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1.
In a previous paper it has been shown that we can relate the transient IP electric field Ep , existing in a rock after a step wave of polarizing current, with the steady-state current density Jss during the current step wave as follows: Ep =ρ' Jss . This relation may be interpreted as a generalized Ohm's law, valid in linear cases, in which ρ’(fictitious resistivity) is defined as the product of the true resistivity ρ with the chargeability m. Supposing E p=— grad Up and applying the divergence condition div Jss = o, one can, for a layered earth, obtain a general expression for the depolarization potential Up as a solution of Laplace's equation ?2Up= o. Since the mathematical procedure for the solution of this last equation is identical to that used in resistivity problems, we propose now the introduction of an apparent fictitious resistivity ρ'a (defined as the product of the apparent resistivity ρa with the apparent chargeability ma) as a new parameter for the interpretations of IP soundings carried out over layered structures with a common electrode array. The most general expression of ρ'a as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'a. Therefore it is possible to interpret a ρ'a field curve using the same standard graphs for resistivity prospecting with the usual method of complete curve matching. In this manner a great deal of work is saved since there is no need to construct proper ma graphs for the interpretation of IP soundings, as it has been done up to now. Finally some field examples are reported.  相似文献   

2.
The exact localization of subterranean cavities and the determination of their dimensions is very important for the planning of geotechnical and mining activities. It is a complicated geophysical task often at the limit of detection. Nevertheless geophysical investigation is the only alternative to a dense and expensive grid of boreholes. This report tests the usefulness of geoelectrical resistivity methods for cavity detection under some new aspects. The basis for evaluation was a theoretical analysis of different conventional and focussing measuring arrays and of special arrays for a geoelectrical research between two boreholes. The limit of detectability of a cylindrical cavity of defined cross-section and depth was calculated for the different measuring arrays on the basis of computation of the apparent resistivity ρa. Furthermore, the influence of possible errors (current supply of the electrodes and the distance between the electrodes) is discussed for focussed systems. The second part of the article is directed at the behaviour of the apparent resistivity ρa, the disturbing potential δVd caused by the cavity and the normal potential δV0 of the measuring array all in relation to a homogeneous earth. Some new results are presented. In the last part of the article theoretical results are compared with some field measurements.  相似文献   

3.
The polarization content of a medium, in both the time and frequency domains, can be described by parameters which differ in inherent physical meaning and their practical significance. For real situations, general expressions for the apparent parameters, previously determined for both domains, exist for the general case of soundings on a horizontally multi-layered earth. The comparative analysis of these expressions, here restricted to the simple case of a two-layered earth, shows that the theoretical sounding curves of the frequency-domain are different from those of the time-domain. In particular, for every resistivity or chargeability contrasts examined, the apparent frequency-effect curve lies always over the corresponding apparent chargeability curve, but both curves reach the same asymptotical values for shortest and largest spacings. The important conclusions which can be drawn from this result is that both techniques are suitable to investigate subsoil polarizability anomalies. However, from a practical point of view, it is more convenient to adopt the frequency-domain technique when the polarizability increases with depth, while, on the contrary, the time-domain technique is more efficacious when the polarizability decreases with depth.  相似文献   

4.
A complex transfer function c (or generalized skin depth) can be derived from data for the secondary magnetic field measured by a dipole system with small coil spacing at height h above the ground. This function has a useful property: For a uniform or layered ground, the real part of c yields the‘ centroid depth’z* of the in-phase current system as a function of frequency. This parameter can be combined with the apparent resistivity ρa derived by conventional methods. The function ρa(z*), if known over a broad frequency range, yields a smoothed approximation of the true distribution ρ(z) without an initial model. The relations between ρa(z*) and ρ(z) are studied for a number of multilayer models. An example of the application of the ρa*) algorithm to data from a groundwater survey is given.  相似文献   

5.
This paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency-domain. From the general expression of the apparent frequency-effect for soundings carried out on a multi-layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency-effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency-effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve-matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency-effect function.  相似文献   

6.
In this paper the locations where ρapp = ρ1 and ? = π/4 and where these parameters reach an extreme value in two-layer magnetotelluric (MT) sounding curves are summarized in an extremely compact form. The key parameters over two-layer models with conductivities σ1, σ2 and upper layer thickness h are the real S and α, where S is the conductivity contrast and α is the distance between the observation site and the conductivity interface, normalized to the half skindepth in the first layer. If the impedance components, various resistivity definitions ( ρRe Z, ρIm Z and ρ|Z|, based on different parts of the complex impedance Z ) and the magnetotelluric phase ? are derived as a function of S and α, then the conditions for the apparent resistivity ρapp and the phase ? are that they either satisfy ρapp = ρ1 and ? = π/4 or attain extreme values which can be given in terms of simple algebraic equations between S and α. All equations are valid for observation sites at any depth 0 ≤ z ≤ h in the first layer. The set of equations, presented in a tabular form, may make it possible to determine a layer boundary from the short period part of the sounding curves, in particular the ρRe Z and the ?MT curves.  相似文献   

7.
A method for direct conversion of observed variations in the magnetotelluric (MT) apparent resistivity ρa into relative variations in the resistivity of elements of a well-studied geoelectric structure is proposed. The method is tested on a 1-D model structure consisting of seven horizontal layers in three of which the conductivity can vary within certain limits. It is inferred that the frequency range and the accuracy of methods of magnetotelluric sounding presently applied to the construction of transfer operators are sufficient for determining relative changes in the resistivity of rocks; the latter, as distinct from ρa, can serve as an effective prognostic parameter. The method can be extended to more complex geoelectric structures.  相似文献   

8.
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.  相似文献   

9.
强地震附近视电阻率各向异性变化的原因   总被引：23，自引：2，他引：21       下载免费PDF全文
讨论了强地震、孕震晚期阶段、震源区及附近介质的物理变化过程,证明了视电阻率变化最显著的方向与最大加载方向之间的正交关系,建立了真、视电阻率各向异性变化与裂隙率ν、骨架电阻率ρo、饱水裂隙电阻率ρf的本构关系,解释了视电阻率各向异性变化的原因.研究认为：在强地震孕震晚期阶段,在震源区及附近地壳近地表的较深部,介质微裂隙发育,其走向沿最大主压应力方位优势取向,低阻水充填微裂隙,导电通道连通,引起最大主压应力方向真电阻率变化最显著的真各向异性变化,从而产生垂直主压应力方向视电阻率变化最显著的视各向异性变化,低阻水在其物理过程中起了显著作用.  相似文献   

10.
It seems that the explicit KR‐α method (KRM) is promising for the step‐by‐step integration because it simultaneously integrates unconditional stability, explicit formulation, and numerical dissipation together. It was shown that KRM can inherit the numerical dispersion and energy dissipation properties of the generalized‐α method (GM) for a linear elastic system, and it reduces to CR method (CRM) if ρ∞ = 1is adopted, where ρ∞ is the spectral radius of the amplification matrix of KRM as the product of the natural frequency and the step size tends to infinity. However, two unusual properties were found for KRM and CRM, and they might limit their application to solve either linear elastic or nonlinear systems. One is the lack of capability to capture the structural nonlinearity, and the other is that it is unable to realistically reflect the dynamic loading. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

11.
Using the Carpenter configuration, in which the distances between the successive electrodes of a four-electrode system are kept at r, s and r (as shown in Fig. 1), where r = ma and s = la, or the Wenner-Carpenter configuration, in which r = s, the corresponding formulae for the apparent resistivities ρAα, ρAβ and ρAγ for the α, β and γ configurations are used to compute maximum gradient values for various values of the reflection coefficient K. For any observed curve for these resistivity types, the maximum slope is determined. A set of standard curves is presented which, provided that K is known, then allows the thickness of the top layer to be determined.In the case that K is unknown, another set of standard curves is presented allowing determination of K provided that the maximum slopes of any two of the three resistivity curves are known.The method has been tested for both field and laboratory observations. Discrepancies between the observed and actual values of resistivity are noted and attributed partly to instrumental errors.  相似文献   

12.
It seems that the explicit KR‐α method (KRM), which was developed by Kolay and Ricles, is promising for the step‐by‐step integration because it simultaneously integrates unconditional stability, explicit formulation, and numerical dissipation together. It was shown that KRM can inherit the numerical dispersion and energy dissipation properties of the generalized‐α method [1] for a linear elastic system, and it reduces to CR method (CRM), which was developed by Chen and Ricles [2] if ρ∞ = 1 is adopted, where ρ∞ is the spectral radius of the amplification matrix of KRM as the product of the natural frequency and the step size tends to infinity. However, two unusual properties were found for KRM and CRM, and they might limit their application to solve either linear elastic or nonlinear systems. One is the lack of capability to capture the structural nonlinearity, and the other is that it is unable to realistically reflect the dynamic loading. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

13.
Abstract

The generation of eddies by a large-scale flow over mesoscale topography is studied with the help of two- and three-layer nonlinear quasi-geostrophic models of the open ocean. The equations are integrated forward in time with no eddies present initially. For a given time, the displacement of the interface between layers two and three (ζ) tends to a well-defined limit (function of the horizontal spatial coordinates) as ρ 3 - ρ 2 → 0 (ρr is the density of layer r). Even for values of α[= (ρ 3 - ρ 2)/(ρ 2 - ρ 1)] as small as 0.01 the potential energy due to ζ is not negligible and it can reach, in some cases, a considerable fraction of the total eddy energy.  相似文献   

14.
江苏地电阻率预测指标研究   总被引：1，自引：1，他引：0  
结合地电阻率的前兆机理和实际观测结果,给出构造活动作用下地电阻率的两类前兆异常变化:一是与观测场地周围应力场变化相关的长趋势变化;二是与震源岩石裂隙破裂相关的大幅下降变化。针对地电阻率的两类前兆异常变化,以江苏5个地电阻率场地的历史观测数据为例,采用一年窗长的归一化速率进行分析,提出将归一化速率值的二倍方差作为地电阻率的异常指标,并对预测指标进行R值检验,得到R=0.513,对应R0=0. 277,R/R0=1. 9,预测结果较理想。  相似文献   

15.
Results from a laboratory investigation into the electrical properties of fully and partially saturated Wildmoor Triassic Sandstone have been modelled using the Archie, Waxman–Smits and Hanai–Bruggeman equations. The results demonstrate the limitation of using simple relationships to describe samples when the matrix resistivity ρr is not significantly greater than the saturating electrolyte resistivity ρw. In these situations Archie's parameters m and n are not accurately determined. Conversely, the more sophisticated Waxman–Smits and Hanai–Bruggeman models provide parameters that better describe the electrical properties of the rock and are able to identify heterogeneity between samples that would otherwise be missed. The ranges of values for matrix resistivity (49 < ρr < 161 Ωm) and cementation factor (1.6 < m < 2.1) obtained from the Hanai–Bruggeman model indicate significant variation between samples. Comparison of laboratory‐determined values for cation exchange capacity (0.06 < Qv < 0.51 meq/mL) and those obtained from the Waxman–Smits model (0.09 < Qv < 0.55 meq/mL) indicates a very strong correlation, suggesting this model is appropriate for describing the rock. There is good agreement between parameters modelled using fully and partially saturated versions of both the Hanai–Bruggeman and Waxman–Smits equations, indicating that the data are consistent with these models and that the assumptions made are appropriate.  相似文献   

16.
王丽  叶青  周康雅  丁烨 《地震工程学报》2020,42(1):143-149,214
江苏南京台北南测道2013—2016年年初出现了与邻近的南京江宁台同步的地电阻率长趋势上升变化,2016年的年中出现了与江宁台和稍远距离的江苏高邮、新沂台同步的趋势下降变化。本文用年变形态、消除年变等数据处理方法并联系该区降雨量分析了南京台等地电阻率长程观测数据,基于视电阻率变化与地下介质内部骨架电阻率ρ°、裂隙水电阻率ρf、裂隙率ν之间的本构关系讨论了地电阻率趋势变化的原因,得到:该台南北向测道地电阻率趋势上升变化起因于台站及周边区域性地下介质的应力调整过程,动力来源可能是本区域地壳局部构造运动。  相似文献   

17.
The apparent resistivity is considered as a linear transformation of the potential by an operator in the form of an infinite matrix A. The inverse transformation expresses the potential as a function of the apparent resistivity or of the difference of potentials. It is found by calculation of the inverse matrix-1A. The relation between apparent resistivities for different arrays is expressed as a product of transformations.  相似文献   

18.
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 ma, the expressions of ma 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.  相似文献   

19.
Electrical resistivity measurements have been conducted as a possible means for obtaining precursory earthquake information. Before five great earthquakes (M>7,h<25 km) in China, the apparent resistivity a showed systematic variations within a region 200 km from the epicenters. In particular, 9 stations in the Tangshan-Tianjin-Beijing region prior to the Tangshan earthquake (M=7.8,h=11 km, 27 July 1976) showed a consistent decrease of apparent resistivity around the epicenter, with a maximum resistivity change of 6% and a period of variation of 2–3 years. Simultaneous water table observations in this region showed a declining water table, and ground surface observations indicated a slight (5 mm) uplift in the epicenter region relative to its surroundings.In order to develop an explanation for the observed change of apparent resistivity associated with these great earthquakes, we have used Archie's Law to explore the effects of changes in rock porosity, water content and electrolyte resistivity on measured resistivity.Tentative conclusions of this study are as follows: (1) the apparent resistivity change is opposite to the effect expected from the simultaneous water table trend; (2) the dilatancy needed to give such resistivity variations (assuming Archie's Law holds) is much larger than that needed to explain the observed uplift (by 2–3 orders of magnitude); (3) salinity change in the pore electrolyte is a possible explanation for the variation in resistivity: an increase in the salinity would cause a proportional decrease in resistivity; the data needed to test this hypothesis, however, are lacking; and (4) the effect of changing geometry of rock pores or cracks due to pressure solution may provide an explanation for the decrease in apparent resistivity; it is different in nature from the effect of a volume change in response to stress although the geometry change is also closely related to the stress change.  相似文献   

20.
Computations of the time-domain electromagnetic response of a multi-layered earth have been carried out for different source-receiver coil systems. The primary excitation is a train of half-sinusoidal waveforms of alternating polarity. The conversion into the time-domain involves Fourier series summation of the matched complex mutual coupling ratios of the layered earth models computed by a digital linear filter method. As an example, the response of a perpendicular coil system on the ground surface for two source-receiver separations has been presented for a five-layer earth model. This has been compared with the responses of homogeneous, two-layer, three-layer, and four-layer models. Next, the investigations have been extended to study the problems of equivalence of three-layer models, the intermediate layer of which is either conductive or resistive. For an intermediate conductive layer (H-type), the studies show that in the early portion of the signal the interpretation of a true three-layer earth is possible to some extent, whereas the ambiguity due to equivalence persists in the late samples. On the other hand, for an intermediate resistive layer (K-type), the three-layer earth and its equivalent model cannot be distinguished from each other over the entire sampling period. On the basis of a computational approach, equivalence has been empirically established as √h/ρ=constant for H-type earth-sections, and as h2ρ=constant for K-type earth sections, where h and ρ are respectively the thickness and resistivity of the intermediate layer.  相似文献   

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