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1.
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   

2.
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 ma 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 ma 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.  相似文献   

3.
It is advantageous to postulate the phenomenological equivalence of chargeability with a slight increase in resistivities rather than a similar reduction in the conductivities. Substitution of these increments in the expression for the total differential of apparent resistivity leads directly to Seigel's formula. Included also are (i) an equally simple demonstration that, for a homogeneously chargeable ground with arbitrary resistivity distribution, the apparent chargeability ma, equals the true homogeneous value m, and (ii) a direct derivation of the completely general resistivity relation where the symbols have the usual meanings.  相似文献   

4.
Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = 1 ? pρ∞/ρdc with ρ∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency-effect, analytical expressions of feα are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.  相似文献   

5.
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   

6.
A part of the Békés Basin (an extensional sub‐basin of the Pannonian Basin, where the basement under thick Pannonian sediments is well known from deep boreholes and from seismic measurements, and where many magnetotelluric (MT) soundings have been carried out for frequencies ranging from 1 to 10?3 Hz) was selected as a test area to assess the imaging performances of various apparent‐resistivity definitions computed with rotational invariants of either the real part of the complex impedance tensor, or its imaginary part, or both. A comparison (based on earlier 3D numerical studies) has been made between the magnetotelluric images obtained in this way and the depths to the high‐resistivity basement, as known from boreholes and seismic investigations. The correlation coefficient between the series of basement depth values at 39 MT sites and the apparent‐resistivity values was found to be stronger and high correlation appeared at a shorter period when it was computed with apparent resistivities based on the real tensor rather than with apparent resistivities based on the imaginary tensor. In the light of our studies, ρRe Z and the impedance phase seem to be more informative than any other combination of magnetotelluric interpretation parameters.  相似文献   

7.
It is seen that the apparent chargeability (Ma)L anomaly over a 2D graphite body splits into two distinct (Vs)L anomalies which closely follow the apparent resistivity profile. This suggests that the electric field amplitude is distorted due to a superficial inhomogeneity creating a (Vs)L anomaly, which bears no relation to the polarized body. The target depth obtained by continuation of such a profile is therefore, not acceptable.  相似文献   

8.
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   

9.
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   

10.
Magnetotelluric response is studied for an inhomogeneous medium having conductivity varying linearly with depth as σ(z) =σ1+αz. For a medium having conductivity increasing linearly with depth, the phase of the impedance approaches 60° at long periods and the apparent resistivity becomes log (ρa) = 2 log (1.36/α1/3) — 1/3 log (T'). The asymptote of log (ρa, T'→∞) when plotted against log (T') has a constant gradient —1/3 and has an intercept on the log (T') axis, which equals 6 log (1.36/α1/3). When a homogeneous layer with a moderate thickness overlies an inhomogeneous half-space, this layer does not affect the asymptote, but it affects the cut-off period and pushes this toward the long period direction. For a medium having conductivity decreasing linearly with depth, the impedance is equivalent to that of a Cagniard two-layer model; the intercept period related to the thickness is T'0=σ1(h2/2)2. Homogeneous multilayer approximations to an inhomogeneous layer are also investigated, and it is shown that the fit to the model variation depends on the number of layers and the layer parameters chosen.  相似文献   

11.
The method of downward continuation is well known to those working in gravity, magnetic, SP and low-frequency electromagnetic exploration. It is demonstrated that the method of continuation can also be usefully employed in the interpretation of induced polarization gradient profiling using point electrodes to determine target depth. The apparent resistance Ra and chargeability Ma measurements obtained with point electrode excitation of the ground have been used to compute the values of (Ra)l and (Ma)l that would be obtained with a linear array. Continuation of the apparent polarizability profile thus obtained with the linear array gives a value for the depth of the target which agrees closely with that obtained by the continuation of the SP profile. On the other hand, continuation of the profile of the secondary transient signal (VS)L alone, yields a depth of the target which is in agreement with the borehole information. However, it is seen that the secondary transient voltage profiling response splits into two anomalies which fall on either side of the SP and/or (Ma)l anomaly centre, and does not coincide with that of the latter.  相似文献   

12.
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   

13.
In order to locate relatively optimum sites for drilling exploratory holes for fresh water, an electrical resistivity survey was conducted along the new Mahukona-Kawaihae Road on the west flank of the Kohala Mountain. Two resistivity soundings made at the same stations, using the Schlumberger electrode configuration, determined an a spacing of 275 feet for horizontal profiling with the Wenner array. The correlation coefficient of the elevation to profile data was 0.41. A procedure for removing elevation effect from observed apparent resistivity was developed. Based on the reduced resistivity profile, four relatively optimum sites for additional exploration, such as by drilling, are specified. There is no specific interpretation of the data that can definitely indicate the occurrence of large underground reservoirs of fresh water anywhere along the profile. This is because the interpretation of horizontal profiling data is essentially relative and not absolute.  相似文献   

14.
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   

15.
When electric soundings are made over an irregular terrain, topographic effects can influence the values of apparent resistivity and lead to erroneous 1D interpretation. A 3D finite-element method has been applied to study the topographical effect of a slope on Schlumberger soundings parallel to the strike. When the resistivity survey is performed at the top of the slope, the apparent resistivity values can be two times higher than in the flat-earth case, depending on the angle (α) and height (H) of the slope, and on the distance (X) between the sounding and the slope top. The results are presented as nondimensional curves which can be used for evaluating topographic anomalies for any value of the parameters α, H and X. It is numerically shown that the topographic effects can be removed from measurements on horizontally layered structures with an irregular earth surface. Real measurements were performed in different geological conditions over an irregular terrain. The correction method based on the nondimensional curves has been applied to the data and has enabled the determination of the correct layered ground configuration using 1D interpretation.  相似文献   

16.
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.  相似文献   

17.
Forward filters to transform the apparent resistivity function over a layered half-space into the resistivity transform have been derived for a number of sample intervals. The filters have no apparent Gibbs' oscillations and hence require no phase shift. In addition, the end points of the filter were modified to compensate for truncation. The filters were tested on simulated ascending and descending two-layer cases. As expected, “dense” filters with sample spacing of In (10)/6 or smaller performed very well. However, even “sparse” filters with spacing of In (10)/2 and a total of nine coefficients have peak errors of less than 5% for p1:p2 ratios of 10–6 to 106. If a peak error of 5.5% is acceptable, then an even sparser filter with only seven coefficients at a spacing of 3 In (10)/5 may be used.  相似文献   

18.
Lahcen Zouhri 《水文研究》2010,24(10):1308-1317
An electrical prospecting survey is conducted in the Rharb basin, a semi‐arid region in the southern part of the Rifean Cordillera (Morocco) to delineate characteristics of the aquifer and the groundwater affected by the marine intrusion related to Atlantic Ocean. Analysis and interpretations of electrical soundings, bi‐logarithmic diagrams and the geoelectrical sections highlight a monolayer aquifer in the southern part, a multilayer system in the northern part of the Rharb basin and lenticular semi‐permeable formations. Several electrical layers have been deduced from the analysis of bi‐logarithmic diagrams: resistant superficial level (R0), conducting superficial level (C0), resistant level (R), intermediary resistant level (R′), conducting level (Cp) and intermediary layer of resistivity (AT). Spatial distribution of the resistivity deduced from the interpretation of apparent resistivity maps (AB = 400 and 1000 m) and the decreasing of resistivity values (35–10 Ωm), in particular in the coastal zone show that this heterogeneity is related to several anomalies identified in the coastal area, which result from hydraulic and geological processes: (i) heterogeneous hydraulic conductivity in particular in the southern part of the Rharb; (ii) lateral facies and synsedimentary faulting and (iii) the relationship between the electrical conductivity and chloride concentration of groundwater shows that salinity is the most important factor controlling resistivity. The distribution of fresh/salt‐water zones and their variations in space along geoelectrical sections are established through converting subsurface depth‐resistivity models. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

19.
The difficulty to use master curves as well as classical techniques for the determination of layer distribution (ei, ρi) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.  相似文献   

20.
Based on rainfall erosion of soil and suspended sediment transport in storm events, a method is proposed to predict peak suspended sediment concentration and suspended sediment yield in watersheds based on rainfall characteristics prior to peak rainfall intensity. The rainfall characteristics factors that dominate peak suspended sediment concentration Cp are rainfall erosion factor Ref, first peak rainfall intensity of area-average rainfall ip1 and antecedent precipitation index Iap; the rainfall characteristics factors that dominate suspended sediment yield Yss in storm events are total rainfall P, suspended sediment yield factor Rsf and antecedent precipitation index Iap. This research focuses on watersheds in Liau-Kwei observation station along Lao-Nung River in southern Taiwan as the research object, and adopts the PSED-model to simulate the discharge hydrograph, suspended sediment concentration hydrograph and suspended sediment yield in 11 storm events for analysis. The analytical results show that there is a good correlation between the above-mentioned rainfall characteristics factors and Cp as well as Yss, thus enabling Cp and Yss to be predicted by using Expressions (13) and (14). These two expressions are utilized to predict Cp and Yss of Typhoon Morakot in 2009, and the results are compared with those from simulation by using the PSED-model. The result of comparison shows there is a good capability in predicting. For the watersheds where it is necessary to predict Cp and Yss of a storm event for the benefit of effective operation of water resource facilities, the aforesaid rainfall characteristics factors can be utilized to establish applicable models for prediction.  相似文献   

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