Effects of transverse electric anisotropy on self-potential anomalies

In the present paper is studied the influence of transverse ground anisotropy on the formation of self-potential (SP) anomalies produced by polarized bodies. It is concluded that SP anomalies produced by vertical dipoles of infinite length are displaced in the opposite direction of the dip angle of anisotropy. The equipotential lines are generally ellipses. SP anomalies produced by a vertical dipole of finite length are also displaced, have a negative and a positive centre and present the characteristics of an SP field produced by an inclined dipole in a homogeneous and isotropic ground. In both models, significant errors in the quantitative interpretation of SP anomalies may result from not taking ground anisotropy into account.     

THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*

In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression. As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.     

GEOELECTRIC AXIAL DIPOLE SOUNDING CURVES FOR A CLASS OF TWO-DIMENSIONAL EARTH STRUCTURES*

With the aim of studying the behaviour of geoelectric axial dipole vertical soundings over complex geology, a systematic theoretical approach is presented for a class of earth structures characterized by horizontal and vertical parallel boundary planes. The two-dimensional cylindrical bodies of infinite length and rectangular cross-section are constrained to have resistivities satisfying Alfano's condition at every intersection line of the graticule, in order to adopt the image-point theory. A detailed analysis is performed for models with any number of horizontal boundaries and two vertical discontinuities. The apparent resistivity formulas are obtained and selected apparent resistivity curves are drawn for different parameter combinations and various directions of the sounding expansion axis. The class under consideration contains as a particular case the HVC model elaborated in Alpin's monograph, where only a small collection of master curves is available for the axial array. The reconstruction of those curves by the present formulation shows the existence of large discrepancies. A test based on the transformation to equivalent half-Schlumberger sounding curves supports the conclusion that an unidentified error must exist in some part of the theoretical approach of the Russian researchers. Finally, some field sounding curves based on geothermal and volcanological surveys are presented and interpreted by complete curve matching, essentially to show the applicability of the theoretical solutions.     

A MODIFIED GEOELECTRICAL PROCEDURE USING POLARDIPOLE ARRAYS—AN EXAMPLE OF APPLICATION TO DEEP EXPLORATION *

Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar-dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field. A special measurement technique is required since the dipole-dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.     

CENTRAL FREQUENCY SOUNDING IN SHALLOW ENGINEERING AND HYDRO-GEOLOGICAL PROBLEMS*

The paper deals with the early stages of development of a convenient form of electromagnetic induction method of sounding referred to as ‘Central Frequency Sounding’ and abbreviated as CFS. The method is introduced as a rapid and useful technique for investigation of shallow engineering and hydro-geological problems. Sets of theoretical two-layer master curves, suitable for interpretation of field data involving measurement of the vertical magnetic component of the field induced at the center of a loop placed on a two-layer earth, have been presented. The approximate but reasonably accurate solutions for a two-layer earth of any arbitrary resistivity contrast have been considered for the purpose and expressed in a form suitable for computation. The computed results have been presented in sets of curves useful for interpretation of field data.     

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.     

A numerical method to calculate the electromagnetic field of a horizontal current dipole

Summary A computer program is described to calculate the field of an oscillating current dipole over a horizontally stratified medium for the quasi-static case. Multi-layer master curves for frequency sounding can be calculated with this program. Examples of these curves are presented.Contribution No. 90 of the Geophysical Institute, Swiss Federal Institute of Technology, Zürich.     

Approximate depth of penetration in EM dipole prospecting

Summary FollowingDoll, approximate expressions for the relative contribution to the total signal by various regions of a homogeneous earth have been derived for the nine electro-magnetic dipole-dipole systems. For the three systems with parallel dipole axes, there exists a vertical focussing effect centered around a depth equal to 0.34 times the dipole spacing. For dipoles with perpendicular axes and non-zero signal, there is no focussing and the near-surface material will have an undesirably large influence on the fields measured. Considering all aspects, the system with colinear axes seems to be the best for em prospecting. For this system, the portion of the ground between approximate depths 0.1L and 1.0L accounts for the bulk of the signal,L being the dipole spacing.NGRI Contribution No. NGRI-70-160.     

RESISTIVITY MEASUREMENTS IN VALLEYS WITH ELLIPTIC CROSS-SECTION*

In this paper an idealized valley of a semi-elliptic cross-section is considered. For a Schlumberger configuration on the axis, sets of master curves are calculated for the ratio of semi-axis a/b= 1, 2, 3, 4, 5 in corresponding to various resistivity ratios of surrounding rocks and valley sediments. For small resistivity ratios, these model curves have the shape of three-layer curves for horizontal bedding and are often equivalent to them within the accuracy of measurements. The axial ratio a/b considerably affects the depth determination of valley sediments. In the special case of a circular cross-section (a/b= 1) the influence of the position of the electrodes on the sounding curve is studied in more detail. The application of the master curves in practice shows that the influence of the specific shape of the valley on soundings should not be neglected. In general, the valleys have a greater “true” depth than can be seen from the interpretation of a sounding by master curves corresponding to the horizontal bedding.     

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.     

磁总场异常垂直梯度三维相关成像

本文提出了磁总场异常垂直梯度三维相关成像方法,用于成像地下等效磁源分布.它首先将地下待成像空间划分为三维规则网格,然后直接计算每个网格节点磁偶板子在观测面理论磁总场异常垂直梯度与实测磁总场异常垂直梯度的互相关,其相关系数值表征等效磁偶极子分布(即磁偶极子发生的概率).理论长方体组合模型数据和实际某矿区磁测资料试验结果表明本文方法计算得到的相关系数值能基本反映地下的磁源分布,且分辨率明显高于磁总场异常三维相关成像的分辨率,也高于基于熵滤波分离异常的磁总场异常三维相关成像的分辨率.     

ENERGY DENSITY SPECTRUM AND AUTOCORRELATION FUNCTION OF ANOMALIES DUE TO SIMPLE MAGNETIC MODELS*

Formulae of the energy spectrum and autocorrelation function have been derived for magnetic anomalies due to four classes of bodies which can be represented in turn by (a) poles, (b) line of poles, (c) dipoles and (d) line of dipoles. The effects of the depth and dimensions of the magnetized sources on the spectrum and the autocorrelation function have been studied. In the case of the dipole models, the orientation of the polarization vector casts a significant influence on the characteristics of the two functions. In all cases, however, the functions change in size and shape as the inclination and declination of the geomagnetic vector are varied.     

Magnetotelluric profiling of vertical conductors

The presence of lateral contrasts of electrical conductivity modifies the original pattern of electromagnetic fields radiated from remote sources. A magnetic transverse plane wave field, interacting with a vertical conductive and outcropping dike placed between two quarter-spaces of unequal electrical conductivities, creates an anomalous vertical component of the magnetic field. This anomalous field has been analysed by computation, and drafting of master curves. Two case histories are presented to illustrate the application and the effectiveness of the solution. It is concluded that: (i) the response is higher for intermediate values of the conducting body induction number; (ii) the curves can be used for the inter-pretation of magnetotelluric, AFMAG, and VLF exploration data; (iii) it is necessary to develop solutions taking into account the vertical as well as the lateral variation of conductivity.     

几种典型近地表有限导体瞬变电磁特征响应研究

近地表有限导体的瞬变电磁响应中包含其形状、结构特征,如何建立这些特征与其响应之间的关系是近地表有限导体探测与识别的核心问题.本文建立了几种典型有限导体响应的三维感应偶极子模型,通过有限导体早期幂函数衰减的幅度与速率、晚期指数衰减的幅度与时间常数共四个模型参数表征有限导体的形状和结构特征,利用最小二乘拟合算法提取这些模型参数,揭示有限导体的形状、结构特征与模型参数之间的内在联系.理论与实验研究结果表明:具有绕球心旋转对称性的球形目标体,其三维感应偶极子响应完全相同,早期响应呈幂函数衰减,晚期呈e指数衰减,信号幅度和时间常数均能很好反映球体半径与材料特性;具有绕轴旋转对称性目标体,其三维感应偶极子响应部分相同,早期幂函数衰减的幅度与速率主要体现目标体的长度特征,晚期e指数衰减的时间常数体现了目标体的外径与壁厚特征;非轴对称性目标体,其三维感应偶极子响应均不相同,各个感应偶极子参数差异较大.本文的研究对提高瞬变电磁系统区分轴对称目标体与金属碎片能力,降低系统探测虚警率具有重要意义.     

VLF ANOMALIES FROM A PERFECTLY CONDUCTING HALF PLANE BELOW AN OVERBURDEN*

A theoretical solution to the electromagnetic problem of a perfectly conducting half plane below a conducting overburden has been obtained. The VLF anomalies have been computed for different overburden conductivity and thickness and also for different dip angles of the half plane. In the computations the contribution to the secondary magnetic field from the electric Hertz potential has been neglected. The anomaly curves which are displayed as EM 16 readings, show a fairly complicated behaviour. This is mainly due to the phase shift and attenuation of the field caused by the conductivity of the overburden and the host rock. From the anomaly curves it is possible to define the apparent depth to the top of the conductor as the distance between the peak value and the cross-over of the real component. The apparent depth is usually larger than the actual depth, but it is possible to determine the actual depth to the conductor from the relation between the peak-to-peak anomaly and the apparent depth. When the peak-to-peak anomaly is fairly large, it is also possible to make estimates of the dip angle. However, a complete set of master curves will be a necessary tool for interpretation of VLF data when there is need to obtain more accurate estimates of the half plane parameters. In a specific case the theoretical calculations are shown to be in good agreement with measured data.     

阵列偶极源辐射场在导电地层中传播的方向特性

利用电偶极子辐射场的矢势导出了阵列偶极子在导电媒质中辐射场的一般形式,所给出的公式不仅适用于近区、感应区,而且还适用于远区.对阵列偶极子辐射场的相干特性进行了详细的讨论,由所得结果可知,对层状地层通过选择适当的方位可使接收到的电磁信号达到极大,极大值的大小与偶极源的个数成正比.本文的研究对解决地层中电磁信号衰减严重问题提供了一种可能的解决办法.     

TRANSFORMATION OF MAGNETOMETRIC DATA INTO TECTONIC MAPS BY DIGITAL TEMPLATE ANALYSIS*

Results of gravimetric surveys can be interpreted by comparing the Bouguer field values with master curves based on simplified geological models. It has been shown in a previous paper how this procedure can be transformed into routine processes which can be computerized. The application of this method has yielded useful results in detailed gravity surveys. The present paper discusses the application of the same interpretation principles to magnetic data. After some modifications, the method elaborated for the gravimetric data can be used for the interpretation of magnetometric survey results. Magnetometric-tectonic maps are obtained which show the structural picture by common geological symbols. In the case of faults, the dimensions of depth of burial and throw are indicated on the maps. The method is illustrated by an example where these procedures have been applied to gravimetric and magnetometric data of the same area. Two different maps are obtained: One shows the tectonics according to density contrasts and the other map depicts the tectonic situation on the basis of magnetic susceptibility contrasts.     

海底表面磁源瞬变响应建模及海水影响分析

根据电磁场理论,推导了磁偶源和接收点均位于海水中时层状海底模型的频域电磁场响应一般表达式,并通过此式,得到了海水为均匀半空间和有限海水深度两种情况下,垂直磁偶极装置、中心回线和重叠回线分别置于均匀半空间海底表面时的瞬变电磁响应（磁场和感应电压）表达式. 这些表达式将瞬变响应和海底的电导率等参数有机联系在一起,为海底瞬变电磁法的正演计算和反演解释提供了理论基础. 仿真计算表明,海水的存在不仅使得瞬变响应曲线形态发生变化,而且影响其对海底电导率的分辨能力.     

Global anomalies of the main geomagnetic field and the dynamic model of their sources

The model of the main geomagnetic field sources, including 12 more dipoles in addition to the main dipole, is presented. The source parameters have been determined for the 100-year-long period at an interval of 5 years. The problem is solved using the iteration method proposed and developed by the authors. Six more sources have been included in the iteration process at its current step. This made it possible to substantially smooth the time variations in the dipole parameters obtained previously and, on the other hand, to describe all global anomalies of the main geomagnetic field using this model. A change in the parameter values can be approximated by rather smooth functions describing specific features of development of the sources operating for 20–30 years. However, the short duration of the obtained series (21 points) makes the problem of prediction substantially more difficult. The parameters of 13 dipoles, extrapolated for 2000 using the linear prediction filter, are in good agreement only with the general development of the sources.     

A new technique of interpreting gravity and vertical magnetic anomalies due to infinite horizontal cylindrical ore bodies

Summary A novel method of interpreting gravity and magnetic anomalies is presented here. Two diagrams of master curves, one for gravity and the other for vertical magnetic interpretation are presented. They are useful in calculating the depth of burial and the radius of infinite horizontal cylindrical bodies irrespective of density contrast or strength and direction of magnetisation. This method also enables us to infer the direction of magnetisation, resultant intensity of magnetisation and from them the susceptibility contrast; and density contrast. ThoughHenderson [8]²) reported the applicability of continuations and derivatives in the interpretation of magnetic anomalies for the first time, the authors have treated them in a more exhaustive manner in the present paper to obtain valuable relationships.