Inversion of gravity and magnetic anomalies over some bodies of simple geometric shape

The general expression for gravity and magnetic anomalies over thin sheets and sloping contacts may be expressed as a polynomial of the formFx ²+C₁Fx+C₂F+C₃x³+C₄x²+C₅x+C₆. The initial parameters of the source are obtained from the coefficientsC ₁, C₂,..., C₆ which may be solved by inverting a 6×6 matrix. The initial parameters are modified by successive iteration process using the difference formula until the root mean square error between the observed and calculated anomalies is a minimum. The regional background which may be in the form of a polynomial is estimated by the computer itself. This method is applied on a number of field anomalies and is found to yield reliable estimates of depth and other parameters of the source.     

Interpretation of spontaneous potential anomalies from some simple geometrically shaped bodies using neural network inversion

A new approach is proposed in order to interpret spontaneous potential (self-potential) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on using neural network inversion of SP anomalies, particularly modular algorithm, for estimating the parameters of different simple geometrical bodies. However, Hilbert transforms are involved to determine the origin location in order to reduce the parameters which minimize the ambiguity in the inverted models. The inversion has been tested first on synthetic data from different models, using only one well-trained network. The results of inversion show that the parameter values derived by the inversion are identical to the true values of parameters. Noise analysis has been also examined, where the results of the inversion produce acceptable results up to 10% of white Gaussian noise. The validity of the neural network inversion is demonstrated through published real field SP taken from southern Bavarian Woods, Germany. A comparable and acceptable agreement is shown between the results of inversion derived by the neural network and those from the real field data.     

Quantitative interpretation of self potential anomalies of some specific geometric bodies

Summary Some direct and quantitative methods of SP anomalies caused by some specific geometric bodies have been developed in this paper. The models of current sources which have been considered are i) single pole, ii) a doublet, iii) a pair of single point poles separated by a horizontal distance, iv) single finite line pole, v) single infinite line pole and vi) two similar double infinite vertical line poles separated by a horizontal distance.     

Quantitative interpretation of self-potential anomalies due to spherical ore bodies

Summary A quantitative method of interpreting self-potential anomaly caused by a spherical ore body using downward continuation method is presented. Master curves to determine the depth, radius and angle of polarization have been prepared.     

Electrochemical modelling of self-potential anomalies

An electrochemical model is proposed, which considers the redox conditions and the electrode kinetics at the mineral surface. Advanced modelling of self-potential (SP) anomalies over ore deposits takes into account the course of the redox potential distribution with depth and the oxidation-reduction processes acting at the mineral-electrolyte interface. The application of this model to a SP anomaly in the vicinity of the German Continental Deep Drilling Program (KTB) can explain the surface and borehole data and gives an estimation of the prevailing thermodynamical conditions in the ground.Exclusively, this paper deals with SP anomalies, which are associated with high conductive graphitic layers. It can be concluded that SP-anomalies give an important hint to electronical conducting structures in the earth's crust.     

Effects of transverse electric anisotropy on self-potential anomalies

In the present paper is studied the influence of transverse ground anisotropy on the formation of self-potential (SP) anomalies produced by polarized bodies. It is concluded that SP anomalies produced by vertical dipoles of infinite length are displaced in the opposite direction of the dip angle of anisotropy. The equipotential lines are generally ellipses. SP anomalies produced by a vertical dipole of finite length are also displaced, have a negative and a positive centre and present the characteristics of an SP field produced by an inclined dipole in a homogeneous and isotropic ground. In both models, significant errors in the quantitative interpretation of SP anomalies may result from not taking ground anisotropy into account.     

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.     

Walsh spectra of gravity anomalies over some simple sources

Walsh transform of gravity anomalies over a point mass, a horizontal and a vertical line mass have been computed to obtain a cyclic shift invariant differential energy density (DED) function. Quantitative relations between DED spectral characteristics with depth to centroid/top of the source have been established. The effects of profile length, sampling interval, random noise and zero padding have been investigated. Applicability of the proposed method has been evaluated through two field examples.     

Direct interpretation of self-potential anomalies produced by a vertical dipole

In the present paper a new method is proposed for the quantitative interpretation of self-potential anomalies which are produced by a vertical dipole. First the mathematical expression of the wavenumber spectrum of the self-potential anomaly is deduced. It is pointed out that at relatively high wavenumbers the behavior of the amplitude spectrum is controlled by the closer to the surface pole at depth h. On the other hand, the “width” of the amplitude spectrum depends on the depth h and the dipole length L.Making a proper mathematical transformation of the amplitude spectrum, and applying the least squares method, it is possible to calculate the depth to the upper pole. The dipole length may then be calculated, by solving numerically a characteristic algebraic equation, as long as the “width” of the amplitude spectrum has been previously defined.The proposed method is applied on a well known self-potential profile from Greece. The calculated parameters of the polarized body are in good agreement with real data. Experimentation with synthetic models in which random noise was introduced, showed that this method gives reliable results if the noise amplitude is not more than 20% of the signal amplitude. It is clearly more efficient than the methods which are based on the model of the point pole or the dipole with a small length. It can also give good results if the horizontal extensions of the polarized body are not more than a few tenths of the depth of the upper pole. If the polarized body is tilted, the depth of the upper pole can be calculated with satisfactory accuracy.The direct interpretation method which is proposed in the present paper, may be useful in mineral exploration, and particularly if the target of interest is the detection of massive sulfide mineralization.     

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.     

Classification of self-potential anomalies on volcanoes and possible interpretations for their subsurface structure

Self-potential (SP) surveys were conducted on 10 island-arc-type volcanoes in Japan. Large-scale SP anomalies that covered entire volcanic edifices and had simple shapes were observed. Neglecting the local fluctuations, we named the SP anomaly that shows voltage gradients anywhere on the flank a long spatial wavelength (LSW) SP anomaly. We first classified these anomalies into three types: 1) no anomaly (SP profile is flat): 2) “W”-shaped profile: and 3) “V”-shaped profile. In some volcanoes, one flank with a flat SP profile and another with half of the W-shaped SP profile coexist. Next, we compared LSW-SP anomalies with various factors that may be related to SP generation and found that the SP profile is approximately flat on the flank where geothermal manifestations exist. This relationship, which is new aspect of the SP data on volcanoes, is important because it can impose a constraint on the model for SP generation and the subsurface structure. Based on the discussion that SP is generated by an electrokinetic mechanism, we propose that resistivity, zeta potential, and hydraulic radius are the possible parameters that control the existence of LSW-SP anomalies. The new relationship between SP and geothermal manifestation are understood in terms of the presence of hydrothermal system. Although the structure of volcanic edifice is probably spatially complicated, the insight into the SP data presented in this study implies that the flanks with flat SP profiles are relatively weak and have high potential for sector collapse.     

Use of the Hilbert transform to interpret self-potential anomalies due to two-dimensional inclined sheets

Self-potential anomalies due to two-dimensional inclined sheet of finite depth extent are analysed from their horizontal and vertical derivatives via the Hilbert transform. The depths to the top and bottom of the sheet and the inclination are obtained by means of simple mathematical expressions. The method is applied to a theoretical example and to a field S.P. anomaly over a sulphide deposit in the Kalava fault zone of Cuddapah basin, India. The presence of random noise is analysed for various levels and its effect is discussed. This interpretation process can be automated for all practical purposes by simple programming.     

On some types of gravity anomalies

Summary The gravity anomaly is a matter of convention. So far, only mixed gravity anomalies have been used. However, if in the future we shall have a sufficiently accurate geoid map covering the entire Earth's surface, it might be convenient to apply another type of gravity anomaly, as suggested Pellinen[1]. The object of this paper is to analyse this question with respect to the solution of the problems of physical geodesy.     

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.     

1-D and 2-D spatial frequency analysis of self-potential field anomalies,produced by a polarized sphere

This paper gives analytical expressions for the 1-D and 2-D frequency spectra of the self-potential field produced by a polarized sphere. In 1-D, the amplitude spectrum of the potential field leads to a criterion for determination of the depthh to the centre of the sphere. The polarization angle of the buried sphere can be calculated from the maximum point of the amplitude spectrum of the electric field. In 2-D, the depth to the centre of the polarized sphere can be calculated if the polarization is vertical.     

A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent

The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results.     

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.     

On the calculation of magnetic anomalies of irregular two-dimensional bodies

Summary An easy method of calculating the magnetic anomalies of two-dimensional irregular bodies is presented. The body under consideration is replaced by a set of line doublets with a pole strength equal to the intensity of magnetisation and parallel to its direction. The magnetic effects of some of the equally spaced doublets are obtained, added and multiplied by the distance between them to yield the magnetic anomaly. The expressions involved here are simpler than those existing in geophysical literature.     

Interpretation of gravity anomalies of dykes by pseudo-magnetic transformation

Summary A simple transformation called pseudo-magnetic transformation is introduced in which the horizontal derivatives of the observed gravity anomalies of any body will be calculated. These horizontal derivatives, called the pseudo-magnetic anomalies, are proportional to the vertical magnetic anomalies of the same body assumed to be polarised horizontally. It is shown that the interpretation of gravity anomalies of dykes is not unique except by computing the pseudo-magnetic anomalies, which will be interpreted by the logarithmic curve fitting technique indicated earlier [5]²).