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1.
Borehole direct current (dc) resistivity problems are solved using finite difference method (FDM) primarily to extend the log interpretation in the two-dimensional (2D) domain. Transitional invaded zone, flushed zone, uncontaminated zone, shoulder beds and borehole filled with mud are simulated simultaneously in the model. Linear variation of resistivity is assumed for transitional invaded zone. Normal, lateral and modified laterolog7 (LL74) electrode configuration (discussed in the text) responses were computed using expanding rectangular grid system. LL74 responses with variable geometric factor did show some superiority over the conventional normal and lateral for conductive target beds sandwiched between the resistive beds. For relatively small borehole diameter, all three probes can detect resistive target bed satisfactorily. However, for highly conductive mud both LL74 and normal electrode configuration fail to detect any signal from the target bed. Bypassing effect of the current for LL74 is more than that in normal log. Lateral log shows a signal of conductive invaded zone generated by the conductive mud. Bucking current ratio peaks and the geometric factor peaks in LL74 can detect the bed boundaries.  相似文献   

2.
Assuming the minimum detectable anomaly to be 10%, depths of detection of a 2D vertical resistive sheet of thickness t are found to be 4.0t, 3.0t, 4.0t and 4.0t with Wenner, two-electrode, three-electrode and dipole-dipole (β-Wenner) arrays, respectively, when the array spread is in-line. On the other hand, the depths of detection obtained with a broadside spread of the arrays right over the sheet are much less and are correspondingly 2.5t, 2.0t, 2.5t and 2.5t. An increase in the depth extent W of the sheet from 10t to 20t does not increase its depth of detection with the arrays. The depths of detection of an infinitely resistive horizontal cylinder of radius R are respectively 1.5R, 1.8R, 2.0R and 2.0R with the above-listed arrays when the array spread is in-line. With broadside spread of any of the arrays, the depth of detection is seen to be 2.5R. In the case of a spherical target of radius R, the detection depths of any of the arrays are found to be small and to vary between 0.8R and 1.1R. Comparatively, the detection depths of resistive targets are much lower than those of conductive targets of the same size and shape, with any electrode array. Among all the arrays studied, the two-electrode array performs worst in the detection of resistive targets while it performs best in detecting conducting targets of limited lateral extent. In the case of a spherical target, either resistive or conductive, there is no distinct change in its detection depth with array.  相似文献   

3.
A numerical comparison of 2D resistivity imaging with 10 electrode arrays   总被引：9，自引：0，他引：9  
Numerical simulations are used to compare the resolution and efficiency of 2D resistivity imaging surveys for 10 electrode arrays. The arrays analysed include pole‐pole (PP), pole‐dipole (PD), half‐Wenner (HW), Wenner‐α (WN), Schlumberger (SC), dipole‐dipole (DD), Wenner‐β (WB), γ‐array (GM), multiple or moving gradient array (GD) and midpoint‐potential‐referred measurement (MPR) arrays. Five synthetic geological models, simulating a buried channel, a narrow conductive dike, a narrow resistive dike, dipping blocks and covered waste ponds, were used to examine the surveying efficiency (anomaly effects, signal‐to‐noise ratios) and the imaging capabilities of these arrays. The responses to variations in the data density and noise sensitivities of these electrode configurations were also investigated using robust (L1‐norm) inversion and smoothness‐constrained least‐squares (L2‐norm) inversion for the five synthetic models. The results show the following. (i) GM and WN are less contaminated by noise than the other electrode arrays. (ii) The relative anomaly effects for the different arrays vary with the geological models. However, the relatively high anomaly effects of PP, GM and WB surveys do not always give a high‐resolution image. PD, DD and GD can yield better resolution images than GM, PP, WN and WB, although they are more susceptible to noise contamination. SC is also a strong candidate but is expected to give more edge effects. (iii) The imaging quality of these arrays is relatively robust with respect to reductions in the data density of a multi‐electrode layout within the tested ranges. (iv) The robust inversion generally gives better imaging results than the L2‐norm inversion, especially with noisy data, except for the dipping block structure presented here. (v) GD and MPR are well suited to multichannel surveying and GD may produce images that are comparable to those obtained with DD and PD. Accordingly, the GD, PD, DD and SC arrays are strongly recommended for 2D resistivity imaging, where the final choice will be determined by the expected geology, the purpose of the survey and logistical considerations.  相似文献   

4.
Five test profiles in time-domain induced polarization measurements over conducting sulphide and graphite mineralisations were run with the two-electrode, three-electrode, modified unipole, pole-dipole, dipole-dipole, Schlumberger, and Wenner α and β configurations. The results show that, compared to the other electrode systems, the simplest two-electrode array produces the largest anomalies with the smallest of spacings.  相似文献   

5.
This paper is an experimental extension of the theoretical investigations by Roy (1975) on the relative performances of the Laterolog 7, normal and some other sondes in logging of resistive formations. Only infinitely resistive formations have been simulated and placed in a tank containing tap water (true resistivity 27 Ωm) as electrolyte—representing both the mud column and the adjacent formations. Two sets of laboratory results (Doll 1951, NN 1958, 1969), have been repeated and we find that, for both these sets, the performance of the normal device is by far the superior of the two. In addition, we have studied the effect of varying the spacings A1A2, O1O2 and AM of Laterolog 7, normal, and two new sondes—Laterolog 4 and modified unipole—for two bore hole diameters in each case. For formation thicknesses less than A1A2 or AM, the Laterolog 7 is unsuitable because its response is flat and close to the base-line value. The normal device is more diagnostic, although, in such a case, it registers a trough or a resistivity low even against a resistive formation. For bed thicknesses clearly greater than A1A2 or AM, the normal sonde is decidedly superior to Laterolog 7, since its anomalies are sharper and larger. When the formation thickness is equal to or only slightly larger than A1A2 or AM, Laterolog 7 is somewhat better as it records a readable positive deflection while the normal does not. However, one must remember that a single run of the conventional resistivity log includes two normals and a lateral at different spacings. Laterolog 4 and modified unipole can in many instances produce better logs than normal, other considerations apart. The results are consistent with our own theoretical predictions and experience in surface resistivity profiling. They do not, however, agree with the prevalent concepts on Laterolog 7 vis-a-vis normal sonde.  相似文献   

6.
Theoretical broadside resistivity profiles over an outcropping dyke of infinite depth extent with three Wenner configurations (namely Alpha, Beta and Gamma), Schlumberger, and two-electrode configurations of various electrode spacings and for various reflection factors are presented. The broadside profiles qualitatively indicate that the shape of the anomaly is invariant with the electrode configurations. The various electrode configurations can be arranged in decreasing order of magnitude of anomalies as Beta Wenner, Alpha Wenner, Schlumberger, Gamma Wenner, and two-electrode. The broadside Wenner profiles also show larger anomalies compared to those in inline profiles.  相似文献   

7.
This paper investigates the relative merits and effectiveness of cross‐hole resistivity tomography using different electrode configurations for four popular electrode arrays: pole–pole, pole–bipole, bipole–pole and bipole–bipole. By examination of two synthetic models (a dipping conductive strip and a dislocated fault), it is shown that besides the popular pole–pole array, some specified three‐ and four‐electrode configurations, such as pole–bipole AM–N, bipole–pole AM–B and bipole–bipole AM–BN with their multispacing cross‐hole profiling and scanning surveys, are useful for cross‐hole resistivity tomography. These configurations, compared with the pole–pole array, may reduce or eliminate the effect of remote electrodes (systematic error) and yield satisfactory images with 20% noise‐contaminated data. It is also shown that the configurations which have either both current electrodes or both potential electrodes in the same borehole, i.e. pole–bipole A–MN, bipole–pole AB–M and bipole–bipole AB–MN, have a singularity problem in data acquisition, namely low readings of the potential or potential difference in cross‐hole surveying, so that the data are easily obscured by background noise and yield images inferior to those from other configurations.  相似文献   

8.
Summary A theoretical solution is obtained for the problem of a three and four layered earth model with transitional boundary. In practice, the transition layer can stand for fresh water bearing sand and fine gravels. The master curves for Schlumberger electrode configuration and table of data are presented for the case when the lower half space is infinitely resistive.  相似文献   

9.
It is shown by the result of digital magnetotelluric soundings in the Tangshan seismic area and its surrounding regions that the crust under the surface conductive sediments is divided into two layers,i. e., the resistive upper crust and the conductive lower crust. The upper crust wherein the Tangshan main shock and most of the aftershocks occurred is a convex lens-like body which is cut by faults at the east, south and west sides. The focus of the mainshock was located at the position of maximum thickness of the resistive upper crust while the spatial variation of Curie point isothermal surface and the deepest limit of the depths of aftershocks coincide with the downward depression of the bottom of the resistive upper crust. Thus, the Tangshan main shock and most of its aftershocks were related closely to the resistive upper crust from the view points of either vertical layering or lateral variations. And there were only a very few aftershocks in the conductive lower crust. The mechanical property of the rocks transforms from being brittle in the upper crust into ductile in the lower crust mainly due to the combination of different factors, e.g., increase of confining pressure, change in minerals, rise in temperature as well as stabilization of slips by high pore—pressure. A small amount of water and a rise in temperature may lead to a decrease of the electric resistivity within the rock while a change in the static pressure and mineral content within the rock causes very little change in the electric resistivity. Thus it is deduced that a resistive upper crust and a more conductive lower crust from the view points of either vertical or lateral variations are related to the brittle and ductile properties respectively. Hence it is possible that there is a relationship between the electric structure of the crust and zones of potential seismic hazard. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 354–363, 1991. The project is supported by the Chinese Joint Seismological Science Foundation, and the Swedish International Development Authority.  相似文献   

10.
When sediment grains are transported as bed load in overland flow, there is a net transfer of momentum from the flow to the grains. When these grains collide with other grains, whether on the bed or in the flow, streamwise flow velocity decreases and resistance to flow increases. Resistance to flow generated in this manner is termed bed‐load transport resistance. Resistance to flow f over a plane bed may be partitioned into grain resistance fg and bed‐load transport resistance fbt. We use the symbols fbtf and fbtm to denote fbt for flows over fixed beds and over mobile beds, respectively, and we compute the effect of bed mobility on flow resistance fmob by subtracting fbtf from fbtm. The data for this study come from 54 flume experiments with fixed beds and 38 with mobile beds. On average fmob is approximately equal to half of fbtm, which is about one‐quarter of f. Hence, fmob is about one‐tenth of f. Predictive equations are developed for fbtf, fbtm and fmob using dimensional analysis to identify the relevant independent variables and regression analysis to evaluate the coefficients associated with these variables. Values of fmob are always positive which implies that mobile beds offer greater resistance to flow than do fixed beds. Evidently bed‐load grains colliding with mobile beds lose more momentum to the bed than do grains colliding with fixed beds. In other words, grain collisions with mobile beds are less elastic than those with fixed beds. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

11.
The indication from surface measurements of a zone of relatively high conductivity (resistivity<200 ohm-m) at depths between 20 and 50 km has become so general over the Earth that regions without this zone can be considered anomalous. However, the depths indicated often span the lower crust and the uppermost mantle, so that before any effect can be definitely attributed to one or the other, the depth resolution in the electromagnetic measurements must be carefully considered. This paper applies the eigenvector decomposition of generalized linear inverse theory to soundings by Schlumberger resistivity, by magnetotellurics, by man-made electromagnetic fields formed by controlled current flow in grounded electric transmission lines, and by natural magnetic field variation studies to improve the bounds on depth, thickness and conductivity of a conductive layer. It is shown that many of the methods are capable of giving the depth to the top of a conductor with remarkable accuracy. Joint inversion of two or more of them offers an advantage in the separation of thickness and conductivity of both conductive and resistive layers. Natural geomagnetic field transfer functions, while accurately mapping the position of the edge of a conductor, do not provide the resolution of the other techniques, largely because the frequencies that can be practically measured at present are much too low.  相似文献   

12.
The transient response of a conductive shell-shell model in the one-loop version was obtained analytically. The results indicate that four zones, namely early, late early, intermediate, and late zone can be identified in the total transient characteristic of the model. In case the measurements are carried out in the late early zone, a conductive target appears as a resistive one. It is suggested that the optimum time of measurement should be so selected as to fall in the intermediate zone.  相似文献   

13.
The theoretical horizontal resistivity profiles Over an outcropping vertical dyke with two-electrode and Schlumberger electrode systems are discussed. The two-electrode array seems very useful in locating the highly conducting thick or thin vein, while the Schlumberger (gradient) array is suited to detect the conducting vein of low and moderately high resistivity contrast and as well as the resistive vein of all widths and resistivity contrasts. Besides, the inline gradient array has a distinction of establishing a clue to evaluate the resistivity contrast of the vein.  相似文献   

14.
In a weathered environment estimates of depth and conductance of metallic sulphide dykes from conventional anomaly index diagrams for a vertical half-plane in air have to be corrected, besides the usual corrections, for: 1. moderate conductivity of the host rocks, and 2. finiteness of strike length S and depth extent D. Model experiments have been carried out to evaluate the response variation of a vertical planar conductor with varying depth extent and strike length for both insulating and conductive surroundings. The results indicate: 1. A conductor with finite depth extent (D/L < 2.5) or strike length (S/L < 5.0) in an insulating medium yields a lower estimate of conductance (mineralization) and a greater depth. 2. A moderately-conductive host rock enhances the anomaly and rotates the phase so that the conductor appears to be more resistive (less mineralized) and shallower. The results have practical significance since in weathered surroundings a highly-mineralized body of finite size could be missed, or misjudged, because of low estimates of conductivity and depth.  相似文献   

15.
Summary The present work aims at investigating the effects of anisotropy on the apparent resistivity measurements over the surface of a three layer Earth. An appropriate model with the anisotropic layer embedded between two isotropic media is chosen for study. The point current source is assumed to be present at the surface of such a model. After writing the values of the potentials in each layer, expressions for apparent resistivities for Wenner and Schlumberger configurations are derived. Also, the expressions for potential for the limiting cases in which the bottom layer is infinitely resistive or infinitely conducting are derived. It is shown that these expressions can be recast into simpler forms corresponding to isotropic layer (s) on an isotropic half-space.  相似文献   

16.
The term “geoelectric null-array” is used for direct current electrode configurations yielding a potential difference of zero above a homogeneous half-space. This paper presents a comparative study of the behaviour of three null-arrays, midpoint null-array (MAN), Wenner-γ null-array and Schlumberger null-array in response to a fracture, both in profiling and in azimuthal mode. The main objective is to determine which array(s) best localise fractures or best identify their orientation.Forward modelling of the three null-arrays revealed that the Wenner-γ and Schlumberger null-arrays localise vertical fractures the most accurately, whilst the midpoint null-array combined with the Schlumberger null-array allows accurate orientation of a fracture. Numerical analysis then served as a basis to interpret the field results. Field test measurements were carried out above a quarry in Les Breuleux (Switzerland) with the three null-arrays and classical arrays. The results were cross-validated with quarry-wall geological mapping. In real field circumstances, the Wenner-γ null-array proved to be the most efficient and accurate in localising fractures. The orientations of the fractures according to the numerical results were most efficiently determined with the midpoint null-array, whilst the Schlumberger null-array adds accuracy to the results. This study shows that geoelectrical null-arrays are more suitable than classical arrays for the characterisation of fracture geometry.  相似文献   

17.
A mathematical expression for potential of a direct current point source in an inhomoge-neous anisotropic earth is derived. The coefficient of anisotropy is given by f= (σr/σz), where σr and σz are the conductivities parallel and perpendicular to the bedding plane. It is assumed that σz varies with depth, whereas σr varies transversely. This potential may be useful in interpretation of geoelectrical data in specified geological situations. Master curves for Wenner and Schlumberger configurations are presented  相似文献   

18.
The objective of this study is to generate the separation-distance-domain (r-domain) transformation of the theoretically calculated wave number domain (m-domain) electromagnetic induction field component Bz(m, ω) of a stratified medium and to search for interpretive information which has been absent in the previously achieved numerical solutions of the problem. The r-domain kernel R?(r, ω) function defining the induction field appears to adequately reflect the layering and electrical properties of the medium if it is expressed as a function of the frequency if the source-receiver separation r is small with respect to the thickness of the first layer. However, exact values of the conductivity cannot be distinguished from those of the neighboring values unless a resistive basement layer is present. This feature is the result of the truncation in series representation of the kernel function R?(m, ω). However, this truncation is regarded as significant in the case of a conductive first layer. In m-domain static-zone studies, a conductive first layer slightly influences its r-domain correspondent. Although the computational cost of obtaining the kernel B(r, ω) by evaluation of the convolution in a cylindrical coordinate system is high, this semi-analytic solution is still superior to those based on the asymptotic assumptions.  相似文献   

19.
This paper deals with the apparent resistivity as observed on the surface due to a dyke of arbitrary shape. In order to give a closed analytical solution it has been necessary to assume that the dyke is either perfectly conductive or resistive relative to the enclosing medium. Furthermore we have considered an infinite line source instead of a conventional point current source; however a simple integral transform is given to transform the point-source-data into the line-source-data. So the present study is equally useful where line sources are inconvenient to handle. Besides considering the conventional method of electrical surveying (bipole method) where the source and sink are separated by a finite distance, we have considered a new variation (unipole method) where the source and sink are separated by an infinite distance, and the source is split into two separate sources each of half strength. A series of apparent resistivity curves for both methods are presented for different parameters of the dyke. The usefulness of these curves lies mainly in the fact that they may provide the necessary guide-lines for semi-quantitative interpretation of the observed data.  相似文献   

20.
Limited field and flume data suggests that both uniform and graded beds appear to progressively stabilize when subjected to inter-flood flows as characterized by the absence of active bedload transport. Previous work has shown that the degree of bed stabilization scales with duration of inter-flood flow, however, the sensitivity of this response to bed surface grain size distribution has not been explored. This article presents the first detailed comparison of the dependence of graded bed stability on inter-flood flow duration. Sixty discrete experiments, including repetitions, were undertaken using three grain size distributions of identical D50 (4.8 mm); near-uniform (σg = 1.13), unimodal (σg = 1.63) and bimodal (σg = 2.08). Each bed was conditioned for between 0 (benchmark) and 960 minutes by an antecedent shear stress below the entrainment threshold of the bed (τ*c50). The degree of bed stabilization was determined by measuring changes to critical entrainment thresholds and bedload flux characteristics. Results show that (i) increasing inter-flood duration from 0 to 960 minutes increases the average threshold shear stress of the D50 by up to 18%; (ii) bedload transport rates were reduced by up to 90% as inter-flood duration increased from 0 to 960 minutes; (iii) the rate of response to changes in inter-flood duration in both critical shear stress and bedload transport rate is non-linear and is inversely proportional to antecedent duration; (iv) there is a grade dependent response to changes in critical shear stress where the magnitude of response in uniform beds is up to twice that of the graded beds; and (v) there is a grade dependent response to changes in bedload transport rate where the bimodal bed is most responsive in terms of the magnitude of change. These advances underpin the development of more accurate predictions of both entrainment thresholds and bedload flux timing and magnitude, as well as having implications for the management of environmental flow design. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.  相似文献   

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