激发极化法基础理论研究——确定二次极化电流的新方法

本文提出一种通过测磁场确定面极化和体极化介质中二次极化电流的新方法.它与以往测电场的方法有所不同.当时域单向长脉冲激发电流通过面极化和体极化介质时,便在其表面和内部产生激发极化效应.在通电时间内和断电后的放电过程中,若极化介质内产生了二次极化电流,它必将在周围产生二次磁场.我们通过观测二次磁场可靠地确定了介质中二次电流的存在与否和量值大小以及矢量方向等重要内容.本文除给出一些实验结果外,还给出了实例.多年来,国内、外学者对体极化介质中二次极化电流的存在问题是有争议的,本文对此给出了具有充分说服力的实验结果,有利于统一这方面的认识.     

体极化介质激发极化法理论研究

本文首先根据实验结果和对体极化介质激发极化机理的分析,并由极化率的定义出发,采用与以往不同的方法,提出等效电阻率概念。其次,根据位场的叠加原理,给出在稳定电流场中二次极化场欧姆定律的微分形式。然后,根据电量不灭定律,提出稳定电流场中二次极化电流密度法向分量连续的边界条件式。最后,给出几种典型条件下的理论计算结果。     

时间域航空电磁法激电效应对电磁扩散的影响

由于激发极化效应的影响,时间域航空电磁晚期道信号经常会出现变号现象.基于电阻率的传统反演方法无法对变号数据进行正确反演,因此通常在数据处理中予以剔除.为深入了解极化介质的电磁扩散特征,认识航空瞬变电磁负响应的产生机理,本文研究时间域航空电磁系统的电磁扩散特征.我们以均匀极化、非极化半空间及层状介质模型为例,通过直接积分的方法求解频率域电场响应,并由欧姆定律得到电流响应,再经过汉克尔变换得到时间域电流响应.通过研究电流随时间在地下极化介质中的传播特征研究电磁扩散过程;通过对比不同激电参数对电磁扩散的影响,研究极化介质中感应电流与极化电流的扩散规律,从而合理地解释极化介质中负响应的产生机理.基于本文研究和分析结果,可加深对时间域航空电磁法中激电效应的认识.     

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.     

谱激电法中频率相关系数的应用

从电子导体激发极化（过电位）的电化学机理出发,导出了面极化系数的频谱表示式,得出面极化频率相关系数 c^（s）=0.5-1;从理论上证明了利用Cole-Cole模型描述体极化激电频谱的合理性,说明体极化频率相关系数c≤c^（s）.理论算例和实测结果表明,可以利用视频率相关系数在极化围岩背景上划分局部异常体,并按结构（矿物颗粒均匀程度和连通情况）区分引起激电异常的极化体.因此,在谱激电法中应重视这一参数的应用.     

频域激发极化法中体极化与面极化内在联系的探讨

矿化的体极化介质,其激发极化效应来自其中所含电子导电矿物颗粒的表面极化效应。基于上述认识,本文从理论上推导出含球状电子导体的体极化介质复电阻率的“微观”数学表达式。将它与体极化介质复电阻率的“宏观”表达式--Cole-Cole模型相比较,得出了:1.Cole-Cole模型中的特征参量与球状电子导体的表面极化系数、含量以及导体半径等的综合关系式;2.电子导体表面极化系数在频域中的一般表达式。这表达式同目前在实验室中观测到的结果是一致的。     

井中声电转换波场辐射能量定量分析

井中声激发极化效应研究是实现声激发极化测井实用化的技术基础,实质上是声波在双相孔隙介质中向电磁波的转化,其结果就是形成井中声电转换波场,最终表现为井中声场辐射能向电磁场能的转化.通过对双相孔隙介质中声激发极化过程声电转换波场能量的理论分析,研究了井中声电转换波场能量的总体构成,提出了井中低频声激发极化电场电能体密度的概念,并推导出具体表达式.通过采用实际地层参数模型进行井中低频声激发极化电场的模拟计算得到了井中低频声激发极化过程中电能体密度与声波频率与地层参数的相关关系.     

激发极化法的“饱和效应”问题

西格尔（H.O.Seigel）从理论计算得到导电颗粒含量为25％的极化球体有最大异常,因此认为:激发极化法只宜于寻找中等浸染程度的矿体,对于含量很高的矿体或良导致密型矿体,激发极化法是不行的。据称这种“饱和效应”的理论得到野外结果的证实。 本文根据我国激发极化法在良导致密型矿体上大都能获得明显视极化率异常的事实,说明西格尔的“饱和效应”理论与事实不符。本文认为良导致密型极化体不存在“饱和效应”问题,激发极化法对它们的勘探也是有效的。可能由于西格尔把低含量理论公式,不计条件地推导到高含量、甚至良导矿体,因此他的结论是错误的。本文最后讨论了电阻率因素对浸染型球体视极化率强度的影响。     

考虑面极化效应时谐变电磁场的计算和模拟相似准则

根据频率域激发极化法（以下简称激电）的现有实验资料,导出了包括面极化激电效应和电磁效应的定解条件,提出了从Maxwell方程组出发同时考虑电法两大效应时谐变电磁场的计算方法。在此基础上讨论了电法的模拟相似准则。     

利用毛管模型研究泥质砂岩电化学测井响应机理

自然电位和激发极化电位测井响应所涉及的离子导体激发极化电位的微观机理解释,主要依据双电层形变假说和浓差极化假说,缺少定量描述的数学模型和理论体系.本文利用孔隙介质的微观毛管模型,给出了毛管模型中双电层理论和阳离子交换量与Zeta电位的关系,推导出毛管中离子流量和电流强度表达式.由电荷守恒定律和物质守恒定律,推导出毛管中离子浓度分布的解析表达式,建立了描述含水泥质砂岩激发极化电位和自然电位的数学模型.从而系统地严格证明了含水泥质砂岩激发极化现象是在电流场和浓度梯度场的共同作用下,由孔隙中离子浓度浓差极化电位和双电层形变电位形成的.并且证明了描述泥质砂岩自然电位的数学方程和描述激发极化电位的数学方程及形成机理是一致的.计算结果表明：激发极化极化率随孔隙度和渗透率的增大而减小;极化率随溶液浓度的增加而减小,随阳离子交换量的增加而增加;证明了地层水浓度、阳离子交换量是影响自然电位大小的主要因素.     

DIRECT CURRENT ELECTRIC POTENTIAL FIELD ASSOCIATED WITH TWO SPHERICAL CONDUCTORS IN A WHOLE-SPACE1

Bispherical coordinates are used to derive an exact mathematical solution for the potential field generated by direct current electric conduction in an earth model consisting of two spherical inclusions in a uniform whole-space. The solution takes the form of a spherical harmonic expansion in bispherical coordinates; coefficients in the expansion are obtained by solving sets of linear equations. Rapid forward modelling of numerous interesting situations in d.c. resistivity prospecting is facilitated by the generality and computational efficiency inherent to this new solution. For example, the accuracy of image (or superposition) methods for calculating potential solutions can be quantified. Similarly, the ability of d.c. conduction methods to resolve two distinct bounded bodies in three-dimensional space can be examined by repeatedly calculating the secondary potential or apparent resistivity response of an earth model as a selected parameter is varied. Synthetic mise à la masse, crosshole, or areal potential data sets can be generated for subsequent use in inversion studies. Improvements in solution technique derived here also apply to a simpler model consisting of a single sphere buried in a half-space.     

On the electrical reflectivity tensor in d.c. electric field modelling

We use the integral equation for a d.c. electric field, published in the literature, to introduce the concept of the electrical reflectivity tensor into d.c. electric field modelling. It is shown that in d.c. electric field modelling, the electric reflectivity tensor can be obtained in exactly the same way as in electromagnetic modelling. As a result, for a d.c. electric field, the quasi‐linear and the quasi‐analytical approximations, as well as the quasi‐analytical series, can be constructed in exactly the same way as in electromagnetic modelling. If the primary field is uniform, and if the anomalous body is a uniform circular cylinder or a uniform sphere, the reflectivity tensor is zero order (constant), relating to the free surface charge density. Thus, for some homogeneous bodies that have simple shapes and are embedded in a uniform primary field, the electrical reflectivity tensor is not only a mathematical mechanism for obtaining approximate solutions, but also a physical reality. Indeed, the free surface charge density is defined as the change of the electric displacement vector across the boundary surface under consideration. If the primary field is caused by a point source, and if the anomalous body is a uniform sphere, the reflectivity tensor is second order, varying slowly within the sphere. The relationship to the free surface charge density can be established only when both the reflectivity tensor and the free surface charge density are approximated by the first terms of their series solutions. If the point source is far from the centre of the sphere, the corresponding reflectivity tensor reduces to zero order, and is independent of the observation position within the sphere, i.e. it is a constant. Therefore, the basic idea of the quasi‐analytical approximation, i.e. taking the reflectivity tensor outside the integral operator, is justified in the case considered here.     

Can Euler deconvolution outline three-dimensional magnetic sources?

Severe limitations of the standard Euler deconvolution to outline source shapes have been pointed out. However, Euler deconvolution has been widely employed on field data to outline interfaces, as faults and thrust zones. We investigate the limitations of the 3D Euler deconvolution–derived estimates of source dip and volume with the use of reduced-to-the-pole synthetic and field anomalies. The synthetic anomalies are generated by two types of source bodies: (1) uniformly magnetized prisms, presenting either smooth or rough interfaces, and (2) bodies presenting smooth delimiting interfaces but strong internal variation of magnetization intensity. The dip of the first type of body might be estimated from the Euler deconvolution solution cluster if the ratio between the depth to the top and vertical extent is relatively high (>1/4). For the second type of body, besides dip, the source volume can be approximately delimited from the solution cluster envelope, regardless of the referred ratio. We apply Euler deconvolution to two field anomalies which are caused by a curved-shape thrust zone and by a banded iron formation. These anomalies are chosen because they share characteristics with the two types of synthetic bodies. For the thrust zone, the obtained Euler deconvolution solutions show spatial distribution allowing to estimate a source dip that is consistent with the surface geology data, even if the above-mentioned ratio is much less than 1/4. Thus, there are other factors, such as a heterogeneous magnetization, which might be controlling the vertical spreading of the Euler deconvolution solutions in the thrust zone. On the other hand, for the iron-ore formation, the solution cluster spreads out occupying a volume, in accordance with the results obtained with the synthetic sources having internal variation of magnetization intensity. As conclusion, although Euler deconvolution–derived solutions cannot offer accurate estimates of source shapes, they might provide a sufficient degree of reliability in the initial estimates of the source dip and volume, which may be useful in a later phase of more accurate modelling.     

Elongated horizontal and vertical receivers in three-dimensional electromagnetic modelling and inversion

Electromagnetic geophysical methods often rely on measurements of naturally occurring or artificially impressed electric fields. It is technically impossible, however, to measure the electric field directly. Instead, the electric field is approximated by recording the voltage difference between two electrodes and dividing the obtained voltage by the distance between the electrodes. Typically, modelling and inversion algorithms assume that the electric fields are obtained over infinitely short point-dipoles and thus measured fields are assigned to a single point between the electrodes. Such procedures imply several assumptions: (1) The electric field between the two electrodes is regarded as constant or being a potential field and (2) the receiver dimensions are negligible compared to the dimensions of the underlying modelling grid. While these conditions are often fulfilled for horizontal electric fields, borehole sensors for recordings of the vertical electric field have dimensions in the order of ≈100 m and span several modelling grid cells. Observations from such elongated borehole sensors can therefore only be interpreted properly if true receiver dimensions and variations of electrical conductivity along the receiver are considered. Here, we introduce a numerical solution to include the true receiver geometry into electromagnetic modelling schemes, which does not rely on such simplifying assumptions. The algorithm is flexible, independent of the chosen numerical method to solve Maxwell's equations and can easily be implemented in other electromagnetic modelling and inversion codes. We present conceptual modelling results for land-based controlled source electromagnetic scenarios and discuss consideration of true receiver geometries for a series of examples of horizontal and vertical electric field measurements. Comparison with Ez data measured in an observation borehole in a producing oil field shows the importance of both considering the true length of the receiver and also its orientation. We show that misalignment from the vertical axis as small as 0.1° may seriously distort the measured signal, as horizontal electric field components are mapped into the desired vertical component. Adequate inclusion of elongated receivers in modelling and inversion can also help reducing effects of static shift when interpreting (natural source) magnetotelluric data.     

基于电场总场矢量有限元法的接地长导线源三维正演

电磁场数值模拟的背景场/异常场算法是三维正演的有效策略之一,优点为采用解析法计算电磁场背景场代替场源项、克服了场源奇异性,缺点为不适用于发射源布置于起伏地表或背景模型复杂的情形.总场算法是直接对电磁场总场开展数值模拟,其难点是有效加载场源、保证近区与过渡区数值解精度.本文以水平电偶源形式分段加载接地长导线源,并以电场总场Helmholtz方程为矢量有限元法控制方程,实现了基于非结构化四面体网格剖分的接地长导线源频率域电磁法三维正演.通过与均匀全空间中水平电偶源产生的电场解析解对比,验证了本文算法的正确性,并分析了四面体外接圆半径与其最短棱边的最大比值和四面体二面角最小值对数值解精度的影响规律.通过与块状高导体地电模型的积分方程法、有限体积法和基于磁矢量势Helmholtz方程的有限元法数值解对比,进一步验证了本文算法正确性,同时说明了非结构化四面体网格能够更加精细地剖分电性异常体,利于获得精确数值解.     

Self-consistent problem of induced polarization of electrokinetic origin

In the first part of the paper, with some constraints, we find the analytical solution of the self-consistent problem of induced polarization (IP) for an electrokinetically polarized sphere. The stationary (on long time intervals) solution of the self-consistent problem is a set of the potential fields that are interconnected with each other: the exciting electric field, the extraneous hydrodynamical field (electroosmotic flow of a viscous incompressible fluid), and the resulting electromagnetic IP field. The extraneous field is the field of the osmotic flow of a charged liquid and the field of the charges that emerge due to the membrane effect in the narrowed segments of the pore channels. The calculations show that the IP fields derived by solving the self-consistent problem and by the Seigel-Komarov phenomenological approach are different. In the second part of the paper, by generalization of the obtained analytical solution, we formulate the self-consistent IP problem for isotropic σ-η media of arbitrary shape, which are bounded by a smooth surface. The problem can be solved by the numerical methods.     

A versatile integral equation technique for magnetic modelling

A requirement currently exists in both mineral exploration and environmental or engineering geophysics for a technique to model the magnetic fields caused by bodies with large to extreme susceptibilities in which both induced and remanent magnetizations are significant. It is well known that modelling such magnetic fields is not amenable to any known approximation. It is a significantly difficult task that requires the solution of a magnetostatic boundary value problem. Analytical solutions to the problem are extremely useful for providing insight but generally of limited application in practical interpretation due to the geometrical complexity of real situations. Available numerical solutions include both volume and surface integral equation formulations. However neither of these are particularly efficient for the purpose. An alternative surface integral equation formulation is presented here which represents the required magnetic field in terms of a double layer over the surface of the body. The technique accommodates both remanent and induced magnetization and is generally applicable to any 3D body in a magnetic environment for which the Green's function is available. The present technique has significant advantages over other integral equation solutions in the geophysical literature. It is particularly economic in terms of the density of the surface discretization and consequently the computational effort. Moreover, it is extremely robust. It is found to yield accurate solutions for the type of thin bodies that cause numerical instability with other surface integral equation approaches.     

偶极子假设引起的大回线源瞬变电磁响应偏差分析

偶极子假设下的场点近似解与场点的瞬变电磁精确解存在一定的误差,文中对偶极子假设引起的误差进行了探索性研究.首先分析了由恒定电流偶极子公式“比拟”出的谐变偶极子位函数解.分别计算了静态场中磁偶极子和电偶极子的近似解与各自对应的未做偶极子假设的电流环和载流导线的精确解之间的误差值,然后分析了谐变偶极子微元与点电荷微元的误差...     

PHYSICAL AND COMPUTER MODELING OF INDUCED POLARIZATION *

The Laboratory of Geophysics of the University of Arizona was presented with an exploration problem by Falconbridge, Ltd. of Canada. Massive mineralized hemispherical “pods” are in the vicinity of a tuff layer of high conductivity and induced polarization response, covered by large thicknesses of resistive volcanics. The initial approach was to utilize electrolytic tank modeling. The extreme resistivity and IP contrasts proved to be difficult to recreate. Two dimensional modeling was attempted next with conductive paper, using copper and silver paint for anomalous masses. This method also proved inadequate. Finally, mathematical equations were solved which could model any arbitrary anomalous body in any steady state electrical field. Plane waves as well as point current sources producing non-plane waves are possible. Finite difference equations were derived for the non-linear partial differential equations under consideration. The equations were solved using a digital computer. Initially, the boundary conditions had to be satisfied at the boundaries of resistivity changes, severely restricting possible geometric shapes for anomalous bodies. The final and successful solution was to apply numerical techniques to obtain solutions of equations which require only that the relative resistivities through the area be specified. The Falconbridge problem and its solution are analyzed.