FREQUENCY ELECTROMAGNETIC SOUNDING USING A VERTICAL MAGNETIC DIPOLE*

A horizontal transmitter loop (vertical magnetic dipole) is used for frequency electromagnetic (FEM) soundings. The frequency ranges from approximately 6 Hz to about 4000 Hz. The vertical and radial magnetic field components are measured for 20 frequencies per decade several hundred meters from the transmitter loop. A very small bandwidth is selected for amplification using a reference signal. An Apple computer is used for data acquisition. A computer program for Marquardt inversion optimizes the parameters for the n-layer case: the resistivities and thicknesses of individual beds and a correction factor for the primary magnetic field. Interpretation of each component individually yields practically the same parameters. Examples from the field are given with interpretation; comparison with dc resistivity measurements is provided. The ratio of vertical/radial magnetic field components vs. frequency can be transformed simply into apparent resistivity vs. apparent depth. This can be done in the field to obtain an estimation of the depth of the layer boundaries. FEM results are compared with Schlumberger d.c. sounding obtained at the same site.     

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.     

双频组合波与近区频域电磁测深

由于近区场的复杂性及背景场的干扰，多年来近区频域电磁测深一直是地球物理领域一个悬而未决的问题，并成为频域电磁测深发展的障碍。本文通过分析近区场的分布特征，并将双频组合波理论引入，提出了一种适于近区频域测深的组合波测深方案，它具有有效地压制背景场，突出地电异常信息的功能，为在近区实施频域电磁测深开辟了一条新途径。     

ELECTROMAGNETIC DEPTH SOUNDING EXPERIMENT*

An electromagnetic frequency sounding experiment with a rigid horizontal transmitter coil carrying a stabilized oscillating current was carried out in South Tunesia. The field data were interpreted in terms of the mutual impedance ratio in the horizontal coils system. Where the measurements were sufficiently accurate they generally could be interpreted to a high degree of fit. It is concluded that a vehicle-mounted electromagnetic frequency sounding system is suitable for a fast survey.     

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.     

THE INTERPRETATION OF INDUCED-POLARIZATION SOUNDING CURVES IN THE FREQUENCY DOMAIN *

Two-layer type curves of apparent frequency effect for the Wenner configuration are presented. The formulation is based on the normal definition of frequency effect in terms of resistivities measured at different frequencies plus the definition of apparent resistivity over two horizontal layers as a function of first and second layer resistivities. The use of these type curves in the interpretation of multilayer apparent frequency-effect curves is described and some field examples are given.     

TOPOGRAPHIC EFFECTS ON ELECTROMAGNETIC DEPTH SOUNDING SYSTEMS *

Computations have been made for the effect of ground slope in combination with transmitter coil misorientation on different electromagnetic depth sounding systems and sets of frequency sounding master curves are presented for different angles. The effect of a thin air layer due to the elevation of coils above ground surface has been studied for different systems. Also discussed are the effects due to an error in transmitter-receiver coil separation.     

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.     

ELECTROMAGNETIC DEPTH SOUNDING USING A SOURCE ORIENTATION MODE*

Electromagnetic depth sounding using source orientation as the sounding variable provides advantages in instrumental simplicity and operational flexibility when compared with conventional modes of electromagnetic sounding. The ease with which the technique may be simulated in a scale model permits its application to sounding over localized structures. The theoretical approach to interpretation is at present limited to structures which approximate a perfectly conducting half space. However, scale model tests suggest that the perfect conductor theory may be applicable to many localized structures.     

ELECTROMAGNETIC SOUNDING OF THE KAPURDI LIGNITE DEPOSIT IN WESTERN RAJASTHAN,INDIA*

In the Kapurdi block of the Barmer lignite field in western Rajasthan, India, lignite occurs as a number of discontinuous seams of varying thickness up to a few m. The country rock is a succession of clay, sand and various members of the clay-sand family. The overburden, comprising sand, Fuller's earth, bentonitic clay, clayey sand/sandy clay and clay, is thick and, electrically, highly conductive. Both its thickness (40–90 m) and conductivity (0.5–1.0 S/m) are highly variable. The lignite seams may occur anywhere in the clay-sand sequence below this overburden. A ten-layered electrical model of the Kapurdi area was parameterized on the basis of galvanic resistivity sounding and core drilling results. This model was then validated by electromagnetic sounding measurements made with a 200 × 200 m square loop transmitter and energizing current of variable frequency (80 Hz to 11 kHz), using central induction sounding techniques. With a loop of this size, only formations in the overburden could be mapped. Subsequent computer modeling has shown that a larger loop of size, say, 800 m and a frequency band of 30–500 Hz are required to map formations below–as well as those within–the overburden. Even then only various clay-sand interfaces can be mapped, i.e., only over-burden thickness and the likely depth range of lignite seams (if they occur) can be estimated. Direct mapping of lignite seams is not feasible in practice. This is true of loop-dipole, as well as central induction sounding. It is interesting that skin depth need not always be a factor limiting depth of exploration in electromagnetic prospecting.     

二维频率测深边界单元法正演计算

在二维层状介质中含有横向非均匀体的地电断面情况下，对电偶源的偶极长度作了延长，并选取了适当的基本解及无穷远边界条件，因而将相应的含源谐变电磁场的边值问题转化为较简单的边界积分方程．用边界单元法求出了相应的电磁场分量，进而计算阻抗视电阻率，并对这一算法作了相应的检验．     

二维频率测深边界单元法正演计算

在二维层状介质中含有横向非均匀体的地电断面情况下,对电偶源的偶极长度作了延长,并选取了适当的基本解及无穷远边界条件,因而将相应的含源谐变电磁场的边值问题转化为较简单的边界积分方程．用边界单元法求出了相应的电磁场分量,进而计算阻抗视电阻率,并对这一算法作了相应的检验．     

三维电磁模拟技术及其在频率测深法中应用

利用现有的并矢格林函数和积分方程理论对轴向频率测深三维问题进行正演模拟，并讨论其精度．三维良导体或高阻体的存在对频率测深电场分量Ｅｘ定义的视电阻率响应（振幅、相位）分布特征的影响各有其特殊的规律性．选择测量电极中心作为频率测深三维问题正演计算结果的记录点，既使视电阻率响应在异常体正上方获得最大异常，同时又使正演计算的拟断面图的异常分布与异常体之间有很好的对应关系．     

三维电磁模拟技术及其在频率测深法中应用

利用现有的并矢格林函数和积分方程理论对轴向频率测深三维问题进行正演模拟，并讨论其精度．三维良导体或高阻体的存在对频率测深电场分量Ｅ_ｘ定义的视电阻率响应（振幅、相位）分布特征的影响各有其特殊的规律性．选择测量电极中心作为频率测深三维问题正演计算结果的记录点，既使视电阻率响应在异常体正上方获得最大异常，同时又使正演计算的拟断面图的异常分布与异常体之间有很好的对应关系．     

三维电磁模拟技术及其在频率测深法中应用

利用现有的并矢格林函数和积分方程理论对轴向频率测深三维问题进行正演模拟,并讨论其精度．三维良导体或高阻体的存在对频率测深电场分量Ｅｘ定义的视电阻率响应（振幅、相位）分布特征的影响各有其特殊的规律性．选择测量电极中心作为频率测深三维问题正演计算结果的记录点,既使视电阻率响应在异常体正上方获得最大异常,同时又使正演计算的拟断面图的异常分布与异常体之间有很好的对应关系．     

二维水平电偶极变频测深阻抗视电阻率的有限元正演计算

在二维地电断面情况下,电偶源变频测深阻抗视电阻率的有限元计算,存在着两个困难:一个是对源的处理;另一个是边界条件的确定。本文提出了解决这两个问题的方法,构成了含源波动方程的边值问题,用有限元法求出了相应的电磁场分量,从而计算出二维地电断面的阻抗视电阻率。对各种地电断面计算的结果表明,计算方法是正确的,可对实际地电断面进行有限元模拟,求得其电磁响应。     

二维水平电偶极变频测深阻抗视电阻率的有限元正演计算

在二维地电断面情况下,电偶源变频测深阻抗视电阻率的有限元计算,存在着两个困难:一个是对源的处理;另一个是边界条件的确定。本文提出了解决这两个问题的方法,构成了含源波动方程的边值问题,用有限元法求出了相应的电磁场分量,从而计算出二维地电断面的阻抗视电阻率。对各种地电断面计算的结果表明,计算方法是正确的,可对实际地电断面进行有限元模拟,求得其电磁响应。     

瞬变电磁测深法

瞬变电磁测深法是一种人工源的电磁方法,适用于寻找火山岩覆盖区以及逆掩推覆体下部的含油气构造、圈定碳酸盐岩地区的低阻和中等电阻的沉积岩系构造。与其它电磁方法比较,有抗干扰能力强、信噪比高、受横向不均匀性的影响小等优点。本文简述了该方法的物理原理、野外测量技术、数据处理及其解释方法     

ELECTROMAGNETIC SOUNDING NEAR A LARGE SQUARE LOOP SOURCE OF CURRENT*

An electromagnetic sounding experiment with a large square loop as source was carried out on the dried-up bed of a water reservoir near the town of Dharmavaram in Andhra Pradesh. The sounding was performed in both geometric and parametric modes, and involved measurements of phase as well as amplitude of the vertical magnetic field inside and outside the loop. The six-frequency EM system used for the experiment was found to be a workable system for electromagnetic sounding. The results of the experiment more or less confirm the conclusions from theoretical modeling. They also show that even though the earth is not always electrically horizontally layered over a sufficiently large lateral extent for the one-dimensional model to be strictly valid, it is still possible to apply such modeling to sounding curves taken one part at a time and obtain layer parameters which check qualitatively with the layer parameters obtained from direct current resistivity sounding.     

FORWARD MODELLING FOR FREQUENCY DOMAIN MARINE ELECTROMAGNETIC SYSTEMS*

An algorithm for the accurate evaluation of rapidly oscillating integrals is described. The method is based on deformation of the integration path into the complex plane of the integration variable. Numerical integration is then carried out along appropriate cuts where the oscillating factor is transformed to the decaying factor. Contrary to standard methods, the proposed technique permits accurate evaluation of numerically divergent integrals. The algorithm is especially useful in forward modelling for high-frequency electromagnetic methods and, in particular, for the new marine electromagnetic system based on measuring signals on the sea bottom at high induction numbers. Results of calculations using both the proposed and standard methods are compared with available analytical solutions.