共查询到20条相似文献，搜索用时 31 毫秒
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Consider a lamina of ore of thickness 2t whose electrical resistivity p2 is much smaller than the resistivity p1 of the surrounding host rock. The induced polarization response of such an ore body is investigated under the assumption that it arises from the variation of p2 with the frequency of measurement. Let p2l and p2h be the resistivities of the ore-body for the low and high frequencies of measurement and L a length of the order of the distance between the transmitting electrodes. A theory is developed under the assumptions that each of the quantities t/L, p2l/p1, p2h/p1, Lp2l/2tp1, and Lp2h/tp1 is small. The main conclusion is that the frequency effect parameter P is given approximately by P=cL(p2l ? p2h)/2tp1, where the constant c is independent of t, p2l, p2h, and p1. Thus for a family of similar ore bodies having differing values of t, P will be the larger the smaller t. Detailed results are given for a semi-infinite submerged dipping dyke and the two dimensional Wenner array. 相似文献
3.
T. LEE 《Geophysical Prospecting》1983,31(5):766-781
The presence of a conducting environment about a spherical ore body must be considered when calculating the transient electromagnetic response of the ore body due to a step current flowing in a large circular loop at the earth's surface. Failure to do this can easily lead to errors in excess of 10% in numerical calculations. Moreover, there is only a limited time interval in which the response of the spherical conductor is easily seen. In a poorly conducting ground the resonance response of the sphere is the first to be excited. Later, however, the non-resonance or wave-type response is excited. These waves destructively interfere and finally the response of the sphere decays with time as t?7/2. For a range of times and depths the best loop for detecting the sphere has about the same radius as the sphere. 相似文献
4.
SIEW HUNG CHAN 《Geophysical Prospecting》1970,18(2):215-235
This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation where K1(λ) is the kernel and B1(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least-squares method. The least-squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions. 相似文献
5.
T. LEE 《Geophysical Prospecting》1977,25(1):61-75
The transient response of a layered structure to plane wave excitation can be considered to be composed of a series of waves and a ground wave. For the case of a half-space of conductivity σ and permeability μ the maximum in the electric field is found at a depth z and time t when t=z2σμ/2. This formula can be used to estimate the depth to a buried horizontal conductor with an accuracy that depends upon the resistive contrast at the conductor's surface. The above ray type of solution can be converted to a solution composed of a number of modes by the use of a Poisson transform and the transformed solutions yield decay constants that are consistent with the previously reported results. In the case of a finite source, the maximum in the electric field is strongly directed. The direction depends upon the geometry of the source and the air-earth interface. Although the maximum varies with direction it can be shown that in some directions similar laws to that above are valid. The depth to a conductor can be estimated from the early part of the transients when the ground wave is removed. The removal of the ground wave from the transient is facilitated by the use of an apparent conductivity formula. Although these results were obtained under restrictive conditions they do provide some insight into the electrical transients that are encountered by studying more complex models. 相似文献
6.
R. D. BARKER 《Geophysical Prospecting》1974,22(4):610-626
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
7.
The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle. The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t)?— (Ibαμ/20t) (σμ2/t)3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t)?—Ibμ/2t. When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described. The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer. Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer. 相似文献
8.
Abstract Geoelectric resistivity measurements by means of direct current for solving hydrogeological problems have become increasingly significant in recent years. Measurements on the surface according to the four-point-method (SCHLUMBERGER or WENNER arrangement) result in so-called “apparent” resistivities ? α as a function of the electrode distance L. The evaluation of these measuring data, here in form of sounding graphs ? α(L/2), consists of the determination of true resistivities as a function of the depth z. Since a direct computation of ? (z) from α (L/2) is not possible in practice, theoretically computed master curves constitute the essential auxiliary means for the evaluation. New simplified calculation techniques allow to establish accurately computed master curves for an underground consisting of more than three layers. By means of such standard graphs special problems of hydrogeology can quantitatively be solved by applying geoelectrical methods. The procedure is demonstrated on hand of complicated cases of aquifers devided into several storeys. 相似文献
9.
EDWARD SZARANIEC 《Geophysical Prospecting》1970,18(Z1):816-825
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
10.
Fast-decaying IP in frozen unconsolidated rocks and potentialities for its use in permafrost-related TEM studies 总被引：1，自引：0，他引：1
We investigate the early time induced polarization (IP) phenomenon in frozen unconsolidated rocks and its association with transient electromagnetic (TEM) signals measured in northern regions. The distinguishing feature of these signals is the distortion of the monotony or sign reversals in the time range from a few tens to a few hundreds of microseconds. In simulating TEM data, the IP effects in frozen ground were attributed to the dielectric relaxation phenomenon rather than to the frequency‐dependent conductivity. This enabled us to use laboratory experimental data available in the literature on dielectric spectroscopy of frozen rocks. In our studies we focused on simulating the transient response of a coincident‐loop configuration in three simple models: (i) a homogeneous frozen earth (half‐space); (ii) a two‐layered earth with the upper layer frozen; (iii) a two‐layered earth with the upper layer unfrozen. The conductivities of both frozen and unfrozen ground were assumed to exhibit no frequency dispersion, whereas the dielectric permittivity of frozen ground was assumed to be described by the Debye model. To simplify the presentation and the comparison analysis of the synthetic data, the TEM response of a frozen polarizable earth was normalized to that of a non‐polarizable earth having the same structure and resistivities as the polarizable earth. The effect of the dielectric relaxation on a TEM signal is marked by a clearly defined minimum. Its time coordinate tmin is approximately three times larger than the dielectric relaxation time constant τ. This suggests the use of tmin for direct estimation of τ, which, in turn, is closely associated with the temperature of frozen unconsolidated rock. The ordinate of the minimum is directly proportional to the static dielectric permittivity of frozen earth. Increasing the resistivity of a frozen earth and/or decreasing the loop size results in a progressively stronger effect of the dielectric relaxation on the TEM signal. In the case of unfrozen earth, seasonal freezing is not likely to have an appreciable effect on the TEM signal. However, for the frozen earth, seasonal thawing of a near‐surface layer may result in a noticeable attenuation of the TEM signal features associated with dielectric relaxation in a frozen half‐space. Forward calculations show that the dielectric relaxation of frozen unconsolidated rocks may significantly affect the transient response of a horizontal loop laid on the ground. This conclusion is in agreement with a practical example of inversion of the TEM data measured over the permafrost. 相似文献
11.
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
12.
A horizontal transmitter loop (vertical magnetic dipole) is used for frequency electromagnetic (FEM) soundings. The frequency ranges from approximately 6 Hz to about 4000 Hz. The vertical and radial magnetic field components are measured for 20 frequencies per decade several hundred meters from the transmitter loop. A very small bandwidth is selected for amplification using a reference signal. An Apple computer is used for data acquisition. A computer program for Marquardt inversion optimizes the parameters for the n-layer case: the resistivities and thicknesses of individual beds and a correction factor for the primary magnetic field. Interpretation of each component individually yields practically the same parameters. Examples from the field are given with interpretation; comparison with dc resistivity measurements is provided. The ratio of vertical/radial magnetic field components vs. frequency can be transformed simply into apparent resistivity vs. apparent depth. This can be done in the field to obtain an estimation of the depth of the layer boundaries. FEM results are compared with Schlumberger d.c. sounding obtained at the same site. 相似文献
13.
The arrival-time curve of a reflection from a horizontal interface, beneath a homogeneous isotropic layer, is a hyperbola in the x - t-domain. If the subsurface is one-dimensionally inhomogeneous (horizontally layered), or if some or all of the layers are transversely isotropic with vertical axis of symmetry, the statement is no longer strictly true, though the arrival-time curves are still hyperbola-like. In the case of transverse isotropy, however, classical interpretation of these curves fails. Interval velocities calculated from t2 - x2-curves do not always approximate vertical velocities and therefore cannot be used to calculate depths of reflectors. To study the relationship between velocities calculated from t2 - x2-curves and the true velocities of a transversely isotropic layer, we approximate t2 - x2-curves over a vertically inhomogeneous transversely isotropic medium by a three-term Taylor series and calculate expressions for these terms as a function of the elastic parameters. It is shown that both inhomogeneity and transverse isotropy affect slope and curvature of t2 - x2-curves. For P-waves the effect of transverse isotropy is that the t2 - x2-curves are convex upwards; for SV-waves the curves are convex downwards. For SH-waves transverse isotropy has no effect on curvature. 相似文献
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15.
F.E.M. Lilley D.V. Woods M.N. Sloane 《Physics of the Earth and Planetary Interiors》1981,25(3):202-209
Quiet daily magnetic variations recorded by magnetometer arrays in Australia are analysed to obtain electromagnetic response parameters for two parts of the Australian continent remote from electrical conductivity anomalies. The parameters are based on measurements of vertical-field and horizontal-field spatial gradient, and three different methods are followed in their computation. The response parameters are checked for consistency with a compilation of globally-determined Earth apparent resistivities, and are then interpreted for one-dimensional conductivity structure in the two different parts of the continent. There is evidence that the rise in electrical conductivity from 10?1 S m?1 to 100 S m?1 which occurs at a depth of order 500 km beneath central Australia may occur at a substantially shallower depth of order 230 km beneath southeast Australia. 相似文献
16.
An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σv (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σv. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis. 相似文献
17.
I. Introduction In this section the problem is stated, its physical and mathematical difficulties are indicated, and the way the authors try to overcome them are briefly outlined. Made up of a few measurements of limited accuracy, an electrical sounding does not define a unique solution for the variation of the earth resistivities, even in the case of an isotropic horizontal layering. Interpretation (i.e. the determination of the true resistivities and thicknesses of the ground-layers) requires, therefore, additional information drawn from various more or less reliable geological or other geophysical sources. The introduction of such information into an automatic processing is rather difficult; hence the authors developped a two-stage procedure:
- a) the field measurements are automatically processed, without loss of information, into more easily usable data;
- b) some additional information is then introduced, permitting the determination of several geologically conceivable solutions.
18.
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
19.
R. E. WHITE 《Geophysical Prospecting》1973,21(4):660-703
A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χj(t), from a set of traces, can be broken down into two stationary components: a signal sequence, αj(t) *s(t—τj), which correlates from trace to trace, and an incoherent noise sequence, nj(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χj(t) =αj(t) * s(t—τj) +nj(t) where the signal wavelet αj(t), the lag (moveout) of the signal τj, and the noise sequence nj(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented. The method requires the calculation of the multiple coherence function γj(f) of each trace. γj(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρj(f) by where Kj(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix. Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described. Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method. 相似文献
20.
On the basis of the dispersion relation of magnetotelluric response functions (MTRF), a filter coefficient algorithm has been
made, with which the corresponding impedance phase data can be estimated using a set of apparent resistivity data. The tests
of theoretical models and observed magnetotelluric (MT) data show that this algorithm is effective. Comparing the impedance
phase estimated using dispersion relation with the observed phase, it can be checked whether the dispersion relation between
the observed apparent resistivities and phase data was satisfied. The use of phase data corrected using the dispersion relation
in the joint inversion for MT impedance is advantageous to obtain more reliable inversion results. The problems on the one-dimensional
joint inversion for the (MT) apparent resistivity and the apparent resistivity of the frequency electromagnetic sounding (FEMS)
with horizontal electric dipole, whose observed frequency bands are linked up each other, are studied. The observed data of
two kinds of electromagnetic (EM) methods at two sites are used to inverse, the comparison with the drilling data show the
results are more reliable. To supply the phase data of FEMS using the dispersion relation, for the apparent resistivity-phase
data and impedance real part-imaginary part apparent resistivities of two kinds of EM methods the imitated MT joint inversions
are made, and more similar results also are obtained.
The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 91–96, 1993.
The projects sponsored by the Chinese Joint Seismological Science Foundation. 相似文献