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.     

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.     

CURRENT CHANNELLING IN SQUARE PLATES WITH APPLICATIONS TO MAGNETOMETRIC RESISTIVITY1

The magnetometric resistivity (MMR) method uses a sensitive magnetometer to measure the low-level, low-frequency magnetic fields associated with the galvanic current flow between a pair of electrodes. While the MMR anomalies of simple structures such as dikes and vertical contacts have been determined analytically, there is a lack of systematic information on the expected responses from simple three-dimensional bodies. We determine the characteristic anomalies associated with square, plate-like conductors, which are excellent models of many base metal mineral deposits. The anomalies of plates of finite size are determined numerically using an integral equation method. A plate is subdivided into many sections and the current flow within each section is solved by equating the electrical field within each section to the tangential electrical field just outside it. When the plate size is small in relation to either the depth or the transmitter spacing, the shape and amplitude of the anomaly produced is closely approximated by a current dipole model of the same length and depth. At the other extreme, a large plate is represented by a half-plane. The dipole and half-plane models are used to bracket the behaviour of plates of finite size. The form of a plate anomaly is principally dependent on the shape, depth and orientation of the plate. A large, dipping plate near the surface produces a skewed anomaly highly indicative of its dip, but the amount of skew rapidly diminishes with increased depth or decreased size. Changes in plate conductivity affect the amplitude of the anomaly, but have little effect on anomaly shape. A current channelling parameter, determined from the conductivity contrast, can thus be used to scale the amplitude of an anomaly whose basic shape has been determined from geometrical considerations. The separation into geometrical and electrical factors greatly simplifies both the interpretation and modelling of MMR anomalies, particularly in situations with multiple plates. An empirical formula, using this separation, predicts the anomaly of two or more parallel plates with different conductances. In addition, the relation between the resolution of two vertical, parallel plates of equal conductance and their separation is determined. The ability of the integral equation method to model plate-like structures is demonstrated with the interpretation of an MMR anomaly in a survey conducted at Cork Tree Well in Western Australia. The buried conductor, a mineralized graphitic zone, is modelled with a vertical, bent plate. The depth to the top of the plate, and the plate conductance, is adjusted to fit the anomaly amplitude as closely as possible. From the modelling it would appear that this zone is not solely responsible for the observed anomaly.     

A CONTRIBUTION TO THE QUANTITATIVE ERROR ANALYSIS IN MAGNETIC AND GRAVIMETRIC INTERPRETATION *

The paper discusses the smallest obtainable parameter errors (variances) in the interpretation with the least-squares method. Useful approximations of the sum of squares contained in the minimum error expressions are obtained using results of numerical integration. The approximations lead to especially simple results for long interpretation profiles, when the parameter errors are proportional to the square root of the point separation. Formulae are developed and examples shown for minimum error calculation in gravimetric interpretation with the cylindrical model and in magnetic interpretation with the two-dimensional plate model. Smallest errors are obtained when the interpretation profile is chosen around the anomaly maximum except for dip and depth extent interpretation of magnetic plates.     

Remanence correction in magnetic interpretation with the infinitely deep plate model

Summary Conditions are given under which two thick plates, differing in dip, apparent susceptibility, and remanence, will produce similar magnetic anomalies. From these conditions correction formulae are developed. Using these formulae the dip and susceptibility of a plate with remanent magnetization can be obtained from those of non-remanent plate. An interpretation procedure is suggested where the magnetic anomaly is first interpreted by means of a plate without remanence, dip and apparent susceptibility are then estimated by using the correction formulae developed. Thickness, position and depth of the plate are unaffected by the remanence correction procedure. The procedure is independent of the field component measured.     

ACCURATE DETERMINATION OF THE DIP ANGLE OF A GEOLOGICAL CONTACT USING THE GRAVITY METHOD*

From a gravity profile over a truncated horizontal plate, the horizontal derivative and, by means of the Hilbert Transform, the vertical derivative are obtained. When the horizontal derivative is plotted against the vertical derivative, the axis of symmetry of the resulting curve is inclined at the angle of dip of the face of the truncated plate. The depths to the upper and lower surfaces of the plate can be obtained uniquely from the symmetrical figure. Because of the derivatives being used, the method avoids the difficulties which arise from other methods of interpretation which depend upon a knowledge of the position of the origin of the gravity field data. The entire procedure for interpretation can be accommodated on a programmable calculator. An illustrative example is given.     

THE MAGNETIC ANOMALY OF 3D SOURCES HAVING ARBITRARY GEOMETRY AND MAGNETIZATION

Magnetic anomalies of complicated 3D sources can be calculated by using a combination of analytical and numerical integration. Two surfaces and the magnetization parameters (the amplitudes of the induced and remanent components and the direction cosines) of the source can be defined by arbitrary functions or by discrete data points in a plane. When combined with a polynomial magnetization function in the direction of the third axis, 3D magnetization distribution can also be modelled. The method gives very general equations for anomaly calculation. It can be used for direct modelling of sources interpreted by seismic or other methods and also for interactive interpretation with fast computers. It is possible to calculate anomalies of, for example, intrusives or folded sedimentary beds whose surfaces are functions of horizontal coordinates and which have polynomial magnetization variations in the vertical direction due to gravitational differentiation and arbitrarily varying magnetization in the horizontal direction due to regional metamorphosis. If the distribution of magnetization parameters in the vertical direction cannot be described satisfactorily by polynomials, models can be used whose surfaces are functions of the vertical coordinate and which can then have any arbitrary magnetization distribution in the vertical direction.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

INTERPRETATION OF THE GRAVITY ANOMALY OVER A CAUSATIVE BODY WITH CIRCULAR SYMMETRY*

The interpretation of the gravity anomaly on a horizontal plane over a causative body having circular symmetry about a vertical axis is considered from a rather unconventional approach. As the analytical expression for the gravity effect of a circular body assumes a closed form only on the axis of symmetry, the interpretation in this approach is carried out with the anomaly profile along the axis—which leads to simpler and faster computation. A numerical method is developed for computation of the anomaly profile along the vertical axis from the horizontal radial profile of the symmetric anomaly by upward continuation. Provision is also made for an end correction when the radial profile has only a limited extension. Some simple geometrical shapes are assumed for the causative body. Its parameters are then determined from least squares fitting of its gravity effects to the observed (upward continued) vertical profile (i) by the steepest descent method and (ii) by the Newton-Raphson method. Some applications of these methods are demonstrated.     

A New Best-Estimate Methodology for Determining Magnetic Parameters Related to Field Anomalies Produced by Buried Thin Dikes and Horizontal Cylinder-like Structures

A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.     

SIMPLIFIED EXPRESSIONS FOR THE MAGNETIC ANOMALIES DUE TO VERTICAL RECTANGULAR PRISMS*

The magnetic anomaly due to a uniformly magnetized vertical rectangular prism and that due to an arbitrary structure which can be divided into a number of such prisms are expressed in forms suitable for rapid computation. Both two-dimensional and three-dimensional cases are considered. The simplified expressions will find use in interpretation techniques where repeated computations have to be made of the anomaly due to prisms as in automated fitting of prism anomalies to observed magnetic anomalies using non-linear optimization techniques or related methods.     

THE INFLUENCE OF LATERAL INHOMOGENEITIES ON THE DIPOLE METHODS*

The theory of electrical dipole soundings proved that this method can produce resistivity measurements, which are comparable with those obtained by electrical soundings of the Wenner or Schlumberger type. Their main advantage is the use of short cable lengths, which is important if the depth of penetration should be large. A considerable disadvantage of the dipole method is the great sensitivity to lateral discontinuities. Though these have an influence on the Schlumberger arrangement as well, they can disturb a dipole sounding to such an extent than an interpretation based on a horizontal layer case is no more possible. There are six different dipole arrays, which differ from each other with respect to the angle enclosed by the two dipole orientations-the current dipole AB and the measuring dipole MN. The theoretical comparison of the dipole arrays with the Schlumberger array concerning their sensitivity to lateral discontinuities is a useful basis for the choice of the most suitable configuration. Considering geological subsurface conditions the right choice of a dipole array can give an optimal result, i.e. a dipole sounding for which the sensitivity to lateral discontinuities is as small as possible under the given circumstances.     

THE ELECTRICAL CURRENT PATTERN INDUCED BY AN OSCILLATING MAGNETIC DIPOLE IN A SEMI INFINITE CONDUCTIVE THIN PLATE*

In a paper by Koefoed and Kegge (1968), which was based on previous work of Wesley (1958), the electrical current pattern has been derived that is induced by an oscillating magnetic dipole in a semi-infinite thin plate of infinitesimal resistivity. In the present paper, the range of validity of the assumptions, on which the work of Wesley is based, is subjected to a theoretical analysis. It is found that the decisive factor for the validity of Wesley's derivation is the quotient of the square of the penetration depth of the electrical current over the product of the thickness of the plate and a distance that is indicative of the size of the current loops in the plate. Wesley's derivation is shown to be valid only when this factor is negligible. It is also shown that in this condition the imaginary component of the anomaly must be negligible. Model experiments are described in which the electrical current pattern is studied also in the range in which the derivation of Wesley is not valid. The procedure used in these model experiments was to measure the tangential component of the magnetic field strength very close to the metal plate that simulated the conductive dyke. In order to express the results of the measurements in terms of the imaginary to real ratio, these results are compared with an interpretation graph for field measurements that was published by Hedström and Parasnis (1958). It is found that the current pattern in the plate is essentially the same as that which follows from Wesley's derivation, provided that the imaginary to real ratio is less than one third. The measurements do not permit to draw conclusions regarding the current pattern in the plate in conditions that correspond to larger values of the imaginary to real ratio.     

Analytic signal approach and its applicability in environmental magnetic investigations

We investigate the analytic signal method and its applicability in obtaining source locations of compact environmental magnetic objects. Previous investigations have shown that, for two-dimensional magnetic sources, the shape and location of the maxima of the amplitude of the analytic signal (AAS) are independent of the magnetization direction. In this study, we show that the shape of the AAS over magnetic dipole or sphere source is dependent on the direction of magnetization and, consequently, the maxima of the AAS are not always located directly over the dipolar sources. Maximum shift in the horizontal location is obtained for magnetic inclination of 30°. The shifts of the maxima are a function of the source-to-observation distance and they can be up to 30% of the distance. We also present a method of estimating the depths of compact magnetic objects based on the ratio of the AAS of the magnetic anomaly to the AAS of the vertical gradient of the magnetic anomaly. The estimated depths are independent of the magnetization direction. With the help of magnetic anomalies over environmental targets of buried steel drums, we show that the depths can be reliably estimated in most cases. Therefore, the analytic signal approach can be useful in estimating source locations of compact magnetic objects. However, horizontal locations of the targets derived from the maximum values of the AAS must be verified using other techniques.     

A CONTROL OF TWO-DIMENSIONAL MAGNETIC INTERPRETATION BY THREE-DIMENSIONAL MODEL BODY ANOMALIES*

In magnetic routine interpretation the comparison of two-dimensional model curves with measured magnetic anomalies is widely used for an approximate evaluation of the position and depth of magnetic models. Before starting an interpretation of a survey by means of two-dimensional models, it is very useful to have an idea of the shape of anomalies caused by extended but finite bodies, taking into account various strike directions: Three sets of anomalies of thin plates (horizontal length 19, downward length 9, width 1) dipping 30°, 60°, and 90° resp. for various strike directions and an inclination of 20° were computed. Some of these anomalies, e.g. those with nearly N-S strike direction look rather complicated, and at the first glance one would not expect that they are caused by such simple bodies. Several profiles crossing the computed anomalies perpendicularly were interpreted two-dimensionally. For less extended anomalies the depths determined for the top of the plates are 10-20% too small, the magnetization amounts to 50–75 % of the value of the finite bodies. The interpretation of the profiles covering more extended anomalies gave very accurately the same values for the position, depth and magnetization for the two-dimensional body as for the original three-dimensional model. Anomalies of vertical prisms with varying extensions in the y-direction were computed. Their differences in amplitude and in the distance maximum-minimum show that interpretation of short anomalies by two-dimensional methods yields depth errors of up to 20 percent. To see the possibilities of the separation of superimposed anomalies dike anomalies were added to the anomaly of a broad body in great depth and several attempts were made to interpret parts of the composite anomalies. The interpreted bodies lie too deep. In complicated cases the depth values can have large errors, but experienced interpreters should be able to keep the errors in the range of one third of the depth values.     

Nomograms for rapid evaluation of magnetic anomalies over long tabular bodies

The magnetic anomaly due to a long tabular body usually consists of a maximum and a minimum. The distances and the amplitudes of the maximum and the minimum, when defined in dimensionless quantities, may be used as characteristics of the source. In this paper, a method based on the positions of the maximum and the minimum on the magnetic anomaly due to a long tabular body has been presented. Characteristic ratios,D andA involving the distances and amplitudes of the maximum and the minimum points on the anomaly curve are defined. Nomograms showing the variations ofD andA with the parameters of (1) the dike and (2) the vertical fault models are presented. The parameters of the causative source are evaluated from the two ratiosD andA and the nomograms, using some simple analytical relations presented here. From the nomograms, it is observed that (a) for a thick dike,A is always greater thanD, (b)A=D for a thin sheet and (c) for a vertical fault,A is always less thanD. Thus from the characteristic ratiosD andA it is possible to evaluate the source parameters and also to distinguish whether the source is a dike, sheet or a vertical fault. The method is fast and is applicable for the magnetic anomalies either in total, vertical or horizontal component. The method has been applied on two field examples and the results are found to be in close agreement with those obtained by using other methods. A simple method of locating the origin on the anomaly curve is included. The limitations of the method are also discussed.     

归一化总水平导数法在位场数据解释中的应用

本文提出归一化总水平导数法,通过对总水平导数进行空间归一化计算实现了异常体水平位置和深度的估计,此外还推导出基于归一化总水平导数的欧拉反褶积法来估算地下地质体的空间位置,两种方法反演结果的相互验证可有效地提高反演结果的可信度.理论模型试验证明空间归一化总水平导数法和归一化总水平导数欧拉反褶积法均能有效地完成异常体的水平位置和深度的估计,所获得的位置参数与理论值相一致.在利用归一化总水平导数法进行磁异常解释时,对数据进行化磁极计算可得到更加准确的结果.将其应用于实际航磁数据的解释,获得了岩脉的大致分布特征.     

Application of the Hilbert transform for gravity and magnetic interpretation

Either the magnetic anomaly or the horizontal gradient of gravity, if plotted against its Hilbert transform and then joined by a smooth curve, the relation figure is obtained. Properties of relation figures for some two-dimensional sources of simple geometry are shown to be useful in distinguishing the source geometry and also in estimating the source parameters, even in the presence of remanence.     

中国大陆科学钻探孔区的数字三分量反射地震调查

本文将简要介绍在大陆科学钻探孔区进行数字三分量地震勘探试验数据采集处理技术,以及取得的初步成果. 鉴于结晶岩地区波场的复杂性,在剖面调查之前要先进行波场特征调查,才能确定三分量地震调查观测系统采集参数.数据处理中与水平分量处理有关的三个困难环节包括静校正、速度分析与动校叠加,必须有所创新.在大陆科学钻探工程中,三分量数字地震调查之所以放在终孔后才进行,主要是因为三分量地震解释要以钻孔资料和VSP成果为基础.如果没有岩芯物性测定资料或VSP纵横波速度计算曲线,横波速度剖面模式就难以建立,水平分量数据处理和解释就难以进行.与单分量地震调查相比,水平分量采集处理提供了转换波信息,可反映独特的很有意义的地质信息.在三分量数字地震调查X分量深度叠加剖面左半边深度2600～3400 m区段出现密集的水平反射层,与Z分量反射剖面和变质岩片倾向不一致.对比主孔气体异常曲线可知,这些水平反射是地层中流体含量升高的反映.     

Shear-wave splitting beneath the Snake River Plain suggests a mantle upwelling beneath eastern Nevada, USA

The Snake River Plain (SRP), a 90-km-wide topographic depression in southern Idaho, is a topographically anomalous feature in the western U.S. Previous seismic studies focused on the northeastern SRP to study its relationship with the Yellowstone hotspot. We present new teleseismic shear-wave splitting data from six broadband seismic stations deployed along the axis of the SRP from June 2000 to September 2001. We also analyze splitting at HLID, a permanent station of the National Seismic Network located ∼100 km north of the plain. Splitting of individual teleseismic phases is consistent at all stations within 2σ errors, and we favor the interpretation of anisotropy with a single horizontal fast axis, although a dipping-axis interpretation is statistically permitted at two of the stations. Our station fast directions, as well as shear-wave splitting data from numerous other stations throughout the Basin and Range, are best explained by a lattice preferred orientation of olivine due to horizontal shear along the base of the plate associated with the gravitational spreading of buoyant plume-like upwelling material beneath eastern Nevada into a southwestward flowing asthenosphere (with respect to a fixed hotspot reference frame). This parabolic asthenospheric flow (PAF) model for the Great Basin is attractive because it explains the observed high elevations, high mantle buoyancy, low-velocity anomaly beneath eastern Nevada, high heat flow, and depleted geochemistry of some erupted basalts. The lack of Pliocene-Recent major volcanism in eastern Nevada suggests that a significant amount of the buoyancy flux is due to compositional buoyancy. Our splitting station delay times vary in a way not predicted by the PAF model, and can be explained by: a zone of aligned magma-filled lenses and/or partially molten dikes beneath the SRP lithosphere, a depleted olivine-rich residuum underneath the sides of the eastern SRP, and/or the effect of lateral lower crustal flow from beneath the eSRP toward its adjacent flanks.