Low-Latitude Reduction-to-the-Pole and Upward Continuation between Arbitrary Surfaces based on the Partial Differential Equation Framework

Summary Magnetic surveys conducted in complex conditions, such as low magnetic latitudes, uneven observation surfaces, or above high-susceptibility sources, pose significant challenges for obtaining stable solutions for reduction-to-the-pole (RTP) and upward-continuation processing on arbitrary surfaces. To tackle these challenges, in this study, we propose constructing an equivalent-susceptibility model based on the partial differential equation (PDE) framework in the space domain. A multilayer equivalent-susceptibility method was employed for RTP and upward-continuation operations, thus allowing for application on undulating observation surfaces and strong self-demagnetisation effect in a non-uniform mesh. A novel positivity constraint is introduced to improve the accuracy and efficiency of the inversion. We analysed the effect of the depth-weighting function in the inversion of equivalent susceptibility for RTP and upward-continuation reproduction. Iterative and direct solvers were utilised and compared in solving the large, sparse, nonsymmetric, and ill-conditioned system of linear equations produced by PDE-based equivalent-source construction. Two synthetic models were used to illustrate the efficiency and accuracy of the proposed method in processing both ground and airborne magnetic data. Aeromagnetic, ground data, and prior magnetic orebody information collected in Brazil at a low magnetic latitude region were used to validate the proposed method for processing RTP and upward-continuation operations on magnetic data sets with strong self-demagnetisation.

East Antarctica magnetically linked to its ancient neighbours in Gondwana

We present a new magnetic compilation for Central Gondwana conformed to a recent satellite magnetic model (LCS-1) with the help of an equivalent layer approach, resulting in consistent levels, corrections that have not previously been applied. Additionally, we use the satellite data to its full spectral content, which helps to include India, where high resolution aeromagnetic data are not publically available. As India is located north of the magnetic equator, we also performed a variable reduction to the pole to the satellite data by applying an equivalent source method. The conformed aeromagnetic and satellite data are superimposed on a recent deformable Gondwana plate reconstruction that links the Kaapvaal Craton in Southern Africa with the Grunehogna Craton in East Antarctica in a tight fit. Aeromagnetic anomalies unveil, however, wider orogenic belts that preserve remnants of accreted Meso- to Neoproterozoic crust in interior East Antarctica, compared to adjacent sectors of Southern Africa and India. Satellite and aeromagnetic anomaly datasets help to portray the extent and architecture of older Precambrian cratons, re-enforcing their linkages in East Antarctica, Australia, India and Africa.

New Magnetic compilation and interpretation of the Bay of Biscay and surrounding continental shelves

Producing accurate structural maps is a pre-requisite to unravel the tectonic evolution of a region. For this purpose, magnetic anomaly maps are helpful data sets for the identification and mapping of geological features. We compiled 154 marine surveys and 7 aeromagnetic campaigns covering the Bay of Biscay, its surrounding continental shelves and western part of the Pyrenees. As the initial data sets had heterogeneous acquisition parameters, we applied a series of transforms before merging the data. We performed a variable reduction to the pole to localize the extrema of the anomaly vertically to their causative sources and facilitate geological interpretations. The resulting intermediate resolution maps compiled at 500 m altitude offshore and 3000 m both on- and offshore, display magnetic trends and patterns. They are enhanced by several potential field operators (analytic signal, tilt angle, vertical derivative) enabling the interpretation of the geometry of the sources causing the anomaly (3D, 2D and 2.5D). The analysis of these magnetic maps allows us to precise the distribution and segmentation of crustal domains previously identified in the Bay of Biscay and its adjacent continental shelves. A series of crustal scale structures mapped onshore and formed during and after the Variscan orogeny show well on this new map compilation, allowing the continuous onshore-offshore mapping of some of them and revealing their role in segmenting the northern margin of the Bay of Biscay. This new compilation notably reveals variations in the magnetic signature of the Ocean-Continent-Transition (OCT) that we interpret as related to an increased magmatic production of the eastern part of the Bay of Biscay OCT during continental breakup. In addition to precise previous structural maps, this new magnetic compilation opens new perspectives for the interpretation of the Bay of Biscay geodynamic setting.

Application of multivariate regression on magnetic data to determine further drilling site for iron exploration

In this study, a new approach of the multivariate regression model has been applied to make a precise mathematical model to determine further drilling for the detailed iron exploration in the Koohbaba area, Northwest of Iran. Furthermore, to figure out the additional drilling locations, the ore length to the total core ratio for the drilled boreholes has been used based on the geophysical exploration dataset. Hence, different regression analyses including linear, cubic, and quadratic models have been applied. In this study, the ore length to the total core ratio of the chosen drilled boreholes has been considered as a dependent variable; besides, the outputs of the magnetic data using the UP10 (10m upward-continuation), RTP (reduction to the pole), and A.S. (analytic signal) techniques have been designated as independent variables. Based on probability value (p-value), coefficients of determination (R 2 and R adj 2 {R}_{\text{adj}}^{2} ), and efficiency formula (EF), the fourth regression model has revealed the best results. The accuracy of the model has been confirmed by the defined ratio of boreholes and demonstrated by four additional drilled boreholes in the study area. Therefore, the results of the regression analysis are reasonable and can be used to determine the additional drilling for the detailed exploration.

Application of magnetic method for mapping buried structures around archaeological site of Masjid Tuha Indrapuri

Magnetic gradiometer survey has been conducted on the yard of the archaeological site of Masjid Tuha Indrapuri, Aceh Besar Regency, Aceh Province. The site is one of the oldest mosques erected during the Aceh Sultanate period. Magnetic method was applied for mapping archaeological structures buried beneath the surface. Total magnetic field data were measured using Proton Precession Magnetometer with grid spacing of 2 meters between stations covering the entire area of the site. Diurnal and international geomagnetic reference field data were corrected to the measured data in order to calculate total magnetic field anomalies that were influenced by the buried magnetic objects. The total magnetic field anomalies distribution shows two elongated structures with U-shaped patterns surrounding the mosque. The patterns are also revealed in reduction to the pole and derivative vertical filters of the total field anomaly data. The anomaly patterns are considered a response from the rest of the buried fences that were built around the mosque in the past.

Using parity decomposition for interpreting magnetic anomalies from dikes having arbitrary dip angles, induced and remanent magnetization

We have developed a technique to reconstruct the magnetic anomaly due to a dike in a way that the effect of magnetization direction is removed, resulting in a new totally symmetric anomaly. The reconstruction algorithm is easy to implement and could avoid the need of reduction to the pole at a low computational cost. The method is based on the decomposition of the function representing magnetic anomalies due to dikes in its even and odd parts. After applying a Hilbert transform to the odd components, we reconstruct the signal by a weighted average of the even part and the Hilbert-transformed odd part of the signal. The method requires knowing the dike’s center position, which is accomplished by locating the center of symmetry of the analytic signal amplitude as well as the effective dip angle obtained by evaluating the anomaly’s tilt angle. Our approach is tested for synthetic and field data. As an illustration of the method’s potential applications, we use it to estimate the width and depth of magnetic dikes.

Evaluating the accuracy of equivalent-source predictions using cross-validation

<p>We investigate the use of cross-validation (CV) techniques to estimate the accuracy of equivalent-source (also known as equivalent-layer) models for interpolation and processing of potential-field data. Our preliminary results indicate that some common CV algorithms (e.g., random permutations and k-folds) tend to overestimate the accuracy. We have found that blocked CV methods, where the data are split along spatial blocks instead of randomly, provide more conservative and realistic accuracy estimates. Beyond evaluating an equivalent-source model's performance, cross-validation can be used to automatically determine configuration parameters, like source depth and amount of regularization, that maximize prediction accuracy and avoid over-fitting.</p><p>Widely used in gravity and magnetic data processing, the equivalent-source technique consists of a linear model (usually point sources) used to predict the observed field at arbitrary locations. Upward-continuation, interpolation, gradient calculations, leveling, and reduction-to-the-pole can be performed simultaneously by using the model to make predictions (i.e., forward modelling). Likewise, the use of linear models to make predictions is the backbone of many machine learning (ML) applications. The predictive performance of ML models is usually evaluated through cross-validation, in which the data are split (usually randomly) into a training set and a validation set. Models are fit on the training set and their predictions are evaluated using the validation set using a goodness-of-fit metric, like the mean square error or the R² coefficient of determination. Many cross-validation methods exist in the literature, varying in how the data are split and how this process is repeated. Prior research from the statistical modelling of ecological data suggests that prediction accuracy is usually overestimated by traditional CV methods when the data are spatially auto-correlated. This issue can be mitigated by splitting the data along spatial blocks rather than randomly. We conducted experiments on synthetic gravity data to investigate the use of traditional and blocked CV methods in equivalent-source interpolation. We found that the overestimation problem also occurs and that more conservative accuracy estimates are obtained when applying blocked versions of random permutations and k-fold. Further studies need to be conducted to generalize these findings to upward-continuation, reduction-to-the-pole, and derivative calculation.</p><p>Open-source software implementations of the equivalent-source and blocked cross-validation (in progress) methods are available in the Python libraries Harmonica and Verde, which are part of the Fatiando a Terra project (www.fatiando.org).</p>

Contribution of applied geophysics in mining prospecting

The Eastern High Atlas (Morocco) contains a variety of rocks with different magnetic susceptibility, among these rocks are those which constitute the Proterozoic and Paleozoic basement of the plain of Tamlelt which is the study area. This work is devoted to the analysis and interpretation of the main magnetic anomalies using the Oisis Montaj program, and the correlation using ArcGis software, from the main « magnetic facies» detected, to the main geological formations affecting the geological basement, highlighted in the plain of Tamlelt. The map of the residual magnetic field shows elongated magnetic anomalies in the direction E-W and NE-SW. the reduction to the pole shows at the level of the plain of Tamlelt a large anomaly elongated in the direction E-W then in the direction NW-SE. The transformation of Tilt Angle allowed to delimit the anomalies of low or high amplitude that limit the shallow structures. The quantitative interpretation of the main magnetic anomalies highlighted in the study area has made it possible to characterize the deep structure of the magnetic bodies, which could contain sulphide clusters, according to the geological and mining context of the studied area.