Euler deconvolution of the analytic signal and its application to magnetic interpretation

Euler deconvolution and the analytic signal are both used for semi‐automatic interpretation of magnetic data. They are used mostly to delineate contacts and obtain rapid source depth estimates. For Euler deconvolution, the quality of the depth estimation depends mainly on the choice of the proper structural index, which is a function of the geometry of the causative bodies. Euler deconvolution applies only to functions that are homogeneous. This is the case for the magnetic field due to contacts, thin dikes and poles. Fortunately, many complex geological structures can be approximated by these simple geometries. In practice, the Euler equation is also solved for a background regional field. For the analytic signal, the model used is generally a contact, although other models, such as a thin dike, can be considered. It can be shown that if a function is homogeneous, its analytic signal is also homogeneous. Deconvolution of the analytic signal is then equivalent to Euler deconvolution of the magnetic field with a background field. However, computation of the analytic signal effectively removes the background field from the data. Consequently, it is possible to solve for both the source location and structural index. Once these parameters are determined, the local dip and the susceptibility contrast can be determined from relationships between the analytic signal and the orthogonal gradients of the magnetic field. The major advantage of this technique is that it allows the automatic identification of the type of source. Implementation of this approach is demonstrated for recent high‐resolution survey data from an Archean granite‐greenstone terrane in northern Ontario, Canada.     

Interpretation of magnetic anomalies by horizontal and vertical derivatives of the analytic signal

Magnetic anomalies are often disturbed by the magnetization direction, so we can’t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index (expressing the geometry) by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.     

Direct analytic signal (DAS) method in the interpretation of magnetic data

We presented a new method for interpreting 2D magnetic data, called direct analytic signal (DAS) method, which directly used the analytic signal of magnetic anomaly to compute the depth and the structural index of the source. The DAS method needs only the computation of the first order derivatives of magnetic anomaly, so that the inversion results are more stable than the results obtained by the other existing analytic signal methods. The DAS method is tested on synthetic magnetic data with and without noise, and the DAS method can successfully obtain the depth and the structural index of the source. We also applied the DAS method to interpret a real magnetic data over a shallow geological source whose source parameters are known from closely drilling information, and the inversion results are in accord with the true values.     

重磁场二维希尔伯特变换——直接解析信号解释方法

通过分析解析信号概念,指出目前重磁场解析信号事实上是重磁场梯度解析信号. 在借助解析信号分量满足二维希尔伯特变换关系的基础上,提出重磁场直接解析信号的概念,并阐述重力异常及化极磁异常希尔伯特变换——直接解析信号的含义,并给出基于直接解析信号对位场增强的四种处理方法:直接解析信号模、水平分量模、改进Tilt angle和改进Theta map. 理论模型和实际航磁资料处理表明上述方法一定程度上可以解决噪声干扰等问题,对分辨和刻画场源有较好的解释效果,能够用于航空重力和航磁资料处理.     

Comments on the interpretation of linear magnetic anomalies

Summary In response to the recent interpretation of marine magnetic anomalies in terms of the crustal spreading hypothesis, a summary is made of other factors including structural, initial cooling, post cooling, and possible spontaneous processes which may cause at least some of the characters of linear magnetic anomalies. Arguments are developed by presentation ofQ values for 571 specimens from fourteen Icelandic lavas and six dikes, and by theQ value, stability factor, and oxidation variation between the cooling faces of one of these lavas. None of the processes described can alone readily account for the observed symmetry of magnetic anomalies with respect to mid-oceanic ridges, but are presented to encourage examination and development of mechanisms other than geomagnetic polarity changes superimposed on a crustal generating system, as the causes of at least some oceanic magnetic anomalies.     

The zero-line method of interpreting total field magnetic anomalies of spherical ore-bodies

Summary A method called the zero-line method for interpreting the total field magnetic anomalies of spherical bodies is described. The contour of zero-anomaly is controlled by a linear equation of the typeAx ² +By ² +Cxy +Dx +Ey +F = 0, where the coefficientsA toF are related to the depth of the sphere and the parameters relating to its position and magnetisation. From the coordinates (x, y) of the various points lying on the zero-contour, five normal equations for the above equation are set and solved for the various coefficients. The various parameters relating to the position and magnetisation of the sphere are then determined from these coefficients. It is expected that similar methods can be developed for interpreting magnetic anomalies of other three dimensional bodies also.     

Interpretation of total intensity magnetic anomalies when anomalous field is arbitrarily large

Summary Not infrequently, in mining geophysics, the anomalous field of the magnetized body is appreciably large and it varies from the direction of the earth's normal field within the vicinity of the magnetized body. Total magnetic intensity data collected on the ground over shallow magnetized bodies cannot be interpreted quantitatively, since all the available methods of interpretation assume that the resultant field lies in the direction of earth's normal field as the anomalous field is small. For geological bodies that can be magnetically represented by infinite line pole, point pole, infinite line dipole, and point dipole, this paper gives quantitative interpretation procedures for total magnetic intensity anomalies without the above assumption using the characteristic points from the theoretical curves (not reproduced). These characteristic curves can be used for the direct determination of depths and offsets by using information from suitably chosen field profiles.Contribution No. N.G.R.I.-71-233.     

Tectonic interpretation of the magnetic anomalies southwest of Vancouver Island

Summary A tectonic interpretation of the magnetic anomalies off the coast of California, Oregon and Washington between 40° and 52° north latitude shows that in the area surveyed the oceanic crust is cut by seven major dislocation zones which divide the region in eight areas. For five of these areas the original connection can be reconstructed. The existence of a window of young crust surrounded by older crust and of a short, isolated length of active oceanic ridge southwest of Vancouver Island as proposed recently by different authors is not confirmed.     

Future of the interpretation theory of gravity and magnetic anomalies

The general methodology of the interpolation theory of potential fields (gravity and magnetic anomalies), and, primarily, the three fundamental ideas underlying this methodology—(I) approximation, (II) linearization, and (III) optimization-are the matter of the utmost importance. The rationale of these ideas and the ways of their practical implementation are discussed in this paper.     

Grandient measurements in the interpretation of magnetic anomalies due to two-dimensional prism-shaped bodies

Summary A direct method of interpreting magnetic anomalies due to two-dimensional prisms is presented here. Measurement of the first vertical derivative supplies additional information concerning the parameters. The normal ground magnetic profile, as well as the gradient profile will have symmetrical points whose distances from the origin are related to the width, depth and height of a two dimensional prism shaped body.     

On the interpretation of magnetic anomalies for strong remanent magnetizations

In this paper some aspects concerning the interpretation of magnetic anomalies are treated, particularly when the remanent magnetization intensity is strong. In this case, since total and induced magnetization vectors can have very different directions, a correct anomaly interpretation strictly depends on the knowledge of their declinations and inclinations.Thus, a specific procedure is described to determine such parameters from well-known semi-empirical techniques and vectorial relations.Furthermore, the classical definition of apparent susceptibility is shown to be inadequate to this problem and a more general formulation is suggested, which is not only related to the true susceptibility and to the Koenisberger ratio, but also to the declinations and inclinations of the induced and remanent magnetization vectors.The two apparent susceptibilities are then compared for some synthetic magnetic anomalies and significant differences are found.     

A method to estimate the total magnetization direction from a distortion analysis of magnetic anomalies1

Knowledge of the declination and inclination of the total and induced magnetization vectors is normally required for the interpretation and analysis of magnetic anomalies. A new method of estimating the direction of the total magnetization vector of magnetized rocks from magnetic anomalies is proposed. The unknown declination and inclination (D*_T and I*_T) can be found by applying a reduction-to-the-pole operator to the measured anomalies for different couples of total magnetization direction parameters (D_T and I_T) and by observing the variation of the anomaly minimum as a function of both D_T and I*_T.and D*_T are estimated using the maximum of this function. Comparing our method to previous methods, one advantage is that our estimates are not zero-level dependent; furthermore, the method allows inclinations to be well estimated, with the same accuracy as declinations; finally declinations are not underestimated. Our method is applied to a real case and meaningful results are obtained; it is shown that the feasibility of the method is improved by removing the low-frequency components.     

Interpretation of magnetic data using analytic signal derivatives

This paper develops an automatic method for interpretation of magnetic data using derivatives of the analytic signal. A linear equation is derived to provide source location parameters of a 2D magnetic body without a priori information about the nature of the source. Then using the source location parameters, the nature of the source can be ascertained. The method has been tested using theoretical simulations with random noise for two 2D magnetic models placed at different depths with respect to the observation height. In both cases, the method gave a good estimate for the location and shape of the sources. Good results were obtained on two field data sets.     

A method for the interpretation of magnetic anomalies of dipping doublets

Summary A simple method for the interpretation of the vertical magnetic anomalies of dipping doublets is presented. In the first step, the line integrals of the anomalies along theX direction, which represent the anomalies of a vertical line double are utilised to obtain the depths to the two poles. In the second step, the profile alongY, through the point of intersection of the doublet with theX axis is used to determine the dip of the dipole.     

Towards the interpretation of Uranus's eccentric magnetic field

Abstract

Coriolis forces stimulate dynamo action in a rapidly-rotating fluid by promoting complexities in the pattern of fluid motions, notably departures from symmetry about the axis of rotation. This pattern and its time variations determine the instantaneous form and temporal behaviour of the magnetic field so produced. Instantaneous magnetic fields will usually exhibit in their broad-scale features approximate alignment with the rotation axis. This is borne out by observations of the magnetic fields of the Earth, Jupiter and Saturn, and it is likely on general grounds that Neptune will be found to have an aligned magnetic field. But, as is shown by laboratory and theoretical studies of thermal convection in rapidly-rotating fluids, for some ranges of rotation speed, rate of heating, etc. certain patterns can occur which in electrically-conducting fluids would produce magnetic fields exhibiting departures from alignment with the rotation axis, which instantaneously could be quite pronounced but would average out to very small values over sufficiently long periods of time. These findings indicate obvious strategies for theoretical studies towards the interpretation of Uranus's eccentric magnetic field (which need not invoke departures from axial symmetry in the thermal, mechanical or electrical boundary conditions of the dynamo region within the planet) and for further observational studies.     

Magnetic-doublet method of interpretation of arbitrarily large total intensity anomalies

Summary In mining geophysics, analysis of total intensity magnetic anomalies in terms of equivalent magnetic-doublets has been extensively used for approximate determination of depth, offset and the length of the disturbing bodies. Total intensity data collected on the ground over shallow magnetized bodies cannot be interpreted quantitatively by the available methods of interpretation which assume that the resultant field lies in the direction of Earth's normal field as the anomalous field vector is small when compared to the normal field vector. In the present investigation, the above assumption has been eliminated and total intensity magnetic anomalies due to disturbing bodies are analyzed in terms of their magnetic-doublet equivalents. From sets of theoretical total magnetic anomaly curves (some are reproduced) Tables have been prepared using the characteristic points and are shown in Tables 1 to 7. These Tables can be used for the direct determination of depth, offset, etc., by using information from suitably chosen field profiles.Contribution No. NGRI 286.