INTERPRETATION OF MAGNETIC ANOMALIES USING SPECTRAL ESTIMATION TECHNIQUES*

The depth of causative bodies may be derived from the power spectrum of their magnetic anomalies. After a short review of the theoretical basis of the method, several examples of its application to synthetic cases are shown. Disturbing effects due to improper choice of the sampling interval and to anomalies only partially contained in the examined segment of the profile are studied. The spectral method is then applied to real cases; the tapering of the anomalies, the application of non-linear filters and the effects of anomaly superpositions are investigated. In conclusion, an appraisal of the method and of its possible practical impact has been given.     

对二维磁异常利用广义逆矩阵的选择法

本文利用广义逆矩阵理论反演解释二维磁异常。实现了加阻尼因子法,实现并改进了奇异值人工截除法;讨论了资料分辨矩阵、信息密度矩阵等辅助信息的利用;详细评价了广义逆矩阵算法的优劣。通过与目前重、磁最优化反演中常用的阻尼最小二乘法、变尺度法的对比,指出广义逆矩阵法优于这些算法。最后以河北迁安一个复杂磁异常的反演实例加以证实。     

对二维磁异常利用广义逆矩阵的选择法

本文利用广义逆矩阵理论反演解释二维磁异常。实现了加阻尼因子法,实现并改进了奇异值人工截除法;讨论了资料分辨矩阵、信息密度矩阵等辅助信息的利用;详细评价了广义逆矩阵算法的优劣。通过与目前重、磁最优化反演中常用的阻尼最小二乘法、变尺度法的对比,指出广义逆矩阵法优于这些算法。最后以河北迁安一个复杂磁异常的反演实例加以证实。     

A NOTE ON THE INTERPRETATION OF MAGNETIC ANOMALIES OF INFINITE THIN SHEETS BY USING RELATION FIGURES*

The concept of relation figures is utilized in the case of a thin infinite sheet for identification and determination of the causative source geometry, and its various parameters. The plot of ?T versus ?V is a conic, the plots between the respective symmetric components and the respective asymmetric components are straight lines, and the resulting diagram between the first horizontal versus the first vertical derivative of either ?T or ?V is a cardioid. The authors are grateful to Shri V. Babu Rao and Dr R. K. Verma for their encouragement. They would like to thank the Director of the N. G. R. I. for permission to publish this paper. The neat drawing of Sri P. Sundara Rao is appreciated.     

INTERPRETATION OF GRAVITY ANOMALIES BY NON-LINEAR OPTIMISATION*

The interpretation of a gravity anomaly in terms of the shape of the anomalous body is a non-linear problem and may, therefore, be carried out using non-linear optimisation techniques. The formulation is extended to include cases where the density contrast and the regional background are also unknown. For a given model the objective function is provided by the discrepancy between the observed anomaly and the calculated anomaly due to the model. Given an initial model, the optimisation procedure searches for a minimum of the objective function by an iterative adjustment of the parameters. A number of suitable objective functions is given. The behaviour of these functions in the parameter hyperspace is quite complex. Accordingly, direct search methods should be employed at the early stages of the search, changing to gradient methods at later stages. The use of constraints is also necessary to ensure the geological feasibility of the model. The required computer time may be largely reduced by careful programming. Two examples of interpretation by optimisation methods are given.     

AUTOMATIC INTERPRETATION OF GRAVITY ANOMALIES ASSOCIATED WITH TWO-DIMENSIONAL MASS DISTRIBUTIONS*

Several new features are described which facilitate an automatic, more meaningful, and more accurate interpretation of gravity anomalies associated with approximately two-dimensional mass distributions. These include a provision for fixed points on the bounds of a distribution, outward dipping boundaries, calculation of the gravity effect at individual elevations of stations, smoothing of models and end-corrections for distributions of limited strike length. It is possible to obtain distributions about a median plane; these distributions are sensitive to shape and allow estimates of optimum depths and minimum density contrasts for the anomalous masses.     

INTERPRETATION OF GRAVITV ANOMALIES BY MEANS OF LOCAL POWER SPECTRA*

A statistical model of the medium is introduced as source of a gravimetric anomaly. On the basis of this model the estimation of the parameters of the medium is proposed based on the statistically transformed power spectrum of the gravity anomaly. The method permits to associate the estimated depths to the disturbing limit with the profile points. Practical examples illustrate usefulness of this method to interpretation.     

INTERPRETATION OF TRANSIENT EM COMMON-LOOP ANOMALIES BY RESPONSE CHARACTERISTICS*

Theoretically exact type curves for a semi-infinite thin conductor are presented for various dip, angles, depth of burial and conductance. The study shows that the common-loop response shape is sensitive to small changes in conductor dip, but is affected more subtly by comparable strike variations. For large sheet conductors a decrease in the strike angle results in a broadening but unlike that for a finite plate there is no reduction in peak amplitude. For dipping conductors, response asymmetry and the direction and magnitude of peak amplitude displacement can be used to assess the disposition and quality of the conductor. A generalized interpretation scheme is proposed, based on dimensionless response characteristics and normalized decay curves, to facilitate the rapid in-field determination of conductor dip, conductance and depth of burial, for any time regime.     

关千ΔT磁异常的解释

本文对于二度问题证明了总磁場强度△T与垂直磁場强度Z的一般表达式具有相同的形式,因此可以把△T异常曲线看成Z异常曲线,利用复变函数理论中的柯西-黎曼条件我们就可根据△T异常曲线计算出与H异常曲线相当的所谓△T的“负共轭调和函数”△T,文中指出了同时利用△T及其原函数△T将有助于磁测资料的解释工作,还举出了两个应用的例子:1)根据△T与△T计算二度体的磁矩及其倾角;2)利用观测水平上的△T及△T值将△T向下解析延拓。     

ESTIMATION OF THE MINIMUM DENSITY CONTRAST OF A HOMOGENEOUS BODY AS AN AID TO THE INTERPRETATION OF GRAVITY ANOMALIES*

Goodacre A.K. 1980, Estimation of the Minimum Density Contrast of a Homogenous Body as an Aid to the Interpretation of Gravity Anomalies, Geophysical Prospecting 28, 408–414. The minimum density contrast value for which a homogeneous body will accurately reproduce an observed gravity low can often be used to determine whether the causative body is a low-density granite batholith or a sedimentary basin. If the minimum density contrast value is large, the anomaly source is probably a sedimentary basin; if it is small, the source may be either a sedimentary basin or a granite batholith. The minimum density contrast method is tested on the Cheshire Basin and the Weardale Granite.     

THE INTERPRETATION OF GRADIENT ARRAY CHARGEABILITY ANOMALIES *

Empirical equalities derived from time domain induced polarization scale modelling with the gradient array over simple geometries, and from the potential field functions for equivalent simple charge configurations are similar. The function for the dyke like body is analogous to the magnetic case allowing both total and vertical magnetic field interpretation techniques to be applied to gradient array chargeability anomalies.     

DIRECT INTERPRETATION OF RESISTIVITY DATA OVER TWO-DIMENSIONAL STRUCTURES*

A direct interpretation scheme is developed which is capable of determining most of the geological features of a ground which can be assumed to be two dimensional in structure. This scheme extends the earlier work of Pekeris (1940) and Koefoed (1968) to the case where the basal layer of a ground is undulating. It also has a limited use for finding the parameters of a dipping dyke in the lower medium. Though the top and dip of the dyke can be determined, this is not true for the thickness.     

CORRELATION METHODS OF TRANSFORMATION AND INTERPRETATION OF GEOPHYSICAL ANOMALIES*

The methods of anomaly transformations considered are based on a system of combined analysis of the geophysical field and a priori) information on the structure of a geological object. The methods involve calculation of a transformative polynomial (describing geophysical noise) which makes it possible to separate the residual field component related to the geological characteristic under study in a correlatively optimal way. The structure of the transformative polynomial is determined by the nature of the geophysical noise that is eliminated by the field transformation. Various correlation methods of anomaly transformations arise, depending on the structure of the transformative polynomial chosen. By way of example, the correlation method employed for separating the geophysical anomalies is shown to be highly effective in investigating the local geological structure.     

EXPERIENCES WITH AUTOMATIC MAGNETIC INTERPRETATION USING THE THICK PLATE MODEL *

Various experiments are described in designing two-dimensional magnetic interpretation algorithms using computer curve fitting techniques. For a single anomaly the position of the anomaly maximum and the half-width of the anomaly give good initial estimates of the plate position and thickness. A nomogram and formulae for improving these estimates is given. Curves and estimates for the effects of finite depth extent of a plate show the limits, when the lower surface of the plate can be neglected in curve fitting. The combined anomaly of two parallel plates can be separated into partial anomalies with no common points using the horizontal derivative of the anomaly. The changes of the anomaly maxima and changes in anomaly half-widths are studied as a function of plate separation. The position of the maxima and the half-widths can be corrected before applying the one-plate procedure for obtaining initial estimates of plate positions and thicknesses. The performance of standard optimization methods of Powell, Davidon, and Marquardt in improving the values of the plate parameters are compared. The Powell method seems to be the most reliable for both single and multi-plate anomalies. All methods become unacceptably slow when the number of plates is greater than 2 or 3. In these cases feasible interpretation times are obtained using the partial anomalies and sequential parabolic search of the parameter values as tailored specially to the thick plate model. Experiments with three different error norms, the classical least squares, weighted least squares and minimax, show that the first norm gives the best overall performance in automatic interpretation. The behaviour of the classical least squares norm as a function of the plate parameters is also briefly described.     

ON THE ORIGIN AND INTERPRETATION OF SELF-POTENTIAL ANOMALIES*

The renewed interest in the self-potential method of exploration for mineral deposits gives an understanding of the self-potential mechanism new importance. The cause of SP anomalies in general lies in the interference between simultaneously occurring nonequilibrium phenomena. However, theories of the mechanism of mineral SP anomalies generally relate the SP anomaly to the equilibrium potential of the chemical reaction supposed to occur on the ore body surface. In this paper, I reformulate these equilibrium mechanisms in terms of nonequilibrium thermodynamics. The result is that the SP anomaly depends not on the equilibrium potential alone, but also on the potential resulting from current transferred across the ore body—electrolyte interface. It is not possible to calculate the overpotential theoretically because of the number of complicating factors, and experimental data are not available. This does not imply that SP data are uninterpretable quantitatively. SP data may be interpreted similarly to other potential field data.     

ANALYSIS OF GRAVITY ANOMALIES OF TWO-DIMENSIONAL FAULTS USING FOURIER TRANSFORMS*

The Fourier transform formula for a two-dimensional fault truncating a horizontal bed at an arbitrary angle of inclination is derived. The amplitude spectrum of the Fourier transform is found to give information about the depth to the top of the upper part of the faulted bed and the inclination of the fault-plane. Under suitable conditions the thickness and the displacement of the bed involved can be obtained. With actual field data, these transforms can be obtained at discrete points by a Fourier analysis of the gravity anomaly. A field example from the Logan fault area near Montreal, Que., Canada, is given.     

ENHANCEMENT OF ELECTROMAGNETIC ANOMALIES BY A CONDUCTING OVERBURDEN*

The effect of a conducting overburden on the electromagnetic response of sulphide ore-bodies has been studied with the help of quantitative electromagnetic model experiments. These experiments were conducted at a fixed, crystal controlled, frequency of 100 kHz using a number of transmitter-receiver configurations, though the results discussed here mostly pertain to a horizontal coplanar system. An analysis of the anomaly profiles—after accounting for the regional anomaly—indicates a general enhancement of the response. This is attributed (a) to the concentration of the current lines in the host-rock effected by the embedded target and (b) to the change in the phase and space orientation of the field vectors, brought about by the conducting overburden. The enhancement is most pronounced in the case of non-symmetrical bodies such as veins and ribbon-like structures represented by sheet models, but is also observed to a lesser degree for isometric structures. These results are expected to pave the way for a more accurate interpretation of the induction prospecting data.     

TWO-DIMENSIONAL MASS DISTRIBUTIONS FROM GRAVITY ANOMALIES*

The oscillatory character of the solution obtained by Qureshi and Mula's method for the direct determination of two-dimensional mass distributions from gravity anomalies is examined.     

A NEW APPROACH TO MAGNETIC PROFILE INTERPRETATION*

By using two components of anomalous magnetic fields and a formulation including complex numbers it is possible to calculate the position parameters of thick plates and both magnetization and position of thin plates directly from any two or three points of anomaly profiles. The formulae (interpretation operators) allow automatic topographic corrections to be made. The new two-component operators give more reliable results than the conventional methods of interpretation. The variance of the parameter values obtained with subsequent points of an anomaly measures directly, the total error of interpretation. The application of infinite thin plate operators to a long profile results in characteristic patterns, from which the estimation of the number of plates and their approximate position is possible.