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.     

Interpretation of marine magnetic anomalies. Part I. A survey of existing methods and analysis of the analytic signal method

In this work, the problem of interpreting linear marine magnetic anomalies in the context of the spreading model is considered. Analysis and a comparison of the methods proposed earlier for solving this problem are carried out and the analytic signal method is considered in detail. In terms of a simplest example, it is shown that the AS method has significant restrictions associated primarily with the size and/or occurrence depth of the bodies.     

An analytic signal approach to the interpretation of total field magnetic anomalies1

The analytic signal (AS) is defined as the square root of the sum of the squares of the vertical and the two horizontal derivatives of the total magnetic field ΔT. This paper verifies theoretically that peaks of the AS correlate directly with their magnetic causative bodies and are positioned symmetrically over them, i.e. the main feature of the AS is that it is independent of the inclination of the magnetic field. This avoids the difficulties that are often faced in the conventional process of reduction to pole for ΔT, when the direction of magnetization of the causative bodies is not known. In addition, the AS has characteristics similar to the derivative features of the magnetic field, so that it is very sensitive to edge effects of the causative magnetic bodies. The theoretical derivations are tested by comparison with calculations on models, and, in a field example from Hunan Province, China, the AS is applied successfully to the interpretation of ΔT, whereas the conventional process of reduction to pole fails, due to the reverse magnetization of the causative body.     

A computer program for interpreting vertical magnetic anomalies of spheres and horizontal cylinders

Summary A common computer program for the interpretation of vertical magnetic anomalies of spheres and horizontal cylinders has been developed. The input consists of the observed anomalies noted against their distances measured from an arbitrary point in the profile and a code number for each model. The program is written so that the positions and magnitudes of the maximum and minimum anomalies are located and their ratios and signs are used to define the initial parameters of the model under consideration. The errors resulting from these approximate values are derived and are solved for the increments to be given to the initial values. The process is repeated until the sum of the squares of the errors is less than 0.25% of the sum of the squares of the observed anomalies. The method has been tested on various theoretical examples and the results justify the validity of the programme.     

Interpretation of vertical magnetic anomalies due to inclined veins striking neither north nor east

Summary In the present paper an attempt has been made to interpret irregular vertical magnetic anomalies due to magnetite ore in the form of inclined thin veins, pods or lenses striking neither north nor east. A chart has been prepared for varying percentage of magnetite ore using arbitrary values of susceptibility contrast for Singhbhum and Palamau districts (Bihar), which would be helpful while interpreting magnetic anomalies to be found in these areas. Depth to width ratio against parameter c as well as two theoretical curves have also been presented. Further two field profiles are being matched with theoretical curves. The depths and widths of thin veins have been calculated using simple rules. An overall checking of these quantities is possible by curve-matching process.     

Interpretation of vertical gravity and magnetic profiles

Summary Methods have been developed by quantitatively interpreting gravity and magnetic data in vertical bore-holes or shafts for geological bodies that can be approximated by spheres and cylinders. Master diagrams that can be directly used by the interpreter are provided.     

A new technique of interpreting gravity and vertical magnetic anomalies due to infinite horizontal cylindrical ore bodies

Summary A novel method of interpreting gravity and magnetic anomalies is presented here. Two diagrams of master curves, one for gravity and the other for vertical magnetic interpretation are presented. They are useful in calculating the depth of burial and the radius of infinite horizontal cylindrical bodies irrespective of density contrast or strength and direction of magnetisation. This method also enables us to infer the direction of magnetisation, resultant intensity of magnetisation and from them the susceptibility contrast; and density contrast. ThoughHenderson [8]²) reported the applicability of continuations and derivatives in the interpretation of magnetic anomalies for the first time, the authors have treated them in a more exhaustive manner in the present paper to obtain valuable relationships.     

Interpretation of magnetic anomalies using a genetic algorithm

A genetic algorithm (GA) is an artificial intelligence method used for optimization. We applied a GA to the inversion of magnetic anomalies over a thick dike. Inversion of nonlinear geophysical problems using a GA has advantages because it does not require model gradients or well-defined initial model parameters. The evolution process consists of selection, crossover, and mutation genetic operators that look for the best fit to the observed data and a solution consisting of plausible compact sources. The efficiency of a GA on both synthetic and real magnetic anomalies of dikes by estimating model parameters, such as depth to the top of the dike (H), the half-width of the dike (B), the distance from the origin to the reference point (D), the dip of the thick dike (δ), and the susceptibility contrast (k), has been shown. For the synthetic anomaly case, it has been considered for both noise-free and noisy magnetic data. In the real case, the vertical magnetic anomaly from the Pima copper mine in Arizona, USA, and the vertical magnetic anomaly in the Bayburt–Sar?han skarn zone in northeastern Turkey have been inverted and interpreted. We compared the estimated parameters with the results of conventional inversion methods used in previous studies. We can conclude that the GA method used in this study is a useful tool for evaluating magnetic anomalies for dike models.     

Interpretation of self potential data for vertical and nearly vertical sheets of infinite horizontal extension

Summary Quantitative interpretation of SP anomalies due to vertical and nearly vertical, thin sheets of infinite horizontal extension has been developed in this paper. The methods proposed utilise selective SP values at some selected points on the profile thus enabling us to get the different parameters of the causative body directly. Also, for the case of vertical sheet, an interpretation technique has been formulated when the base station is within the zone of influence of the potential field of the causative body.     

Interpretation of magnetic anomalies of dikes using correlation factors

The magnetic anomaly due to a buried dike consists of the sum of two easily separated elementary functions. These functions, which have simple symmetry, are called even and odd functions. The correlation factors (r _0,1 for the even andr _0,2 for the odd function) between least-squares residual anomalies from even and odd functions are computed. Correlation values are used to determine the depth to the top and the half-width of the dike. The method also includes the determination of the index parameter and the amplitude coefficient. The validity of the method is tested against a theoretical and a field example where the parameters of the latter were determined by other investigators in comparing the results.     

Characteristic curves for interpreting the vertical magnetic anomalies of dipping doublets

Summary Standard charts from which a complete solution of the vertical magnetic anomalies of dipping doublets can be obtained very rapidly are derived and presented. The most important distances to be scaled from the field profile are the distances between the maximum and minimum anomalies, half maximum anomalies and one-third maximum anomalies only. The use of the charts for claculating the various parameters and locating the origin is also incorporated.     

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 gravity and magnetic anomalies caused due to spherical bodies

Summary The method of continuation has been used to obtain the master curves for gravity and magnetic anomalies caused by spherical bodies. The procedure to calculate the depth of burial and radius of spherical bodies has been outlined.     

Interpretation of gravity and magnetic anomalies when observation plane is inclined

Summary Not infrequently, in mining geophysics, measurements have to be made on the slopes of a hill that contain mineralisation. In this paper, procedures are evolved for interpreting gravity and vertical component magnetic data collected on such slopes and caused by geological bodies that can be approximated by infinite line pole, point pole, infinite line dipole and point dipole. From sets of theoretical magnetic anomaly curves (not reproduced), graphs have been constructed using characteristic points and are reproduced in Figures 5 to 10 and 12 to 17. These can be used for direct determination of depths, offsets, etc., by using information from suitably chosen field profiles. In the case of gravity, the mass can be computed as usual by a surface integration, provided a correction factor (1/cos²) is used, being the angle of the slope.     

Calculation of magnetic declination and horizontal intensity on the basis of the vertical intensity

If the magnetic vertical intensityZ is known over a certain area, it is possible, under more precisely defined conditions which are often complied with, at arbitrary points of the same area—though with the exception of the marginal area—to calculate the deviations of the horizontal intensityH and the magnetic declinationD, H and D, from constant values. Below some details of the calculation in practice are given, i. a. by means of an example, the mathematic basis for the calculations being outlined in the introduction (the succeeding text may, however, be read independently thereof). A graticule, as seen in Fig. 1, was used in the calculations, and the method itself is described under «2. Procedure». In Figs. 2 and 3, the figures at the crosses denote the values ofH andD computed in this way, indicated in gammas and arc-minutes, respectively; (the isomagneticH-lines in Fig. 2 are drawn on the basis ofobserved H-values; in Fig. 3 the observedD0values themselves are given in figures in small type). The accuracy of and the possibilities for application of the method are discussed in the later sections.

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Zusammenfassung Wenn man die magnetische Vertikalintensität in einem Gebiet kennt, ist es unter gewissen Bedingungen, die oft erfüllt sind, möglich in willkürlich gewählten Punkten des Gebietes — mit Ausnahme des Randgebietes — die Abweichungen H und D der HorizontalintensitätH und der DeklinationD von konstanten Werten zu berechnen. Weiter unten sind Einzelheiten der praktischen Ausführung anhand eines Beispiels mitgeteilt. Die mathematische Grundlage der Berechnungen ist in der Einleitung skizziert; doch können die folgenden Abschnitte auch unabhängig von ihn verstanden werden. Für die Berechnungen wurde ein, Integrationsgitter (Abb. 1) verwendet, und die Methode selber ist unter «2. Procedure» beschrieben. In Abb. 2 und 3 zeigen die Zahlen bei den Kreuze die in dieser Weise berechneten Werte vonH undD, angegeben in Gammawerten und Bogenminuten; (die isomagnetischen Linien in Abb. 2 sind auf Grund vonbeobachteten H-Werten gezeichnet worden; in Abb. 3 sind die beobachtetenD-Werte in kleiner Typen gedruckt). In den Abschnitten 3 und 4 werden die Genauigkeit und die Anwendungsmöglichkeiten der Methode diskutiert.

     

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.     

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.     

Interpretation of gravity and magnetic anomalies near Naples,Italy, using computer techniques

Some aspects of the analytical procedure for an automatic fitting of gravity and magnetic anomalies are discussed. An example of application relative to the Campania volcanic district near Naples, Italy, is reported. Gravity anomalies in that area mainly reflect the depth to the carbonate basement rocks. A small gravity high over Vesuvius may indicate buried volcanic layers. Magnetic anomalies near L. Patria and Castel Volturno are interpreted to be caused by buried intrusive rocks of higher susceptibility. Computer models of subsurface rock units with appropriate densities and susceptibilities have been generated to match the observed anomalies.     

A direct method of interpreting gravity and magnetic anomalies: The case of a horizontal cylinder

Summary A new method of interpreting the gravity and magnetic anomalies is introduced with special reference to the magnetic anomalies of a horizontal cylinder. The method consists of calculating the functions of the anomaly and its distance from an arbitrary point. These form a simple linear equation with coefficients related to the parameters defining the body. Since each observation forms a separate linear equation, the required normal equations are formed by the method of least squares and solved for the coefficients and hence for the various parameters defining the target. The discussion here is confined to the vertical magnetic anomalies. The application of the method to horizontal and total field anomalies of two dimensional bodies is also outlined.