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.     

A Method to Remove Electromagnetic Coupling from Induced Polarization Data for an "Exponential" Earth Model

--The electromagnetic (EM) coupling effect in induced polarization (IP) data is an important problem. In many works it has been computed only considering homogeneous or layered earth models with discretely uniform conductivity. In this study, an algorithm has been developed to compute the EM coupling effect in IP data measured on the earth, whose conductivity varies (increases or decreases) exponentially with depth. The EM coupling effects for Percent Frequency Effect (PFE) and phase data are computed for a dipole-dipole array with different separations, however the method can be applied to any electrode array. The results obtained for the cases of increasing and decreasing conductivity as a function of depth indicate that the EM coupling effect strongly depends on the subsurface resistivity and the dipole length. Here an "exponential" earth model is considered to remove EM coupling from the IP data in frequency and phase domain. For this purpose, first, the region of pseudo-section is divided into segments, and within each segment a typical average apparent resistivity („_a) curve is constructed. An exponential conductivity model is fitted to average „_a data. The conductivity model is then used to compute EM responses. Next the data are corrected for the EM coupling contribution. This decoupling process is applied to field data from a galenite-pyrite mineralization area at the Dolluk site, in western Turkey. The results from the decoupling method developed here are compared with other techniques.     

MODEL STUDIES ON SOME ASPECTS OF RESISTIVITY AND MEMBRANE POLARIZATION BEHAVIOUR OVER A LAYERED EARTH*

Electrolytic model tank experiments to study resistivity and time domain induced polarization (IP) response over layered earth models were initiated primarily to facilitate the understanding of field results. Alternate layers of clay and sand (or clay-coated sand) with, in some cases, a surficial layer of water were assembled in the tank and resistivity and IP measurements made for a range of electrode spacings using the Wenner configuration. Graphite and silver-silver chloride electrodes were used as current and potential electrodes respectively. Clay-coated (3% by weight) sand was found to generate stronger polarization than either clay or sand alone. Apparent chargeability m_a was observed to be positive for a nonpolarizable surface layer. For a polarizable surface layer, the sign of IP was controlled by the polarizability, the thickness of the second layer, and the spacing of the electrode spreads. The apparent chargeability m_a can theoretically change sign from positive to negative and vice versa with a gradual increase in electrode spacing, and such negative IP effects were obtained in a few observations. A simultaneous decrease in IP and an increase in resistivity, which is a qualitative diagnostic feature for the occurrence of clean freshwater sand aquifers, could also be generated in the model tank experiment. Combined resistivity and IP soundings were carried out near Fredericton Junction and Tracy, New Brunswick, Canada. Field curves are presented along with the model curves for qualitative comparison and understanding of IP behaviour over a layered earth. Twenty-five out of twenty-seven soundings show only positive apparent chargeabilities, whereas two show chargeability sign changes (positive/negative/positive). The model study gives reason to believe that surface soils and Quaternary gravel boulder deposits near Fredericton Junction are relatively non-polarizable. As an auxiliary experiment, sand and clay were taken in different proportions by weight and mixed thoroughly with water in a cement mixer. The mixtures were then compressed with a suitable die and plunger under 3.6 Pa pressure to prepare cylindrical samples of height 18 cm and diameter 15.5 cm. IP measurements were done on the flat faces using the Wenner configuration with a= 2 cm. Chargeability was found to be negative for 100 and 90% clay mixtures. It reached a positive maximum for an 80% clay-20% sand mixture and then decreased gradually with increasing sand and decreasing clay content.     

Resistivity and induced polarization response of a thin sheet

The relevant potential theory is given for a current point source in the presence of a conductive slab embedded in a homogeneous host region of infinite extent. The thin sheet representation is obtained from the exact integral formulation by a simple mathematical limit process. The same result is also deduced directly at the outset by applying a thin sheet boundary condition. The apparent resistivity for a two electrode array is then computed for the case where the bore hole intersects the thin sheet at right angles. The corresponding results for the dilution factor, relevant to the induced polarization response, are also obtained. It is shown that the apparent resistivity and the dilution factor are constant when the potential and the current electrode straddle the sheet but there is a characteristic decrease as the electrodes move away from the sheet.     

AN INTERPRETATION THEORY FOR INDUCED POLARIZATION VERTICAL SOUNDINGS (TIME-DOMAIN)*

In this paper it is shown how one may obtain a generalized Ohm's law which relates the induced polarization electric field to the steady-state current density through the introduction of a fictitious resistivity defined as the product of the chargeability and the resistivity of a given medium. The potential generated by the induced polarization is calculated at any point in a layered earth by the same procedure as used for calculating the potential due to a point source of direct current. On the basis of the definition of the apparent chargeability m_a, the expressions of m_a for different stratigraphie situations are obtained, provided the IP measurements are carried out on surface with an appropriate AMNB array. These expressions may be used to plot master curves for IP vertical soundings. Finally some field experiments over sedimentary formations and the quantitative interpretation procedure are reported.     

NUMERICAL MODELLING OF STANDARD AND CONTINUOUS VERTICAL ELECTRICAL SOUNDINGS1

Analytical solutions of vertical electrical soundings (VES) have mostly been applied to groundwater exploration and monitoring groundwater quality on terrains of fairly simple geology and geomorphology on which the electrode arrays are symmetrical (e.g. Schlumberger or Wenner configurations). The sounding interpretation assumes flat topography and horizontally stratified layers. Any deviations from these simple situations may be impossible to interpret analytically. The recently developed GEA-58 geoelectrical instrument can make continuous soundings along a profile with any colinear electrode configuration. This paper describes the use of finite-difference and finite-element methods to model complex earth resistivity distributions in 2D, in order to calculate apparent resistivity responses to any colinear current electrode distribution in terrains in which the earth resistivities do not vary along the strike. The numerical model results for simple situations are compared with the analytical solutions. In addition, a pseudo-depth section of apparent resistivities measured in the field with the GEA-58 is compared with the numerical solution of a real complex resistivity distribution along a cross-section. The model results show excellent agreement with the corresponding analytical and experimental data.     

Three-dimensional tomography using high-power induced polarization with the similar central gradient array

Induced polarization (IP) 3D tomography with the similar central gradient array combines IP sounding and IP profiling to retrieve 3D resistivity and polarization data rapidly. The method is characterized by high spatial resolution and large probing depth. We discuss data acquisition and 3D IP imaging procedures using the central gradient array with variable electrode distances. A 3D geoelectric model was constructed and then numerically modeled. The data modeling results suggest that this method can capture the features of real geoelectric models. The method was applied to a polymetallic mine in Gansu Province. The results suggest that IP 3D tomography captures the distribution of resistivity and polarization of subsurface media, delineating the extension of abrupt interfaces, and identifies mineralization.     

含激电效应的CSAMT一维正演研究

地电体对频率域电磁波激发源的响应为电磁感应和激电效应的综合响应.传统CSAMT法进行数据正反演时认为大地介质电阻率是与频率无关的实数,而实际上因为激电效应,地下可极化体的电阻率是一个与频率相关的复数.为推进二者总体响应研究,并扩展激电法的应用范围,同时提高电磁法勘探的精度,本文基于Dias模型,以复电阻率代替不考虑地电体极化效应的直流电阻率,对CSAMT场源一维层状模型进行了正演模拟,为提取CSAMT信号中所含激电信息提供理论基础.结果表明,考虑激电参数后,视电阻率及相位响应曲线出现明显异常（包括远场、过渡场、近场）;极化前后振幅比值异常峰值、相位差值异常峰值可直观体现激电异常;异常峰值与极化层层厚、埋深以及电阻率变化有连续的对应关系.认为从频率域电磁法信号中提取激电信息有乐观的前景.     

三维激发极化法反演研究及其在金属矿勘探中的应用

激发极化法在金属矿、硫化矿等资源勘探方面应用较广.随着勘探设备与计算机硬件的发展,所采集到的数据具有观测数据量大、布极方式多样等特点.针对实测数据的特点,我们研究完成了基于并行技术的激发极化法对数反演算法,该算法具有如下特点：（1）通过压缩存储技术和并行技术的集成实现了可以处理大数据特征的反演算法;（2）利用对数反演来约束每次计算得到新模型的电导率恒为正,充电率在0到1之间变化,从而保证反演的稳定性和可靠性.本文首先设计了两组对比模型进行试验,通过对不同区块数据采用不同加权的方式来减弱噪声对反演结果影响的效果;其次,采用并行技术提高了反演的计算速度,并利用理论模型分析了不同电极装置对反演分辨率的影响.最后,在甘肃某金属矿开发前景区利用激发极化法开展了中梯装置的采集工作,利用加权后的观测数据反演推断出了测区金属矿开发靶区的大致位置及分布特征.     

RESISTIVITY SOUNDING ON A MULTI-LAYERED EARTH WITH TRANSITIONAL LAYERS. PART I: THEORY*

The electrical potential generated by a point source of current on the ground surface is studied for a multi-layered earth formed by layers alternatively characterized by a constant conductivity value and by conductivity varying linearly with depth. The problem is accounted for by solving a Laplace's differential equation for the uniform layers and a Poisson's differential equation for the transitional layers. Then, by a simple algorithm and by the introduction of a suitable kernel function, the general expression of the apparent resistivity for a Schlumberger array placed on the surface is obtained. Moreover some details are given for the solution of particular cases as 1) the presence of a infinitely resistive basement, 2) the absence of any one or more uniform layers, and 3) the absence of any one or more transitional layers. The new theory proves to be rather general, as it includes that for uniform layers with sharp boundaries as a particular case. Some mathematical properties of the kernel function are studied in view of the application of a direct system of quantitative interpretation. Two steps are considered for the solution of the direct problem: (i) The determination of the kernel function from the field measurements of the apparent resistivity. Owing to the identical mathematical formalism of the old with this new resistivity theory, the procedures there developed for the execution of the first step are here as well applicable without any change. Thus, some graphical and numerical procedures, already published, are recalled. (ii) The determination of the layer distribution from the kernel function. A recurrent procedure is proposed and studied in detail. This recurrent procedure follows the principle of the reduction to a lower boundary plane, as originally suggested by Koefoed for the old geoelectrical theory. Here the method differs mainly for the presence of reduction coefficients, which must be calculated each time when passing to a reduced earth section.     

Depth of detection of highly conducting and volume polarizable targets using induced polarization

We define the apparent frequency effect in induced polarization (IP) as the relative difference between apparent resistivities measured using DC excitation on the one hand and high‐frequency excitation (when the IP effect vanishes) on the other. Assuming a given threshold for the minimum detectable anomaly in the apparent frequency effect, the depth of detection of a target by IP can be defined as that depth below which the target response is lower than the threshold for a given electrode array. Physical modelling shows that for the various arrays, the depth of detection of a highly conducting and volume polarizable target agrees closely with the depth of detection of an infinitely conducting and non‐polarized body of the same shape and size. The greatest depth of detection is obtained with a two‐electrode array, followed by a three‐electrode array, while the smallest depth of detection is obtained with a Wenner array when the array spread is in‐line (i.e. perpendicular to the strike direction). The depth of detection with a Wenner array improves considerably and is almost equal to that of a two‐electrode array when the array spread is broadside (i.e. along the strike direction).     

两层大地中三维体的激发极化与电阻率响应的积分方程模拟

用散射、叠加方法推导出两层大地的并矢格林函数。使用这些函数,含三维异常体的二层大地的边值问题转变为积分方程。使用矩量法,可解此积分方程。 使用偶极-偶极装置计算了激发极化和电阻率响应的几个数值结果,并对这一算法作了几方面检验。     

A new method for geoelectrical investigations underwater1

A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.     

IP RESPONSE FOR A 2D HORIZONTAL CYLINDER1

The induced polarization response for a 2D horizontal cylinder embedded in a half-space is calculated for a uniform electric source. Response curves, in the form of apparent charge-ability taking into account the effect of the air-earth interface, exhibit a sharp decrease in amplitude with an increase in depth of burial of the target. The resistivity contrast between the cylinder and the host plays a dominant role in determining the IP response, i.e. the amplitude decreases considerably with the increase in resistivity contrast. The decrease is due to the defocusing effect caused by the resistive cylinder. The current lines tend to deviate away from the cylindrical target. In the case of a highly conducting cylinder, apparent defocusing takes place as current lines are confined to the surface of the conducting cylinder. An increase in chargeability contrast is reflected as a steady rise in the response. The peak response at the centre is reduced by about half the magnitude when the air–earth interface is not considered. The variation of response along the profile, though noticeable, is not as high as that obtained at the centre.     

水下激发极化测深异常特征研究

利用有限单元法对水下激发极化测深进行数值模拟以研究其异常特征和适用条件.水下的电阻率测深和激电测深均可对水底地质体进行近距离探测,提高探测分辨率.而水底地形对视电阻率测深的影响很大.水底极化体有限元正演模拟的结果表明,水底地形对激发极化测深结果没有影响.采用水下激发极化法进行地质体探测是可行、有效的.通过计算不同水体和水底岩石电阻率对视极化率幅值的影响发现,水体电阻率是影响水下极化率测深的主要因素.由于海水的电阻率过低,观测视极化率异常微弱而不适合开展水下激电工作.     

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.     

A DIGITAL LINEAR FILTER FOR RESISTIVITY SOUNDING WITH A GENERALIZED ELECTRODE ARRAY*

This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities. Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.     

EM AND IP RESPONSE OF A STEEL WELL CASING FOR A FOUR-ELECTRODE SURFACE ARRAY. PART II: NUMERICAL RESULTS*

Some numerical results for the apparent resistivity of a homogeneous half space containing a vertical steel well casing as measured by a dipole-dipole array are presented. The basic model includes the electromagnetic and induced polarization effects by allowing for frequency dependent eddy currents and an electrochemical boundary of the well casing. It is shown that the well casing produces an apparent complex resistivity response that could be mistaken for an induced polarization anomaly existing above a hydrocarbon deposit. This response of the well casing is strongly dependent on frequency.     

1D and 2D Cole-Cole-inversion of time-domain induced-polarization data

A new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole-Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time-domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole-Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D. The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two-dimensional resistivity model for each time channel. The time-dependent resistivity of each cell was then interpreted as the response of a homogeneous half-space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half-space Cole-Cole inversion. The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany.     

REMARQUES SUR L'INTERPRETATION DES SONDAGES DE POLARISATION PROVOQUEE ESSAI DE THEORIE QUANTITATIVE *

The transient phenomena associated with induced polarization are very complex and it is necessary to have both a proper understanding of the physical processes and a good supply of mathematical aids in order to make any advance in the quantitative interpretation of I.P. surveys. The analogy between the classical electrical sounding method and the induced polarization sounding method has led a number of workers to interpret the results of the latter like the results of the former. To clarify this idea, it seems very interesting to calculate a mathematical model in order to know the form of the anomaly that can be probably expected. The case of a thin horizontal polarizable layer, with the same uniform and isotropic conductibility as the homogeneous background, has been studied in this paper. The result of the calculation for the case of a single current electrode and a single potential electrode is given. From these data, the theoretical curve of IP sounding using the Wenner electrode array is computed. The master curve is compared with experimental curves obtained on scale models. A good correlation between these curves is noticed. In addition, it can be concluded that the mathematical model is proving the validity of the experiments on interpretation scale models.