Depth and structural index from normalized local wavenumber of 2D magnetic anomalies

Recent improvements in the local wavenumber approach have made it possible to estimate both the depth and model type of buried bodies from magnetic data. However, these improvements require calculation of third‐order derivatives of the magnetic field, which greatly enhances noise. As a result, the improvements are restricted to data of high quality. We present an alternative method to estimate both the depth and model type using the first‐order local wavenumber approach without the need for third‐order derivatives of the field. Our method is based on normalization of the first‐order local wavenumber anomalies and provides a generalized equation to estimate the depth of some 2D magnetic sources regardless of the source structure. Information about the nature of the sources is obtained after the source location has been estimated. The method was tested using synthetic magnetic anomaly data with random noise and using three field examples.     

Gravity and magnetic investigation on the distribution of volcanic rocks in the Qinggelidi area,north‐eastern Junggar Basin (north‐west China)

A detailed investigation on the location of magmatic intrusions in the Carboniferous strata of the Qinggelidi area, north‐eastern Junggar Basin, is presented based on the interpretation of gravity and magnetic data constrained by petrophysical data, seismics and surface geology. The wavelet multi‐resolution analysis based on the discrete wavelet transform is adopted to the regional‐residual separation of gravity and magnetic anomalies. A power spectrum analysis is applied to estimate the source depths corresponding to different scales. A comparative analysis on the characteristics of local gravity and magnetic anomalies improved our understanding of volcanic rock distribution in the Carboniferous strata. Generally speaking, in total 75 anomalies are recognized, among which 23 are inferred to be the responses of basalts, diabases and andesites with high density and strong magnetization. Twelve anomalies are assumed to be caused by andesites, rhyolites and volcanic breccias with medium‐low density and high magnetization. There are still five anomalies that are believed to be generated by volcanic tuffs with low density and weak magnetization. Lastly, four cross‐sections in 3D gravity and magnetic modelling are displayed to provide a more thorough image of volcanic rocks in our study area.     

A New Algorithm for Depth Determination from Total Magnetic Anomalies due to Spheres

We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones.     

Interpretation of gravity data by the continuous wavelet transform: The case of the Chad lineament (North-Central Africa)

A slightly bended gravity high along the Chad lineament in Central North Africa is analyzed and interpreted by the continuous wavelet transform (CWT) method. We use scale normalization on the continuous wavelet transform, allowing analysis of the gravity field in order to determine the sources at different depths. By focusing on homogenous standard sources, such as sphere or cube, horizontal cylinder or prism, sheet and infinite step, we derive the relationships between the source depth and pseudo-wavenumber. Then the source depth can be recovered from tracing the maximal values of the modulus of the complex wavelet coefficients in the CWT-based scalograms that are function of the pseudo-wavenumber. The studied area includes a central gravity high up to 75 km wide, and a secondary high that occurs at the southern part of the anomaly. The interpretation of the depth slices and vertical sections of the modulus maxima of the complex wavelet coefficients allows recognition of a relatively dense terrane located at middle crustal levels (10–25 km depth). A reasonable geological model derived from the 2.5D gravity forward modelling indicates the presence of high density bodies, probably linked to a buried suture, which were thrusted up into the mid-crust during the Neo-Proterozoic terrane collisions between the Saharan metacraton and the Arabian-Nubian shield. We conclude that the Chad line delineates a first order geological boundary, missing on the geologic maps.     

The theory of the continuous wavelet transform in the interpretation of potential fields: a review

We consider the use of the continuous wavelet transform in the interpretation of potential field data. We report its development since the publication of the first paper by Moreau et al . in 1997. Basically, it consists in the interpretation in the upward continued domain since dilation of the wavelet transform is the upward continuation altitude. Thus within a range of altitudes, the wavelet transform of the noise is decreased faster than the wavelet transform of the potential field caused by underground sources; this means that the signal-to-noise ratio is much better than those involved in other enhancing methods (e.g., Euler deconvolution, gradient analysis, or the analytic signals). Similarly to the Euler deconvolution, its first target parameters were the source positions and shape. The method has then been developed to estimate size and directions of extended sources (e.g., faults and dikes of finite dimensions) and also the magnetization direction in the case of magnetic data. Latest developments show that when combined with a Radon transform, the continuous wavelet transform can help in the automatic detection of elongated structures in 3D, simultaneously to the estimation of their strike direction, shape and depth. Several applications to real case studies have been shown before; however for clarity's sake in the present paper, only synthetic cases have been reproduced to clearly sum up the development of the methodology.     

Detection of potential fields source boundaries by enhanced horizontal derivative method

A high‐resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced‐to‐the‐pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries. The EHD method is highly flexible, and different conditions of signal‐to‐noise ratios and depths‐to‐source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high‐order vertical derivatives is also suggested. This involves both frequency‐ and space‐domain transformations and gives more stable results than the usual Fourier method. The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep‐seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high‐resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum. Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method.     

Fast local wavenumber (FLW) method for the inversion of magnetic source parameters

The current local wavenumber methods for the interpretation of magnetic anomalies compute the locations of geological bodies by solving complex matrices. Presently, such methods require to know the structural index, which is a parameter that represents the source type. The structural index is hard to know in real data; consequently, the precision of current methods is low. We present the fast local wavenumber (FLW) method, and define the squared sum of the horizontal and vertical local wavenumbers as the cumulative local wavenumber. The FLW method is the linear combination of the umulative local wavenumberand other wavenumbers, and is used to compute the locations and structural index of the source without a priori information and matrix solution. We apply the FLW method to synthetic magnetic anomalies, and the results suggest that the FLW method is insensitive to background and oblique magnetization. Next, we apply the FLW method to real magnetic data to obtain the location and structural index of the source.     

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.     

Localized cultural denoising of high-resolution aeromagnetic data

We show how a denoising technique based on the wavelet transform can be used to deal with localized noise related to DC electrified railway lines. This method, which performs localized and sharp filtering of cultural noise, was applied to high‐resolution aeromagnetic data acquired in the Phlegrean volcanic area, southern Italy, in 1999 and 2001. The helicopter‐borne survey was aimed at giving new detailed insights into the distribution of the magnetization of the area and, therefore, into the volcanological characteristics of the region. The surveyed area is characterized by the presence of towns, buildings and DC electrified railway lines whose magnetic effects influenced the measurements and were responsible for some of the measured anomalies. This cultural noise has, therefore, to be minimized as much as possible in order to allow the data to be interpreted accurately. Due to the excellent space‐scale localization properties of the discrete wavelet transform, the cultural disturbance was removed very precisely, leaving the field in the adjacent areas unchanged.     

Magnetic anomalies — India and Antarctica

Magnetic anomalies over the continental shelf off the east coast of India (Orissa) suggest the presence of a highly magnetic rock type magnetized with an intensity of 900 nT in a direction, azimuth(A) = 150° and inclination(I) = +65°. This suggest the occurrence of igneous volcanic rocks which is confirmed from samples found below Tertiary sediments from a few boreholes in this region. The depth of this rock type as estimated from magnetic anomalies varies from approximately 1–2 km near the coast to 4–4.5 km towards the shelf margin. This direction of magnetization is the reverse of the reported direction of magnetization for the Rajmahal Traps of the Cretaceous period (100–110 m.y). A small strip of the body near the continental shelf margin appears, however, to possess normal magnetization suggesting the occurrence of normal and reversed polarities side by side, a characteristic typical for oceanic magnetic anomalies. The reversed polarity of the rocks on the continental shelf suggests that they correspond probably to the MO reversal (115 m.y.) on world magnetostratigraphic scale and provide a paleolatitude of 47°S for the land mass of India which agrees with the palaeoreconstruction of India and Antarctica. In this reconstruction, the Mahanadi Gondwana graben on the Indian subcontinent falls into line with the Lambert Rift in Antarctica, suggesting a probable common ancestry. The volcanic rocks on the continental shelf off the east coast of India might represent a missing link, that is, rocks formed between India and Antarctica at the time of the break-up of Gondwanaland. Satellite magnetic anomalies (MAGSAT) recorded over the Indian shield and interpreted in terms of variations in the Curie point geotherm provide a direction of magnetization which also places this continent close to Antarctica. As such MAGSAT anomalies recorded over eastern Antarctica are found compatible with those recorded over the Indian shield.     

Translation-invariant wavelet denoising of full-tensor gravity –gradiometer data

Denoising of full-tensor gravity-gradiometer data involves detailed information from field sources, especially the data mixed with high-frequency random noise. We present a denoising method based on the translation-invariant wavelet with mixed thresholding and adaptive threshold to remove the random noise and retain the data details. The novel mixed thresholding approach is devised to filter the random noise based on the energy distribution of the wavelet coefficients corresponding to the signal and random noise. The translationinvariant wavelet suppresses pseudo-Gibbs phenomena, and the mixed thresholding better separates the wavelet coefficients than traditional thresholding. Adaptive Bayesian threshold is used to process the wavelet coefficients according to the specific characteristics of the wavelet coefficients at each decomposition scale. A two-dimensional discrete wavelet transform is used to denoise gridded data for better computational efficiency. The results of denoising model and real data suggest that compared with Gaussian regional filter, the proposed method suppresses the white Gaussian noise and preserves the high-frequency information in gravity-gradiometer data. Satisfactory denoising is achieved with the translation-invariant wavelet.     

A new least-squares minimization approach to depth and shape determination from magnetic data

We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.     

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.     

Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area,west central Sweden

In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated g_zz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of g_zz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.     

Interpretation of magnetic and gravity gradient tensor data using normalized source strength – A case study from McFaulds Lake,Northern Ontario,Canada

In this paper, we present a case study on the use of the normalized source strength (NSS) for interpretation of magnetic and gravity gradient tensors data. This application arises in exploration of nickel, copper and platinum group element (Ni‐Cu‐PGE) deposits in the McFaulds Lake area, Northern Ontario, Canada. In this study, we have used the normalized source strength function derived from recent high resolution aeromagnetic and gravity gradiometry data for locating geological bodies. In our algorithm, we use maxima of the normalized source strength for estimating the horizontal location of the causative body. Then we estimate depth to the source and structural index at that point using the ratio between the normalized source strength and its vertical derivative calculated at two levels; the measurement level and a height h above the measurement level. To discriminate more reliable solutions from spurious ones, we reject solutions with unreasonable estimated structural indices. This method uses an upward continuation filter which reduces the effect of high frequency noise. In the magnetic case, the advantage is that, in general, the normalized magnetic source strength is relatively insensitive to magnetization direction, thus it provides more reliable information than standard techniques when geologic bodies carry remanent magnetization. For dipping gravity sources, the calculated normalized source strength yields a reliable estimate of the source location by peaking right above the top surface. Application of the method on aeromagnetic and gravity gradient tensor data sets from McFaulds Lake area indicates that most of the gravity and magnetic sources are located just beneath a 20 m thick (on average) overburden and delineated magnetic and gravity sources which can be probably approximated by geological contacts and thin dikes, come up to the overburden.     

DEPTH ESTIMATION OF MAGNETIC SOURCES BY MEANS OF FOURIER AMPLITUDE SPECTRA*

The Fourier transform of a square-shaped section of a magnetic survey, digitized in a square grid, forms a rectangular matrix of coefficients which can be condensed to a series of average amplitudes dependent only on their frequency and no longer on the direction of the respective partial waves. These average amplitudes together represent a spectrum which–when plotted in a semilogarithmic coordinate system (log amplitude versus frequency)–often shows straight segments which decrease with increasing frequency. By continuing the given field downwards these straight segments become horizontal at a certain depth, the so-called “white depth”. This white depth may be used as a first estimate for the depth of magnetic sources producing the respective part of the field. It is shown that the sources which correspond to such use of the white depth can be expected to be “randomly distributed with some positive autocorrelation”. As an example for such a depth estimation the interpretation of the aeromagnetic survey of NW-Germany by a relief in 8–16 km depth is given. The relief divides the subsurface in an upper nonmagnetic layer and a lower layer with magnetization M= 2 Am^?1.     

Age of the source of the Jarrafa gravity and magnetic anomalies offshore Libya and its geodynamic implications

The interpretation of the Jarrafa magnetic and gravity highs, NW Libyan offshore, suggests that it may be caused by a body of high-density and high magnetization. Analysis of their power spectra indicates two groups of sources at: (1) 2.7 km depth, probably related to the igneous rocks, some of which were penetrated in the JA-1 borehole, (2) 5 km depth, corresponding to the top of the causative body and (3) 10 km depth, probably referring to the local basement depth. The boundary analysis derived from applied horizontal gradient to both gravity and magnetic data reveals lineaments many of which can be related to geological structures (grabens, horsts and faults).The poor correlation between pseudogravity fields for induced magnetization and observed gravity fields strongly suggests that the causative structure has a remanent magnetization (D = −16°, I = 23°) of Early Cretaceous age, fitting with the opening of the Neo Tethys 3 Ocean.Three-dimensional interpretation techniques indicate that the magnetic source of the Jarrafa magnetic anomaly has a magnetization intensity of 0.46 A/m, which is required to simulate the amplitude of the observed magnetic anomaly. The magnetic model shows that it has a base level at 15 km.The history of the area combined with the analysis and interpretation of the gravity and magnetic data suggests that: (1) the source of the Jarrafa anomaly is a mafic igneous rock and it may have formed during an Early Cretaceous extensional phase and (2) the Jarrafa basin was left-laterally sheared along the WNW Hercynian North Graben Fault Zone, during its reactivation in the Early Cretaceous.     

Modelling of magnetic data for scaling geology

Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak^?β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.     

Interpretation of Magnetic Anomalies and Estimation of Depth of Magnetic Crust in Slovakia

The magnetic map of Slovakia used in the paper was compiled as part of a project titled Atlas of Geophysical maps and profiles in 2001. The residual magnetic data were analyzed to produce Curie point estimates. To remove distortion of magnetic anomalies caused by the Earth’s magnetic field, reduction to pole transformation was applied to the magnetic anomalies using the magnetization angle of the induced magnetization. Anomalies reduced to the pole tend to be better correlated with tectonic structures. We applied a 3-km upward continuation to the residually compiled magnetic anomalies in order to remove effects of topography. The depth of magnetic dipoles was calculated by an azimuthally averaged power spectrum method for the entire area. Such estimates can be indicative of temperatures in the crust, since magnetic minerals lose their spontaneous magnetization according to Curie temperature of the dominant magnetic minerals in the rocks. The computed Curie point depths in the Slovakia region vary between 15.2 km and 20.9 km. Heat flow higher than 100 mWm⁻² occurs at the central volcanics and eastern part of Slovakia, where the Curie point depths values are shallow. The correlation between Curie point depths, heat flow and crust depth was investigated for two E-W cross sections. Heat flow and Curie point depth values are correlated with each other however, these values could not be correlated with crust depth. The Curie point isotherm, which separates magnetic and non-magnetic parts of the crust, is represented in two cross sections.     

Gravity and magnetic signatures of volcanic plugs related to Deccan volcanism in Saurashtra, India and their physical and geochemical properties

The Bouguer anomaly and the total intensity magnetic maps of Saurashtra have delineated six circular gravity highs and magnetic anomalies of 40-60 mGal (10⁻⁵m/s²) and 800-1000 nT, respectively. Three of them in western Saurashtra coincide with known volcanic plugs associated with Deccan Volcanic Province (DVP), while the other three in SE Saurashtra coincide with rather concealed plugs exposed partially. The DVP represents different phases of eruption during 65.5±2.5 Ma from the Reunion plume. The geochemical data of the exposed rock samples from these plugs exhibit a wide variation in source composition, which varies from ultramafic/mafic to felsic composition of volcanic plugs in western Saurashtra and an alkaline composition for those in SE Saurashtra. Detailed studies of granophyres and alkaline rocks from these volcanic plugs reveal a calc-alkaline differentiation trend and a continental tectonic setting of emplacement. The alkaline plugs of SE Saurashtra are associated with NE-SW oriented structural trends, related to the Gulf of Cambay and the Cambay rift basin along the track of the Reunion plume. This indicates a deeper source for these plugs compared to those in the western part and may represent the primary source magma. The Junagadh plug with well differentiated ring complexes in western Saurashtra shows well defined centers of magnetic anomaly while the magnetic anomalies due to other plugs are diffused though of the same amplitude. This implies that other plugs are also associated with mafic/ultramafic components, which may not be differentiated and may be present at subsurface levels. Paleomagnetic measurements on surface rock samples from DVP in Saurashtra suggest a susceptibility of 5.5×10⁻² SI units with an average Koenigsberger ratio (Q_n) of almost one and average direction of remanent magnetization of D=147.4° and I=+56.1°. The virtual geomagnetic pole (VGP) position computed from the mean direction of magnetization for the volcanic plugs and Deccan basalt of Saurashtra is 30°N and 74°W, which is close to the VGP position corresponding to the early phases of Deccan eruption. Modeling of gravity and magnetic anomalies along two representative profiles across Junagadh and Barda volcanic plugs suggest a bulk density of 2900 and 2880 kg/m³, respectively and susceptibility of 3.14×10⁻² SI units with a Q_n ratio of 0.56 which are within the range of their values obtained from laboratory measurements on exposed rock samples. The same order of gravity and magnetic anomalies observed over the volcanic plugs of Saurashtra indicates almost similar bulk physical properties for them. The inferred directions of magnetization from magnetic anomalies, however, are D=337° and 340° and I=−38° and −50° which represent the bulk direction of magnetization and also indicate a reversal of the magnetic field during the eruption of these plugs. Some of these plugs are associated with seismic activities of magnitude ≤4 at their contacts. Based on this analysis, other circular/semi-circular gravity highs of NW India can be qualitatively attributed to similar subsurface volcanic plugs.