THE ELECTRICAL CURRENT PATTERN INDUCED BY AN OSCILLATING MAGNETIC DIPOLE IN A SEMI-INFINITE THIN PLATE OF INFINITESIMAL RESISTIVITY*

Several papers have been published in which the electromagnetic anomalies are described that are produced by conductive ore bodies of different shapes. No publications are available, however, in which the electrical current pattern is described that is induced in these ore bodies. Yet an insight in this electrical current pattern would be valuable in order to assess the possibilities of different electromagnetic techniques, for instance with regard to the determination of the dip and of the depth extent of plate shaped ore bodies. In the present paper computations are given of the electrical current pattern induced by an oscillating magnetic dipole in a semi infinite plate shaped orebody of infinitesimal thickness, in which the penetration depth of the current is infinitesimal to a higher order than the thickness of the plate. The computations are based upon an equation derived by Wesley for the magnetic field produced in these conditions, combined with the relation between the electrical current density in a laminar sheet and the magnetic field produced by this current at the surface of the sheet. The results of the computations show that, if the horizontal distance between the dipole source and the sheet is sufficiently small, the maximum current density of the return current may occur at a depth below the upper edge of the sheet which is appreciably smaller than the depth of the upper edge of the sheet below the surface. The depth of the return current becomes large when the horizontal distance between the source and the sheet is large.     

THE VERTICAL MAGNETIC FIELD OF AN ALTERNATING CURRENT DIPOLE FOR HORIZONTALLY STRATIFIED MEDIA *

For the computation of the vertical component H_z of the magnetic field of a horizontal A.C. dipole lying on the earth's surface, a recurrence formula is presented for a horizontally stratified half space, to obtain the (n+ 1)-layer case from the w-layer case. By means of several computed diagrams for the two-layer case, H_z can be determined for different ratios of conductivity of the subsoil and that of the overburden. Thereby the distance from the dipole as well as the layer thickness h are expressed in terms of the wave length A of a plain wave in the overburden. Assuming a sufficiently large conductivity difference, the results show that evidence about the subsurface conditions can be obtained if the distance between the measuring coil and the dipole is of the order of A/3, and if the thickness h of the layer varies within the range A/100 < h < A/6. As an example for the 3-layer case, a nonconducting intermediate layer is assumed.     

A NOTE ON THE INTERPRETATION OF MAGNETIC ANOMALIES OF INFINITE THIN SHEETS BY USING RELATION FIGURES*

The concept of relation figures is utilized in the case of a thin infinite sheet for identification and determination of the causative source geometry, and its various parameters. The plot of ?T versus ?V is a conic, the plots between the respective symmetric components and the respective asymmetric components are straight lines, and the resulting diagram between the first horizontal versus the first vertical derivative of either ?T or ?V is a cardioid. The authors are grateful to Shri V. Babu Rao and Dr R. K. Verma for their encouragement. They would like to thank the Director of the N. G. R. I. for permission to publish this paper. The neat drawing of Sri P. Sundara Rao is appreciated.     

谐变磁偶极激发下层状介质中球的电磁响应

本文在前人基础上,从理论计算角度研究了两层大地下球形导电体的偶极激发音频电磁场。探讨了电模式、磁模式场的耦合及其意义,并列出了剖面数据和频率响应数据,以适应移动源音频电磁法的实际需要。     

谐变磁偶极激发下层状介质中球的电磁响应

本文在前人基础上,从理论计算角度研究了两层大地下球形导电体的偶极激发音频电磁场。探讨了电模式、磁模式场的耦合及其意义,并列出了剖面数据和频率响应数据,以适应移动源音频电磁法的实际需要。     

THE ROTATING CURRENT DIPOLE METHOD - A FIELD TEST*

The outputs and neutral of a three phase generator are converted to six amplitude variable phases in a 3.5 kW 400 Hz transmitter. These outputs are applied to six groundimplanted electrodes, producing a horizontally rotating current dipole in the subsurface. An investigation of the radiation pattern in the vertical magnetic field indicates, in symmetry and closure control, considerable advantages in this form of galvanic energization. These include optimization of inductive anomalies and the ability to interpret phase observations on a spatial basis in depth sounding and orebody location.     

THE INDUCED POLARIZATION RESPONSE OF A THIN HIGHLY-CONDUCTIVE ORE BODY*

Consider a lamina of ore of thickness 2t whose electrical resistivity p₂ is much smaller than the resistivity p₁ of the surrounding host rock. The induced polarization response of such an ore body is investigated under the assumption that it arises from the variation of p₂ with the frequency of measurement. Let p2l and p2h be the resistivities of the ore-body for the low and high frequencies of measurement and L a length of the order of the distance between the transmitting electrodes. A theory is developed under the assumptions that each of the quantities t/L, p2l/p1, p2h/p1, Lp2l/2tp1, and Lp2h/tp1 is small. The main conclusion is that the frequency effect parameter P is given approximately by P=cL(p2l ? p2h)/2tp1, where the constant c is independent of t, p2l, p2h, and p1. Thus for a family of similar ore bodies having differing values of t, P will be the larger the smaller t. Detailed results are given for a semi-infinite submerged dipping dyke and the two dimensional Wenner array.     

ELECTRICAL POTENTIAL DUE TO A POINT CURRENT SOURCE OVER AN INHOMOGENEOUS ANISOTROPIC EARTH*

A mathematical expression for potential of a direct current point source in an inhomoge-neous anisotropic earth is derived. The coefficient of anisotropy is given by f= (σ_r/σ_z), where σ_r and σ_z are the conductivities parallel and perpendicular to the bedding plane. It is assumed that σ_z varies with depth, whereas σ_r varies transversely. This potential may be useful in interpretation of geoelectrical data in specified geological situations. Master curves for Wenner and Schlumberger configurations are presented     

QUASI-STATIC ELECTROMAGNETIC FIELDS OF A HORIZONTAL ELECTRICAL DIPOLE ON THE SURFACE OF A POLARIZABLE HALF-SPACE *

The expressions for quasi-static electromagnetic fields of a horizontal electrical dipole placed on the surface of a polarizable half-space have been derived for low and high values of induced polarization parameter and presented along with numerical results. It has been observed that the polarity of the mutual impedance function is negative for low values and positive for high values of the induced polarization parameter in the entire time domain, whereas the induced voltage function is positive for low values of induced polarization parameter and becomes negative for high values. In the case of low values of induced polarization parameter the transient electromagnetic field in the beginning increases with time, later on it starts to decay with time. The present study shows that the decay rate of electromagnetic field is highly dependent upon the induced polarization parameter. In the light of the present study the conductivity of the polarizable medium may be determined more accurately.     

DETERMINATION OF ELECTRIC ROCK PARAMETERS FROM THE FIELD STRUCTURE OF A MAGNETIC DIPOLE*

In the theoretical part of the present paper, formulas have been analyzed for a magnetic dipole in a homogeneous and unbounded medium. The magnetic field is elliptically polarized in the region between the quasistatic zone and the far field. Since the position and the shape of the polarization ellipses depend on the complex wave number, k, it is possible to determine k by measuring the polarization ellipses. From k, the conductivity and the dielectric constant of the medium are easily calculated. The functions required for the measuring method have been computed and plotted in graphs. In the experimental part it was examined how far the theory may be applied to measurements of propagation through rock at frequencies ranging from 100-1000 kHz. These measurements showed that reasonably defined mean values of rock parameters can be given only if the deviations of the field from the theoretically expected field are not too high. These deviations have been named field distortions and have been examined by means of statistical methods (variance ratio tests). Gallery cavity and inhomogeneity or anisotropy of the medium account for these distortions.     

ON THE POSSIBILITIES OF DETERMINING DIP IN MAGNETIC INTERPRETATION WITH THE INFINITELY DEEP PLATE MODEL*

Dip and magnetic susceptibility of very deep magnetic plates can be estimated approximately from either vertical, horizontal or total field measurements. A general accuracy of 2–5 degrees is easily obtained, if the other plate parameters, most notably horizontal position of the plate, are precisely determined. For reliable interpretation, measurements around the anomaly maximum or on the dip-side flank of the anomaly should be preferred. The depth extent of the plates must be great, some ten times the plate width at least. The method is best suited to form a part of a plate interpretation scheme, where the other plate parameters are found by some other suitable means. The method can be applied to a simultaneous determination of dips of several plates, but because of its error sensitivity an iterative formulation should then be preferred.     

AN APPROACH TO THE IDENTIFICATION OF FINE SEDIMENTS BY INDUCED POLARIZATION LABORATORY MEASUREMENTS*

Time-domain-induced polarization (IP) laboratory measurements were performed on about 200 fine sediment samples with varying water content. The results permitted an analysis of IP properties of clays, loams, silts, and sands. Particular emphasis has been given to the analysis of the chargeability m as a function of lithotype and the water content. By analyzing decay curves, a new parameter was identified. It is a statistically specific characteristic of the lithotype and is independent of the water content. Therefore, it provides a diagnostic parameter for lithotype identification. In association with the values of chargeability and electrical resistivity, this parameter permits a reliable evaluation of water content and yields useful information about the porosity and permeability of the lithotype.     

RESPONSE OF A TWO-LAYER GROUND TO AN INFINITE CABLE CARRYING ALTERNATING CURRENT WITH REFERENCE TO TURAM ANOMALIES *

A formula is developed for the vertical magnetic field due to an alternating current passing through a long horizontal cable placed on a two-layer ground. The variations of the phase and amplitude ratio of the vertical field, along profiles perpendicular to the cable line are investigated. Within the limits encountered in practice, it is found that if the upper layer is conductive, as compared to the lower layer, the phase may vary appreciably whereas the amplitude ratio changes as in the case of vacuum.     

AN ITERATIVE METHOD FOR THE SOLUTION OF ANON-LINEAR INVERSE PROBLEM IN MAGNETIC INTERPRETATION*

A method is presented for determining the lower surface of a two-dimensional body producing a magnetic anomaly when its upper surface and the intensity of magnetization are given. The magnetization vector is assumed to lie along a specified direction but the sense of magnetization may be different in different vertical sections of the body and may be regarded as unknown. The method is illustrated using the computed anomalies of some theoretical models.     

INDUCTION ANOMALY DUE TO AN ELONGATED COVERED ORE-ZONE EXCITED BY A LONG CURRENT CARRYING CABLE*

A detailed analysis of the electromagnetic anomaly due to an elongated mineralized zone of low resistivity in presence of a fixed-transmitter (a long cable carrying an, alternating current Ie^Iωt) is presented where (i) the host rock is not highly resistive and might contain some disseminated mineralization, (ii) the ore-body has an inhomogeneous conductivity, (iii) there is a contrast in magnetic properties of the ore-body and the host rocks, and (iv) source is close to the conducting system i.e., anomalous zone is lying shallow. The numerical computation of the generalized analytical expressions have been made. The selective screening behaviour of the cover is delineated and suitable frequency ranges for maximum detectability of a covered conductor have been obtained. A paradoxical decrease of the in-phase component of the response function with the increase of the core conductivity has been found for large conductivities of the cover. For moderate values of response parameter the inhomogeneity in the conductivity is found to significantly affect the induced field. The present analysis of the various features of the secondary field will aid to the existing interpretation sensitivity of the induction prospecting data for porphyry conducting ore deposits with zonal wall-rock alteration and sulphide distributions.     

ON THE ELECTRICAL BEHAVIOUR OF A POLARIZABLE SAMPLE STUDIED BY THE NORMALIZED TIME-INTEGRAL AND BALLISTIC METHODS*

In this paper the experimental data obtained studying the decay of a sample of pisolitic bauxite both by a ballistic method and the normalized time-integral procedure are compared. This comparison allowed me to note two peculiarities. First, the apparent capacitance of the sample, as well as its normalized time-integral, seems to show a characteristic behaviour within the same interval of the charging time. Secondly, while the apparent capacitance plotted versus time (measured from the energization interruption instant) appears to assume values which seem to tend towards asymptotic value of the apparent capacitance, it is to be noted instead that in these circumstances the relative normalized time integral shows no tendency to reach any limiting value.     

A CONTRIBUTION TO THE QUANTITATIVE ERROR ANALYSIS IN MAGNETIC AND GRAVIMETRIC INTERPRETATION *

The paper discusses the smallest obtainable parameter errors (variances) in the interpretation with the least-squares method. Useful approximations of the sum of squares contained in the minimum error expressions are obtained using results of numerical integration. The approximations lead to especially simple results for long interpretation profiles, when the parameter errors are proportional to the square root of the point separation. Formulae are developed and examples shown for minimum error calculation in gravimetric interpretation with the cylindrical model and in magnetic interpretation with the two-dimensional plate model. Smallest errors are obtained when the interpretation profile is chosen around the anomaly maximum except for dip and depth extent interpretation of magnetic plates.     

A TWO-LAYER GROUND IN THE FIELD OF AN INFINITELY LONG CABLE*

When the fixed-source electromagnetic method is applied the quantities measured are influenced by the resistivity of the whole environment. This occurs mostly in the cases of measurements in areas with prevailing high resistivities, and if a weathered layer with considerably lower resistivity than that of the original rock has been formed near the surface. For this reason it is important to be acquainted with the properties of the two-layer ground with an overlying conductive layer. In the present paper attention will be drawn to theoretical calculations connected with the field of the homogeneous ground and that of the two-layer ground.     

THE SCATTERING OF SH-CHANNEL WAVES BY A FAULT IN A COAL SEAM*

The imaging of faults in coal seams by the in-seam seismic method has now become standard practice. In the UK over 300 surveys have been undertaken and the technique is now part of the exploration arsenal of colliery planners. From these users comes the pressure for two major improvements, namely an increase in range and target identification. This paper is directed towards the latter problem. It has long been recognized that the reflected channel waves must contain information on the fault structure that caused the reflection, and model experiments have been undertaken to investigate the reflection process. Only recently, however, have attempts been made to quantify the reflection process. Calculations using both the finite-difference and finite-element techniques have been carried out, and estimates of the reflection coefficient as a function of frequency have been obtained. The object of this paper is to extend these considerations by calculating analytically the scattering matrix of an SH-channel wave after interaction at a fault plane. The scattering matrix is calculated as a function of frequency, hade angle, and fault throw. The method employed is based on the decomposition of the incident SH-channel wave into Fourier components, the calculation of plane wave reflection and transmission coefficients within the constraints of geometrical acoustics, and finally the synthesis of the scattering matrix by application of the Helmholtz-Kirchhoff integral. The calculation throughout is restricted to normal modes.     

激波在磁盔－电流片位场中的传播：（Ⅰ）激波与磁盔间的相互作用

利用新近获得的子午面磁盔－电流片背景太阳风稳态解，对激波从盔底沿电流片方向往外传播时与磁盔间的相互作用进行了数值模拟研究，重要新结果是：１．磁盔的存在使受扰介质速度跃变中央出现下凹，随着激波传出磁盔区并沿电流片方向传播，速度下凹逐渐减弱以致消失；２．激波将磁盔拉长并把盔顶的环形（垂直赤道面）磁场带到行星际空间，成为行星际磁场南向分量的来源之一；３．５个太阳半径（Ｒ⊙）内的磁盔部分将出现精细结构，沿盔外边界形成两条高速带，以及马蹄形密度（亮）环形结构等．这些结果表明，太阳附近高速等离子体与磁盔间存在重要的动力学相互作用过程，对行星际空间的太阳风三维结构有重要影响．