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.     

Current and voltage source induced polarization transients: a comparative consideration

The article discusses the excitation of transient induced polarization responses using current and voltage sources. The first method has found a wide application in induced polarization surveys and—directly or indirectly—in the theory of the induced polarization method. Typically, rectangular current pulses are injected into the earth via grounding electrodes, and decaying induced polarization voltage is measured during the pauses between pulses. In this case, only the secondary field is recorded in the absence of the primary field, which is an important advantage of this method. On the other hand, since the current injected into the ground is fully controlled by the source, this method does not allow studying induced polarization by measuring the current in the transmitter line or associated magnetic field. When energising the earth with voltage pulses, the measured quantity is the transient induced polarization current. In principle, this method allows induced polarization studies to be done by recording the transmitter line current, the associated magnetic field, or its rate of change. The decay of current in a grounded transmitter line depends not only on the induced polarization of the earth but also on the polarization of the grounding electrodes. This problem does not occur when induced polarization transients in the earth are excited inductively. A grounded transmitter line is a mixed‐type source; hence, for a purely inductive excitation of induced polarization transients, one should use an ungrounded loop, which is coupled to the earth solely by electromagnetic induction.     

SOME ASPECTS OF INDUCED POLARIZATION (TIME DOMAIN)*

In the first part, the author, recalling the principle of d/c current measurements, shows by means of some examples, different experimental results relative to the induced polarization phenomenon. He presents the case of the negative induced polarization which can be explained by geometric effects. He gives some examples of saturation curves and discusses the problem of the linearity of the I.P. phenomenon. Then he shows some aspects which demonstrate that I.P. decay curves do not always conform to the general law. He concludes by showing the influence of the current electrodes, the position of which, relative to the polarizable bodies, may alter the shape of the I.P. anomalies. In the second part, the author presents different case histories of I.P. mineral surveys where I.P. is compared to other geophysical methods and drilling results.     

Effect of coupling noise on the interpretation of results of electromagnetic horizontal sounding and modeling

The time variation of a source of alternating current produces an electromagnetic coupling between the transmitting and receiving systems in induced electrical polarization and resistivity surveys that employ horizontal electrical sounding. The coupling alters, sometimes significantly, the resistivity and chargeability values and, consequently, compromises the interpretation of the data. This work develops the analysis of this coupling on the time domain for both a homogeneous Earth and an Earth constituted of several homogeneous horizontal layers. Based on the results, it evaluates the theoretical variation of the voltage and compares it to observed data of an induced electrical polarization and resistivity survey with horizontal electrical sounding. The comparative study of the voltage decay curves assesses the contribution of the electromagnetic coupling to the values of the chargeability and apparent resistivity as a function of the bipole length and the period of the source current. Besides that, the respective pseudosections have delineated the horizontal and vertical variations of those two electrical properties, providing the interpretation of the geoelectrical section. This research is important for the oil industry because it may furnish information that help to: (i) define the structure of the sedimentary strata; (ii) estimate the clay content of the sandstones; and (iii) detect the possible presence of metallic sulphide halos at fractured zones of the sediments above the oil reservoir. It may be adapted to analysis of EM coupling in both resistive and induced electric well logs.     

Effect of clayey media parameters on the negative response of a coincident loop1

The aim of this work is to consider the phenomenon of negative response and its detectability in a polarizable half-space formed of Clay-water mixture which commonly exists in water aquifers and which can be used as a simple indicator of the presence of Underground water. We make use of an analytical treatment for the transient voltage induced in a coincident loop lying on a half-space as a basis for our computations. A Cole-Cole model is used to represent the Clay with appropriate parameters. As saturated Clay is characterized by high conductivity and moderate chargeability, it is hardly detectable relative to the practical noise level. However, there are optimum Clay parameters that offer a maximum negative response. It is also observed that for a very short time constant τ in the Cole-Cole model, the amplitude of the negative response decreases with the decrease of the time constant due to the fast decay of the polarization current. Finally, it is found that there is an optimum value for the loop radius which gives the largest value of the negative response and this loop radius depends on the model parameters.     

岩石激发极化弛豫时间谱与孔隙结构、渗透率的关系

激发极化衰减曲线包含丰富的地层信息,且由多个指数衰减叠加而成.本文采用奇异值分解法对泥质砂岩的激发极化衰减谱进行多指数反演,得到光滑连续的激发极化弛豫时间谱,合适的弛豫时间分布点数为32～64.激发极化弛豫时间谱能够表征饱和NaCl溶液的岩石孔隙结构.结合孔隙度和弛豫时间几何平均值,能够显著提高渗透率的求取精度.     

A study on the discrete image method for calculation of transient electromagnetic fields in geological media

We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized: the real number of the electromagnetic field solution based on the Gaver–Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the “ground excitation–stratum measurement” method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drillhole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research.     

THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A POLARIZABLE SPHERE IN A CONDUCTING HALF SPACE1

A polarizable sphere embedded in a conducting half-space can give rise to negative voltage transients in a coincident-loop time-domain electromagnetic system. Such transients have been observed in field situations. Our results are obtained from a model in which the contributions of the host rock, the currents in the sphere, and the interaction between the sphere and the host rock are separated and superposed. This model uses approximations to the integral equation solutions rather than finite-element or finite-difference approximations, and so allows very rapid computation. The theoretical demonstration suggests that interpretation of the negative voltage transients as a polarization response is valid, but more detailed interpretation of polarization properties may not be possible, because the superposition of the polarization response on the normal response depends strongly on the position of the target.     

TRANSIENT ELECTROMAGNETIC FIELD OF A POLARIZABLE HALF-SPACE DUE TO VARIOUS CURRENT PULSES *

In this paper, the expressions for the induced voltage function V(T) and mutual impedance function Z_m(T) have been derived for specific range of time T and specific values of induced polarization parameters a for ramp and saw-tooth type of current pulses. The computed results for various cases are also presented. The low values of induced polarization parameter a represent the medium possessing membrane polarization, whereas high values exhibit electrode polarization medium. The method has practical applicability and is best suited for the interpretation of transient electromagnetic fields over a polarizable half-space.     

SIGN REVERSALS IN THE TRANSIENT METHOD OF ELECTRICAL PROSPECTING (ONE-LOOP VERSION)*

The transient electromagnetic fields observed by the MPPO-1 equipment in practice over geological structures cannot always be adequately explained by Maxwell's equation when the imaginary part of the conductivity of the rocks is neglected. If, for any reason, the conductivity of the rocks is a complex function of frequency such that the imaginary part is appreciable the model calculations must include this. This explains why some observed transient electromagnetic decay curves change sign with time.     

基于核主成分分析的时间域航空电磁去噪方法

时间域航空电磁数据往往在测量过程中受到天然和人文噪声的干扰.如果不能很好滤除这些电磁噪声,那么将会降低资料质量、影响反演的精度,甚至获得错误的解释结果.本文提出了一种基于核主成分分析的去噪方法,通过核主成分分析提取叠加后衰减曲线的主成分,然后使用能量占比方法分离反映地下介质的有效信号和噪声,最后使用反映地下介质的特定成分进行重构.本文所推荐的去噪方法不仅能剔除天然噪声,例如天电产生的尖脉冲或者振荡,而且能有效地抑制人文噪声.分别使用基于核主成分分析的去噪方法,以及AeroTEM软件的处理方法对同样的吊舱式时间域直升机航空电磁勘查系统实测数据进行处理,并比较其结果.处理结果表明：所推荐的去噪方法要优于AeroTEM软件.     

TRANSIENT ELECTROMAGNETIC RESPONSE OF A SPHERE IN A LAYERED MEDIUM*

The Galerkin method of solving integral equations is well suited to the solution of the integral equations describing the transient response of a sphere embedded in a layered medium, which is excited by a large co-axial loop. The transient response is calculated by transforming the steady state solutions obtained in the frequency domain. The analysis shows that the scattering matrix is extremely diagonally dominant and the maximum number of modes required to obtain convergence does not rapidly increase with frequency. The number of modes required is about eight. This type of scattering matrix can be taken to be an expression of the principle of elementary superposition. This principle is reflected in the decay curves. These show that the early part of the decay curves asymptotically approach the decay curves to be expected for a layered structure without the sphere. The slope of the latter stages of the decay curve gives a decay constant that is the same as was obtained for spheres in free space excited by planar or dipolar sources. The point of departure in time of these curves from the layered ground curves is delayed either by placing the sphere at a greater depth or by placing a more conductive overburden above the sphere.     

Mathematical modeling of membrane polarization occurring in rocks due to applied electrical field

Membrane polarization occurs in sediments with different surface area of capillaries (pores) and is regarded as a slow type of polarization. This phenomenon is the foundation of the well known methods of induced polarization (IP): time domain and frequency domain induced polarization. The characteristic parameters of induced polarization which are required for studying physical properties of rocks are measured in the laboratory. Data measured in the laboratory confirmed the distinctions of IP processes at time-on and time-off. Additionally linear dependence of voltage and applied current is not always observed. This paper presents the first step of studying: theoretical consideration for time-on and mathematical modeling of membrane polarization, ion concentrations of electrolyte in the pores of different models of pores space, and arising voltage. The problem of concentration of ions along the pores can be solved using the diffusion equation with specified initial and boundary conditions. Reduced boundary conditions for time-on show that transient concentrations at the boundaries are linear with time. It allows obtaining the analytical solution for this equation. Mathematical modeling has been performed for different combinations of pores. It is shown that if electrical current flows from the pores with greater transfer numbers to the pores with smaller transfer numbers, an excess of ions will be observed at this boundary. If the difference of transfer numbers is negative, there is a decrease in the concentration of ions at the vicinity of the boundary. This decrease will continue until the concentration at this boundary reaches zero. In this case the galvanic chain will be interrupted and electrical current flowing through the sample does not penetrate to this cell. The duration of the process of ions distribution in the pore and time of blockage t ₀ is proportional to the radii of contacted pores and inversely proportional to the transfer number difference and square of the current flowing through this cell. It was shown by both laboratory measurement and field processes that induced polarization relates to low porous rocks with small transfer number differences.     

极化方法在成都地磁台的应用研究

以成都台FHDZ-M15地磁组合观测系统产出的秒采样观测数据为研究对象,应用极化方法提取该台站附近几次中强震前的超低频(ULF)磁异常信号.成都台极化值长期曲线具有一定的年变化特征,利用傅里叶拟合消除周期变化后,对残差进行分析.结果显示,极化值增高现象与其后2个月内台站周边区域的M_L≥5.0地震有很好的对应关系,高值异常持续3—5日,与外空场活动无关,且逆冲型地震前的极化值异常幅值高于走滑型地震.      

TRANSIENTS AND FIELD BEHAVIOUR IN INDUCED POLARIZATION*

This paper deals with electromagnetic fields in the so called “Transient Induced Polarization Technique”. Field equations are integrated in the case of a polarizable sphere inbedded in a sterile overburden. The existence of a remanent polarization vector P which slowly decays once the charging current has been cut off is taken as the initial condition. When the surface between the air and overburden is (as a first step) disregarded, the Laplace transform of the EM fields is given. The integral of the electric field (which is fairly often the result of prospection work) is independent of the various time constants related to electrochemical processes, but it stands as a good measurement of the total electrostatic dipole created by the charging current. We investigate the geometrical circumstances that can bring negative values of I.P. signal. Such negative values can be found in two cases: 1. The discharge currents are. distorted by the ground surface. 2. The I.P. signal is picked up by electrodes inside the polarizable material. The last part is dedicated to an account of experimental work performed on models and of an actual case history. The mathematical derivations are included in an appendix.     

瞬变电磁法的探测深度问题

用解析分析、时域有限差分、时-频分析的方法,以地面中心回线装置和阶跃脉冲激励源为例,分析讨论了瞬变电磁测深法的勘探深度问题,以便为野外勘探工作设计提供依据,达到预期的探测目的.解析计算证实了瞬变场在地下以有限速度传播,数值模拟表示出了准静态条件下瞬变场的反射.研究结果表明,由于时间域电磁场遵循因果律,瞬变电磁法的探测深度主要由观测时间决定. 瞬变电磁场的初始传播速度与大地电阻率无关,继后在大地色散作用下,阶跃脉冲前沿逐渐变得平缓,各频率分量的传播速度与电阻率有关,在低阻地层中探测同样的深度需要较长的观测时间. 最大探测深度是在给定时间内电磁波往返地下某一深度的单程距离,最小探测深度受仪器性能的限制,但是埋藏较浅的异常体也有可能在晚时段被观测到.从时-频密度谱中可得到瞬变电磁场信号时间与频率的关系.     

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.     

On the estimation of the maximum depth of investigation of transient electromagnetic soundings: the case of the Vizcaino transect,Mexico

We test an approach proposed in the literature for estimating the maximum depth of investigation (MDI) of in-loop transient electromagnetic soundings (TEM) with data from the Vizcaino transect, a profile of 38 TEM soundings crossing the Baja California peninsula. The validity of this approach is confirmed by comparing the MDI with the deepest interface of 16 stratified models. In these soundings, all located over the Vizcaino basin, the measured data are not affected by induced polarization. The models indicate the presence of a dipping conductor interpreted as a zone of seawater intrusion with a large lateral extension of over 70 km. The remaining 22 soundings, located over igneous and metamorphic rocks, show reversals in the voltage polarity, indicating the presence of induced polarization effects. The layered Cole-Cole models for these soundings suggest a significant decrease in the MDI. This is confirmed by analyzing the depth behavior of the subsurface current densities. We further analyze the noise level of a data set comprising close to 2000 late-time voltages of about 400 TEM sites acquired in northwestern Mexico. No difference was found between the stationary noise levels of winter and summer, presumably because near thunderstorms are practically absent in this part of Mexico.     

A Simple Analogue Experiment to Account for Power-law and Exponential Decays of Earthquake Sequences

— An event rate decays either exponentially in earthquake swarms, or according to the power law in aftershock sequences, suggesting different physics for these decays. In order to investigate the physics, I measured decays in the rate of acoustic emissions (AE) that occur to relax thermal stress after turning off a home cooking apparatus. Such AE are analogous to an earthquake induced by fluid intrusion because thermo-elasticity was precisely analogous to poro-elasticity. To consider what controlled the decays, different heating rates and durations were specified in several experimental runs for which the mechanical and thermal properties were identical. Temperature decayed exponentially with the same time constant. However, both a power-law decay with a p value roughly equal to two and an exponential decay were observed. To ascertain what was occurring at the AE source, the stress and frictional strength at the AE source were numerically estimated. The stress at the AE source decayed exponentially for both power-law decay and exponential decay. In power-law decay, strength was initially very low and recovered immediately and significantly. However, in exponential decay, the change in strength during the initial stage was not as large as that in power-law decay. It was demonstrated that the time constant of exponential event-rate decay was identical to that of temperature decay if strength is constant.     

瞬变电磁场的直接时域数值分析

为了深入了解瞬变电磁场的勘探原理,直接在时间域对负阶跃脉冲激发的二维瞬态场进行了数值分析.采用的方法是从反映电磁场基本规律的麦克斯韦方程组出发,导出时域电场的齐次扩散方程,对所研究的空间区域作差分离散,源作为初始条件加入,利用准静态近似处理空中边界,然后进行时间的逐步递推,由此展现瞬变电磁场在地下扩散随时间发展的全过程.通过模拟计算不同时刻瞬态电场在地下的分布形态及地面上感生电动势相应的变化,揭示了低阻异常体对感应涡流的聚集作用,低阻覆盖层对瞬变场扩散的减速作用,及瞬变场的延时效应.因此,瞬变电磁法对低阻体是敏感的,有上覆低阻层时探测同样的深度需要较长的时间,而延时效应瞬变场的晚期时段可反映埋藏较浅的异常体.