Feasibility of central loop TEM method for prospecting multilayer water-filled goaf

With deep mining of coal mines, prospecting multilayer water-filled goaf has become a new content that results from geophysical exploration in coalfields. The central loop transient electromagnetic (TEM) method is favorable for prospecting conductive layers because of the coupling relationship between its field structure and formation. However, the shielding effect of conductive overburden would not only require a longer observation time when prospecting the same depth but also weaken the anomalous response of underlying layers. Through direct time domain numerical simulation and horizontal layered earth forward modeling, this paper estimates the length of observation time required to prospect the target, and the distinguishable criterion of multilayer water-filled goaf is presented with observation error according to the effect of noise on observation data. The observed emf curves from Dazigou Coal Mine, Shanxi Province can distinguish multilayer water-filled goaf. In quantitative inversion interpretation of observed curves, using electric logging data as initial parameters restrains the equivalence caused by coal formation thin layers. The deduced three-layer and two-layer water-filled goafs are confirmed by the drilling hole. The result suggests that when observation time is long enough and with the anomalous situation of underlying layers being greater than the observation error, the use of the central loop TEM method to prospect a multilayer water-filled goaf is feasible.     

Modelling and inversion of electromagnetic data using an approximate plate model

This paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two-layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two-dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates . The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate-like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.     

DEFINITION AND APPLICATION OF THE FREQUENCY -EFFECT TRANSFORM FUNCTION TO THE INTERPRETATION OF IP SOUNDINGS*

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.     

ON THE INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA FOR THE TWO-LAYER CASE*

For helicopter-borne electromagnetic systems, the distance between the transmitting and the receiving coils is small compared with the altitude above ground. For this case, a major simplification can be made for the calculation of model curves. Some two-layer curves for the interpretation of frequency measurements are presented. A very simple procedure is demonstrated for the conversion of the relative secondary field into apparent resistivity and apparent distance for the mapping of airborne electromagnetic data. Furthermore, an approximation is described for the determination of the thickness and the resistivity of a layer lying on a perfectly conducting half-space.     

RESISTIVITY SOUNDING ON A TWO-LAYER EARTH WITH TRANSITIONAL BOUNDARY*

A theoretical solution is obtained for the problem of a two-layer earth with transitional boundary. In practice, the transition layer can stand for the weathered zone in hard rock areas where the degree of weathering diminishes with depth. Master curves and tables of data are presented for the case when the lower half-space is infinitely resistive.     

TIME-DOMAIN ELECTROMAGNETIC SOUNDING—COMPUTATION OF MULTI-LAYER RESPONSE AND THE PROBLEM OF EQUIVALENCE IN INTERPRETATION*

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.     

AIRBORNE RESISTIVITY MAPPING USING A MULTIFREQUENCY ELECTROMAGNETIC SYSTEM*

Airborne electromagnetic methods are most commonly used in mineral exploration. However, new developments, such as multifrequency capability and digital on-board field recording, as well as improvements in instrumentation resulting in high signal-to-noise ratios in recorded data, have made their application in geological mapping possible. A three-frequency airborne EM survey carried out over an area northwest of Timmins, Ontario, was interpreted in terms of thickness and resistivity of the layers of a two-layer earth section. Since both in-phase and quadrature components are measured, this provides six independent parameters at each point in space. Based on prior geological information and a preliminary interpretation of the field records, two two-layer models of the subsurface seemed to be appropriate for most of the survey area. An automatic computerized interpretation procedure was devised to interpret the field data at each point in terms of thickness and resistivity parameters of those two models. When the geology is more complex, the data do not fit the models and no interpretations are made. Two maps illustrating the variation of the resistivity and the thicknesses of the layers were constructed from the interpreted data. These maps agree with the known geological information about the distribution of glacial clay in the area. Areas where the layered models do not fit are known to be areas where the geology is complex with a large number of dykes and other lateral inhomogeneities. The study shows that multifrequency airborne EM surveys can be very useful in geological mapping over inaccessible terrain and can significantly help the mapping geologist where outcrops are scarce.     

CSAMT单分量数据解释方法

可控源音频大地电磁法（CSAMT）一直沿用大地电磁法（MT）的办法,通过计算电场分量与磁场分量的比值,求取卡尼亚视电阻率.而CSAMT场源已知,电场分量和磁场分量都与地下电阻率存在一定的关系,可以单独采用CSAMT电场分量或者磁场分量提取地下介质的视电阻率.本文通过分析电场分量与磁场分量的数据特性,提出利用CSAMT电场单分量数据进行视电阻率的计算,用改进的广义逆矩阵反演方法,使初始模型中的地电层数等于频道个数,克服了以往反演计算中层数较少的问题;实现全场区电场分量视电阻率曲线的拟合反演.同时对单分量视相位计算方法进行分析,结合山西大同地区积水采空区探测及数据解释结果,论证本文提出的单分量解释方法的有效性.

     

TRANSFORMATION OF MAGNETOMETRIC DATA INTO TECTONIC MAPS BY DIGITAL TEMPLATE ANALYSIS*

Results of gravimetric surveys can be interpreted by comparing the Bouguer field values with master curves based on simplified geological models. It has been shown in a previous paper how this procedure can be transformed into routine processes which can be computerized. The application of this method has yielded useful results in detailed gravity surveys. The present paper discusses the application of the same interpretation principles to magnetic data. After some modifications, the method elaborated for the gravimetric data can be used for the interpretation of magnetometric survey results. Magnetometric-tectonic maps are obtained which show the structural picture by common geological symbols. In the case of faults, the dimensions of depth of burial and throw are indicated on the maps. The method is illustrated by an example where these procedures have been applied to gravimetric and magnetometric data of the same area. Two different maps are obtained: One shows the tectonics according to density contrasts and the other map depicts the tectonic situation on the basis of magnetic susceptibility contrasts.     

The geoelectrical properties of the earth around the Karymshina multidisciplinary observation site in southern Kamchatka

This paper is concerned with the Earth’s electromagnetic field, a deep geoelectrical section, and the dynamics of earth conductivity. This analysis is based on MTS curves along directions that to a first approximation go along and across southern Kamchatka. It is shown that the longitudinal and transverse MTS curves are subject to the influence of local and regional geoelectrical inhomogeneities. The coast effect was studied by 3-D numerical modeling. The patterns we have found were used for interpretation of generalized MTS curves. The resulting parameters of the geoelectrical section were refined by reducing the longitudinal curve to the standard curve of apparent resistivity. The results from this interpretation are to be refined as more geoelectrical information is forthcoming. The dynamics of lithospheric conductivity were studied from data acquired during the 2005–2008 monitoring of magnetotelluric impedance in the range of periods between several hundred and several thousand seconds. The basis for the analysis was assumed to be the transverse impedance and its phase. The latter was found to exhibit anomalous bay fluctuations that might have been related to earthquakes. A possible origin of these anomalies is discussed.     

THE REDUCTION OF LATERAL EFFECTS IN RESISTIVITY PROBING*

To be able to make use of all existing probe interpretation techniques, it is desirable that field resistivity observations be conducted in such a way that it is possible to construct an equivalent curve for the surface variation of potential about a point source. Further, the usual parallel layer interpretation will only be justified in as much as the observed potential curve is compatible with such a subsurface geometry. Thus, whilst a potential curve may be constructed from suitable finite potential differences obtained using a Wenner configuration of electrodes, it can be shown, using the tri-potential technique of measurements, that these potential differences may arise partly from lateral resistivity variations. In this paper, a ladder network technique is employed to display these lateral effects and an adjustment method proposed to reduce them. The adjusted potential differences obtained form a consecutive series suitable for summation to give the potential function. These values are subject to further minimum adjustments required for them to comply with slope and curvature conditions for a layered medium. After forming the potential curve by summation, a final numerical smoothing process is carried out. From this smoothed potential curve, corresponding Wenner and Schlumberger curves can readily be derived for interpretation. The method proposed thus attempts to extract from the observed data the maximum part which can be reconciled with a purely depth variation of resistivity. A method is also proposed for compounding the ‘errors of closure’ of the network to provide a Lateral Inhomogeneity Index which gives a measure of the departure of the observed data from the basic interpretation requirements. The method involves no great labour, but can readily be programmed for a computer if desired. Examples are given of the application of the method to field observations. In the interest of objectivity, the final smoothing has been confined to a single stage but in certain very extreme examples a further stage may prove desirable.     

Theoretical study of slope effects in resistivity surveys and applications

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.     

THE COLLOCATION APPROACH TO THE INVERSION OF GRAVITY DATA1

Gravity data inversion can provide valuable information on the structure of the underlying distribution of mass. The solution of the inversion of gravity data is an ill-posed problem, and many methods have been proposed for solving it using various systematic techniques. The method proposed here is a new approach based on the collocation principle, derived from the Wiener filtering and prediction theory. The natural multiplicity of the solution of the inverse gravimetric problem can be overcome only by assuming a substantially simplified model, in this case a two-layer model, i.e. with one separation surface and one density contrast only. The presence of gravity disturbance and/or outliers in the upper layer is also taken into account. The basic idea of the method is to propagate the covariance structure of the depth function of the separation surface to the covariance structure of the gravity field measured on a reference plane. This can be done since the gravity field produced by the layers is a functional (linearized) of the depth. Furthermore, in this approach, it is possible to obtain the variance of the estimation error which indicates the precision of the computed solution. The method has proved to be effective on simulated data, fulfilling the a priori hypotheses. In real cases which display the required statistical homogeneity, good preliminary solutions, useful for a further quantitative interpretation, have also been derived. A case study is discussed.     

A simple direct interpretation method for an electrical sounding carried out over an inclined interface

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.     

A NUMERICAL COMPUTATION PROCEDURE FOR THE DIRECT INTERPRETATION OF GEOELECTRICAL SOUNDINGS*

In this paper a numerical method of direct interpretation of geoelectrical soundings is described. It has similarities with already existing direct methods, but owing to its simplicity and, in particular, to the possibility of applying it also without digital computers, it proves useful mostly in the field, where very often an accurate method for the interpretation of multi-layer curves is required. The direct interpretation system splits up into three steps: i) the evaluation of the resistivity transform after application of Hankel's inversion theorem; ii) the determination of the layer distribution after application of Koefoed's recurrent procedure; iii) the control of the solution. Each step is considered and the practical procedures suggested. Finally two field examples are presented and discussed.     

THEORETICAL ANALYSIS OF APPARENT RESISTIVITY OVER A DYKE OF ARBITRARY SHAPE*

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.     

Vertical electric dipole over an inhomogeneous and anisotropic earth

Summary The propagation of electromagnetic waves in a two-layer anisotropic earth from an oscillating vertical electric dipole placed over it has been studied. Formal expression for the vector potential in the top layer has been determined for the general case when both the layers are electrically anisotropic. The conductivity and the permittivity tensors of the layers are assumed to have simple diagonal forms. Three special cases of practical interest have been considered in detail, for which the results are given in terms of tabulated functions. It has been shown that at the surface of the earth, only the electric field components are influenced by the anisotropy.     

A NUMERICAL METHOD OF CALCULATING THE KERNEL FUNCTION FROM SCHLUMBERGER APPARENT RESISTIVITY DATA*

A method to calculate the resistivity transform of Schlumberger VES curves has been developed. It consists in approximating the field apparent resistivity data by utilizing a linear combination of simple functions, which must satisfy the following requirements: (i) they must be suitable for fitting the resistivity data; (ii) once the fitting function has been obtained they allow the kernel to be determined in an analytic way. The fitting operation is carried out by the least mean squares method, which also accomplishes a useful smoothing of the field curve (and therefore a partial noise filtering). It gives the possibility of assigning different weights to the apparent resistivity values to be approximated according to their different reliability. For several examples (theoretical resistivity curves in order to estimate the precision of the method and with field data to verify the practicality) yield good results with short execution time independent of shape the apparent resistivity curve.     

Behavior of electric potential fields over random conductivity,layered earth models

Solutions are derived for the potential distributions over one-layer and two-layer random conductivity earth models for the direct current resistivity method. Monopole and Wenner arrays are considered. It is shown that the random potential due to a spatially stationary Gaussian random conductivity is also Gaussian but not spatially stationary. The ensemble and sample statistics of the random kernel and apparent resistivity are examined. Representative curves of these functions are presented to show the effects of a random conductivity profile on them. It is shown that the effect of the random nature of the conductivity profile on an apparent resistivity sounding curve is greatest for small electrode spacings.     

INDUCED POLARIZATION RESPONSE OF A HORIZONTALLY MULTILAYERED EARTH WITH NO RESISTIVITY CONTRAST*

The induced polarization response of a horizontally multilayered earth with no resistivity contrast can rapidly be calculated on a desk calculator or minicomputer for any electrode array. The formulation is a simple series summation of the products of weighting coefficients and the true induced polarization responses for each of the layers. The coefficients are directly derivable from the corresponding resistivity model. This series approach to IP formulation was originally described by Seigel but has not been treated extensively in the present-day geophysical literature. This method can be applied to either time or frequency domain induced polarization measurements. Once the coefficients are known, apparent induced polarization response can readily be obtained by judicious substitution of known, suspected, or assumed values of the true induced polarization of each layer. Basic formulation is presented for the IP potential coefficients (pole-pole or two array) with no resistivity contrast between the layers. From these coefficients, response of any number of layers for any electrode array can be obtained by suitable differentiation. Some examples of Wenner array for a three-layered earth and dipole-dipole array for a four-layered earth are used to illustrate the application. The results of this technique are valid for many natural situations of modest resistivity contrast. However, they definitely cannot be used if there are highly contrasting resistivity layers present. Such an approach is conceptually simple and is useful for survey planning, checking or setting the “depth-of-penetration”of a given array. For field induced polarization data that fits reasonably well to the no-resistivity-contrast model, this simple approach facilitates quantitative interpretation.