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本文在下述前提下用分离变量法求得了径向非均质情形近似电位场的分布,并进一步给出了简化计算公式。这些前提是:1.忽略电极系上绝缘环的影响;2.限于介质电阻率为缓变的情形,忽略电流折射的影响,近似地认为电极系上电流密度均匀分布;3.把电极系当作线电极来处理。 相似文献
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本文发展了积分方程法用于层状介质中三维不均匀体的大地电磁模拟算法（简称MT）.分为二个步骤:第一步,异常体用等效的散射电流代替,通过层状介质中的格林函数,建立以散射电流为未知参数的积分方程;第二步,把求得的散射电流乘上相应的格林函数,即得地面上的二次电磁场,由此而计算出各种MT响应. 文中采用了数值滤波与插值、群变换以及格林矩阵带状化三个方面的数值处理方法,提高了计算效率.通过与已发表的三维MT计算结果对比及格林函数互易性检验,表明了该算法的正确性.在此基础上,进行了数值模拟,初步讨论了三维MT曲线的畸变特点. 相似文献
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第一类积分方程的若干问题 总被引：2，自引：0，他引：2
未知函数不在积分号外出现的积分方程谓之第一类积分方程.这类积分方程在实际问题中是大量出现的,应用相当广泛,因此吸引了国内外不少学者的注意.本文仅对国外的某些情形作一概略的介绍. 相似文献
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电学填埋场渗漏检测方法是利用漏洞电流引起的感应电势异常来定位防渗膜上的漏洞位置.当漏洞电流较小时,检测电极上的极化电位噪声极易将电势的异常值淹没,导致漏洞定位的失败.基于电极极化电位噪声的特点,提出了采用低频交变方波供电的方式来剔除该类噪声.在小型模拟填埋场中的实验结果表明:当回路电流为70 mA,膜上供电电极接电源正极时,防渗层上的两个漏洞只有一个被检出;膜上供电电极接电源负极时,则两个漏洞皆未被检出;将两次实验数据对应相减,则两个漏洞皆被准确定位. 相似文献
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波动问题的级数解边界元法 总被引：5，自引：0，他引：5
本文提出了一种处理波动问题的级数解积分方程边界单元法,它是利用相应的齐次微分方程解的完备系作为加权函数来建立边界积分方程的。这一方法避免了传统的奇异边界积分方程存在的奇异积分问题,应力计算精度也较高。文中还利用这一方法处理了由于局部不规则地形引起的SH波的散射问题,波场输入十分方便。 相似文献
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在坑道超前探测方法中,直流电阻率法原理和操作简单,应用前景广阔,其中侧向聚焦电阻率法应用在测井中已经成为一种常用方法.本文研究了三维坑道直流聚焦法电极组合,首先计算分析了两个同性点电源的电流分布规律,指出由于电流的相互排斥作用,电流密度在这两个点电源的中垂线下一定深度处产生最大值,这个深度与这两个点源之间的距离成正比.基于上述原理,设计出三种电极组合：四点电源、五点电源和九点电源布极方式.其次,用三维有限单元数值模拟的方法计算了上述三种电极系的空间电位分布,得出九点电源方式对电流聚束效果较好,而且当主电极电流小于屏蔽电极电流时效果最好. 相似文献
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成层半空间深埋电极产生的电位分布 总被引：2，自引：1，他引：1
首先给出了点电流源在均匀半空间中所产生电位的解析表达式;其次研究了源电极位于表层和底层时成层半空间介质中的电位分布;最后研究了源电极位于任一层时成层半空间介质中的电位分布. 相似文献
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墙体渗漏的几何尺寸通常很小,所引起的电导率空间差异小,用现有的高密度电法和瞬变电磁勘探方法检测这些很小的渗漏位置,其空间分辨率不够.本文在墙体两侧用电极供电,记录供电电极正向导通、正向关断、反向导通和反向关断这四个过程的瞬态响应全波波形,以穿过墙体的渗漏电流在地层内所产生的直流和瞬变电压异常为有用信号,用不同时刻的电压分布显示渗漏引起的电压异常,实现渗漏位置的直接检测.本文先将墙体视为绝缘体,渗漏位置的电流视为点状电流源,给出了测量平面内的电位分布,这是渗漏引起的电位异常,称为有用信号.然后用镜像法计算了墙体为普通导电介质时的直流场分布,这是墙体不渗漏时的响应,称为渗漏检测的无用信号.用Maxwell方程分析了电极在导通、关断时激发的瞬变电磁响应.与直流响应不同,瞬态响应同时具有幅度衰减和相位移动,其中相位移动对应着传播过程,在墙体界面和渗漏点均产生反射,以类似于波动的形式构成渗漏的有用信息.最后给出了连续记录的30个不同位置的电极所测量的电压分布曲线,直观地显示了瞬变电磁场和直流场的响应以及渗漏位置.验证了本文所给出的直流、瞬变联合渗漏检测方法. 相似文献
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M. OKABE 《Geophysical Prospecting》1981,29(1):39-59
The generalized integral equation for the electric potential governed by a quasi-harmonic equation can be derived via a variational formulation. For surface current distributions it is not always a Fredholm integral equation of the second kind. Numerical solutions of the general heterogeneous problem can be obtained with the “reciprocal averaging technique”, where the solution is obtained a second time after exchange of source and field points. 相似文献
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Numerical computations using the integral equation method are presented for resistivity and IP responses due to arbitrarily shaped 3-dimensional bodies in a layered earth. The unknown surface charge density distribution is expressed as the solution of Fredholm's integral equation of the second kind. Use of moment method (with pulse basis function and point-collocation) yields the matrix equations for the unknowns. The contributions to Green's function are solved (a) analytically for the primary and (b) by convolution for the secondary contributions resulting in a fast algorithm. The further step of computing potential, apparent resistivity, chargeability etc., for any electrode system, is straightforward. Our results show a good agreement with those from finite difference methods and physical tank experiments. The CPU time is only 138 s on a super-minicomputer for an apparent resistivity pseudo-section, even with 96 elementary cells as used for discretization. A large number of models for different geological situations were studied; some are presented here. 相似文献
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T. Lee 《Pure and Applied Geophysics》1972,99(1):130-140
Summary The potential field due to a point electrode, above an inclined interface, has been given in the form of a multiple integral, involving modified Bessel functions of the second kind (Skalskaya [9]2). From this formula it is only possible to derive formulae, from which type curves may be computed, for a limited number of cases. By considering the asymptotic expansion of the Hankel transform of this potential function, it is possible to derive results which will permit the complete interpretation of a Schlumberger sounding, carried out in the direction of strike; for an arbitrary angle of dip of the contact. The method of interpretation is suitable for use on a digital computer and has been found to give rapid and reliable results. 相似文献
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O. KOEFOED 《Geophysical Prospecting》1966,14(1):71-79
In a previous paper by the present author a method was developed for direct interpretation of resistivity observations made with a Schlumberger electrode configuration. This method consisted of two steps. The first of these was to derive the kernel function in the integral expression for the apparent resistivity from the observed data; the second step was to derive the resistivity stratification from this kernel function. The first of these two steps depends on the electrode configuration that has been used. In the present paper the above mentioned method is modified so as to make it apply to a Wenner electrode configuration. The procedure is indicated by which the method may be adapted to any other electrode configuration in which the distances between the electrodes are finite. The second step in the interpretation, i.e. the derivation of the resistivity stratification from the kernel function, is independent of the electrode configuration used, and therefore needs no further discussion in the present context. 相似文献
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M. OKABE 《Geophysical Prospecting》1982,30(5):653-672
A Fredholm integral equation of the first kind with respect to the surface charge density is presented via a weighted residual formulation in the standard isotropic problem. The surface charge densities are numerically obtained by solving the well-known Fredholm integral equation of the second kind, where the new equation can be regarded as a constraint. The accuracy of boundary element solutions is examined in connection with the violation of such a constraint and the “modified reciprocal averaging techniques” are proposed. 相似文献
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G. Petiau 《Pure and Applied Geophysics》2000,157(3):357-382
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E.H. ELORANTA 《Geophysical Prospecting》1986,34(6):856-872
An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the ‘second kind’ developed for the potential of the electric field. In this method the discontinuity-surfaces of electrical conductivity are divided into ‘sub-areas’ that are so small that the value of their potential can be regarded as constant. The equations are applied to 3-D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise-a-la-masse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite. 相似文献
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R. N. EDWARDS 《Geophysical Prospecting》1984,32(5):955-969
The cross-hole variant of the magnetometric resistivity (MMR) method requires two bore holes in the vicinity of a conductive target. In the first, two fixed current electrodes are located, one above the other. They are linked to a low frequency current source by cables, the whole system forming a vertical current bipole. In the second, a sensitive coil measures the axial magnetic field as a function of depth. For a uniform earth, if both holes are vertical, the measured component vanishes by symmetry. However, the presence of a local conductor channels the current and causes an anomalous magnetic component which is interpreted to indicate the position, shape and relative conductance of the target. Mineral deposits are often lamellar in form. The conductive disc is the simplest bounded lamella for which MMR responses may be computed. It is excited by a single current source on its axis. The second source and the surface of the earth are assumed to be far away, a valid assumption for down-hole measurements. The numerical method introduces a new integral equation describing the interaction of current dipoles located in the plane of the disc. The equation is solved analytically for a disc of infinite radius, a layer, and the result is compared with a corresponding known boundary value solution. The computed radial current in the disc and the magnetic field generated by it are described in terms of a current channelling number. The magnitude of the computed field is of the order of one nanoTesla for a typical mining problem. 相似文献
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提出了位场曲化平的新方法. 给定观测曲面S上的位场、S对下方水平面P的相对高程,确定P上的位场. 利用由P向上延拓到S的积分式,建立这两个面上位场及相对高程三者所满足的方程,它是第一类Fredholm积分方程. 用Fourier逆变换式把这一空间域积分式化为波数域积分式,再由指数函数的Taylor展开进一步化为级数式. 积分方程的解采用逐次逼近法迭代计算,即用S上的位场观测值作为P上位场的初始迭代值,用导出的级数式求得S上的位场计算值、由S上的位场观测值与计算值之差校正P上的位场,多次迭代,直到满足迭代终止准则. 我们还给出该积分方程的波数域迭代计算方法. 模型算例表明,重力异常曲化平的均方差和磁异常曲化平的均方差分别为0.0008 mGal和0.0019 nT,在主频为2.26 GHz的笔记本电脑运行,2048×2048数据量,计算时间是975 s. 野外磁场实际资料处理也证实这种方法的有效性. 相似文献