increase in any or both of the dipole lengths. For the equatorial set up, this decrease (or increase) is very small.     

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.     

视电阻率法测矿井岩石应变实验的初步总结

本实验目的是揭示受力岩石中应力与电阻率的关系,以验证形变电阻率法能否用于地震预报工作。 实验在一离地面深100多米、正在开采的矿坑中进行。视电阻率的测量用四极对称装置,干电池供电,最高电压13.5伏,最大观测均方误差为1-2％。五个测点上贴了电阻丝应变片,以测定岩石主应变的大小、方向以与视电阻率极大值进行对比。应变计的读数值最大误差不超过3-4με。实验中考虑了岩石有严重极化现象的影响。 实验的初步结果表明:岩石的视电阻率和应变值的变化,总趋势相当一致,所以用形变电阻率法来测量应变是极有希望的。对1973年在四川省南坪发生的几次地震进行震例分析的结果,得到同样的结论。 文中对实验中存在的问题,也作了一些讨论。     

INVESTIGATION OF SOME NON-LINEAR PHENOMENA OF INDUCED POLARIZATION USING A PHYSICAL-AND-MATHEMATICAL MODEL*

The electrical behaviour of a polarizable sample formerly studied (Time-Domain) through both the classical and the condenser methods is simulated using the theoretical responses given by a three dimensional physical-and-mathematical model, which has been proposed in a previous paper by one of us on the basis of certain hypotheses. The apparent capacitance responses of the sample are qualitatively simulated in order to tackle the problem under this point of view; moreover, an attempt to obtain a quantitative simulation of experimental data within the limits of the present reliability of the model, using theoretically obtained Model Master Curves characterized by dimensionless parameters, is done. This research is carried out in the frame of a broader study referring to a possible scheme of simulation of the so-called induced ionic polarization, concerning a number of idealized pseudo-reversible, potentially irreversible, non-linear phenomena.     

PROGRESS IN THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDINGS: AN ALGORITHM*

An algorithm is presented for the direct interpretation of resistivity sounding data. The algorithm is based on the method of successive reductions to lower boundary plane of the resistivity transform function. A novel aspect of the algorithm is that error limits are assigned to the initial values of the resistivity transform, and these error limits are carried through in all the subsequent computations. The width of the error range is then used as the basis for assigning weight factors in the final computation of thicknesses and resistivities of the layers. The errors in the resistivity transform derived from the solution given by the algorithm are usually not more than twice as large as those in the original data.     

AN INTERACTIVE COMPUTER/GRAPHIC-DISPLAY-TERMINAL SYSTEM FOR INTERPRETATION OF RESISTIVITY SOUNDINGS*

A fast computer-procedure giving the apparent resistivity curve as well as the partial derivatives with respect to the layer-parameters is presented. It is based on the linear filter method developed by D. P. Ghosh in 1971. The sampling frequency is 10 points per decade, and 3 decades are covered. The maximum relative error is less than 10^?3, and in most cases orders of magnitude smaller. The computation time on a CDC 6400 for one curve given in 30 points ranges linearly from .17s for a two-layer case to .36s for a ten-layer case. The procedure is used to plot master curves interactively on a graphic display terminal (Tektronix 4010) connected to the CDC 6400. By trial-and-error adjustments a set of layer-parameters is found, giving essentially the measured curve.     

RESISTIVITY INVERSION WITH A PRIORI INFORMATION*

An inversion algorithm for interpreting electrical soundings based on a probabilistic treatment of the a priori information not only includes all the previous ones, but allows consideration of the constraints between the parameters. By introducing the a priori information, a unique solution among all the equivalent ones is obtained which is coherent with the geological background. Several examples dealing with the usual problems in the automatic interpretation of the electrical soundings illustrate the advantages of this algorithm. Good results are obtained with this method.