Abstract Identifying mafic-ultramafic intrusions is critical for exploring magmatic sulfide deposits, especially those with abrupt morphological changes that may host mineralization. A dynamic iterative re-weighting matrix inversion method enhances the resolution of magnetic susceptibility anomaly reconstruction and improves the characterization of intrusion morphology. This method initially constructs a weighted matrix based on cross-correlation coefficients between observed data and theoretical responses generated by unit source. It then optimizes a dual-objective function balancing data fitting and weight distribution, iteratively refining the weighted matrix to adapt to subsurface structures. Finally, the optimized weighting matrix is used as a constraint to solve for the magnetic susceptibility anomaly model. A synthetic model test demonstrates significant improvement in detecting a single magnetic body with varying dip angles at different depths. Applied to the Tianfang magmatic sulfide deposit in Sichuan Province, China, this method successfully maps intrusion distribution and morphology using UAV (unmanned aerial vehicle) aeromagnetic data. Two potential favorable ore-prospecting areas are identified: (i) transitional zones between steep and gentle dips, and (ii) neck regions of bottle-shaped intrusions. The integration with polarizability and resistivity anomalies led to two high-confidence drill targets, with drilling confirming disseminated sulfide mineralization at predicted depths of 340–400 m. These results indicate the effectiveness of dynamic re-weighting matrix inversion in guiding magmatic sulfide deposit exploration. The method may also be useful for exploring other mafic-ultramafic hosted deposits and magnetite ores.

In recent years, deep learning (DL) techniques have emerged as a transformative paradigm for solving geophysical inversion problems, leveraging their powerful nonlinear mapping capacities and efficient predictive capabilities. However, current purely data-guided DL methods for two-dimensional (2D) magnetic inversion suffers from limited generalization beyond training distributions and inadequate integration of physical laws. To address these challenges, this study develops a joint physics-guided and data-guided deep learning method for 2D magnetic inversion. By deeply embedding the physical forward operator into the network training process, we establish a physical connection between the magnetic field response and the magnetic susceptibility distribution. We designed a dual-guided loss function of physics and data, and determined the optimal parameter combination through the weight sensitivity experiment. On the basis of the traditional root mean square error, we introduced the physical constraints of the forward modeling data and the observed data of the predicted model, effectively solving the defect of insufficient generalization ability of the pure data-guided method. To reduce sample construction costs and improve inversion efficiency, this study employs an efficient 2D magnetic field forward algorithm based on the Fourier finite element method. By applying Fourier transform to reduce the dimensionality of the magnetic potential partial differential equation, we use finite-element iterative solutions to achieve fast forward calculations. The network architecture adopts an improved U-Net, incorporating residual learning modules and feature fusion mechanisms into the classic encoder-decoder structure. Through a combination of five-level downsampling and transposed convolution upsampling, it achieves deep feature extraction while preserving the boundary details of anomalies. Additionally, to ensure practical applicability, this study constructs a set of randomized synthetic models with varying magnetic susceptibility values for the sample dataset, designed to simulate realistic subsurface structures. The proposed physics-guided U-Net inversion method is validated using both synthetic and field data, and benchmarked against data-guided DL inversion methods. Synthetic data experiments verify the feasibility and reliability, noise tests evaluate the model's robustness under noise interference. Finally, in the field case of the Galinge iron deposit in China, the magnetic susceptibility distribution inverted by the proposed method for hidden iron ore bodies matches the distribution detected by borehole data, confirming the algorithm's practicality and providing a new technical pathway for real-world magnetic prospecting under complex geological conditions.

This study introduces a novel method for the inversion of magnetic data using a focusing inversion technique. The method utilizes an arctangent stabilizing functional, which is reformulated into a pseudo-quadratic form by a weighting matrix. To optimize the process, the reweighted regularized conjugate gradient (RRCG) method is employed. The proposed technique is effective in restoring compact structures in subsurface structures without the need for a focusing parameter. The inversion method involves constructing an objective function for minimization, which incorporates the discrepancy between observed and predicted data and the deviation of the model from expected characteristics, which is known as the stabilizing functional. The data fit component determines how closely the inversion results match the observed measurements, while the model regularization term influences specific desired properties of the reconstructed density distribution. The study demonstrates the effectiveness of the proposed technique through its application to a synthetic dataset and one real-world aeromagnetic dataset from the McFaulds Lake area in Ontario, Canada.

We present an integrated methodology for three-dimensional inversion of large-scale airborne electromagnetic (AEM) and magnetic survey data that simultaneously recovers electrical conductivity, chargeability, and both induced and remanent magnetizations. A central feature of the AEM component is the explicit incorporation of induced polarization (IP) effects. Neglecting IP responses can lead to biased conductivity models, particularly in mineralized systems where disseminated sulfides contribute strongly to chargeability. Using the Generalized Effective-Medium Theory of Induced Polarization (GEMTIP), the inversion produces physically consistent 3D distributions of conductivity and chargeability. To enhance magnetic interpretation, we also implement a vector magnetic inversion that resolves both induced and remanent magnetization from Total Magnetic Intensity (TMI) data, enabling geologically realistic magnetization models in terranes with significant remanence. This integrated workflow was applied to airborne AEM and TMI datasets collected over the Asankrangwa Gold Belt in central Ghana. The inversion results delineate a key exploration target defined by coincident magnetic low and elevated chargeability, interpreted as sulfide-rich gold mineralization and subsequently confirmed by drilling. These results demonstrate that jointly accounting for IP and remanent magnetization in 3D inversion substantially improves subsurface characterization and provides a powerful tool for mineral exploration in structurally and lithologically complex environments.

Abstract The shared tectonic history of southwestern Australia and East Antarctica facilitates the exchange of geological insights between the regions. In this study, we present coupled susceptibility and density models obtained through the joint inversion of magnetic and gravity data. By assuming a common geological source for both signals, our coupling method minimizes misfits and variation in information, thereby enhancing a correlation between susceptibility and density. The resulting anomalies demonstrate structural continuity between the continents, aligning closely with major shear zones and seismic reflectors. Combining these results with machine learning, geochemical, and petrophysical databases, we predict a high‐resolution (10 km) heat production map for East Antarctica. Utilizing a Markov Chain Monte Carlo (MCMC) algorithm, we further develop a geothermal heat flow map with greater spatial variability than previous studies, yielding an average of mW/ in East Antarctica and mW/ in southwestern Australia. Our results provide a crucial high‐resolution boundary condition for ice sheet simulations, enabling more realistic estimates of basal meltwater production and ice temperatures.

Water resources underpin human society and economic growth, yet freshwater is unevenly distributed, leaving arid regions severely water-stressed. The Beishan mining district in Inner Mongolia exemplifies this challenge: despite abundant minerals, it lacks surface water and depends almost entirely on groundwater. To improve exploration in such complex settings, we propose a Bayesian joint inversion that leverages the complementary sensitivities of Surface Nuclear Magnetic Resonance (SNMR) and Transient Electromagnetic (TEM) data within a probabilistic framework. Using a transdimensional Markov Chain Monte Carlo (MCMC) algorithm, the method adaptively balances data weighting and model complexity. Tests on synthetic and field datasets show that combining SNMR’s direct sensitivity to water content with TEM’s high-resolution resistivity imaging enhances aquifer detection across depths and enables quantitative uncertainty assessment. Applied in Beishan, the approach delineates promising aquifers, with results confirmed by drilling, offering a robust basis for groundwater exploration and sustainable management in arid regions.

Magnetic inversion through three-dimensional (3D) susceptibility reconstruction can effectively identify the deep extension characteristics and structural variations in faults. Therefore, the reliability of inversion results from magnetic anomaly data is a key issue that must be addressed in fault detection and quantitative evaluation of fault activity. In recent years, deep neural network-driven magnetic data inversion methods have rapidly become a research focus in the field of geophysical magnetic data inversion. However, existing methods primarily rely on convolutional neural networks (CNNs), whose inherent local feature extraction capabilities limit their ability to model the spatial continuity of large-scale subsurface magnetic structures. Moreover, the general lack of prior physical constraints in these network models often leads to unreliable inversion results. To address these limitations, this paper proposes a physics-informed multi-scale deep learning inversion method for magnetic anomaly data. The method designs a dual-stream Transformer-CNN fusion module (TCFM). It leverages the self-attention mechanism in Transformers to model global susceptibility correlations while efficiently capturing local geological features through CNN convolutional operations. This enables collaborative modeling of multi-scale subsurface magnetic structures, significantly enhancing inversion accuracy. Furthermore, by incorporating deep physical priors, we design a depth-aware weighted loss function. By strengthening optimization constraints in deep regions, it effectively improves the vertical resolution of inversion models for deep magnetic structures. Comparative experiments with U-Net++ and Transformer demonstrate that the proposed method achieves smaller errors and higher inversion accuracy. Applied to measured aeromagnetic data from the Dandong region of China, the method yields reliable inversion results. Variations in magnetic susceptibility within these results successfully delineate the spatial distribution of fault zones, providing a geophysical basis for regional seismic hazard monitoring and assessment.

Inversion of magnetic and transient electromagnetic data for the characterization of skarn polymetallic mineralization in the Qimantagh Metallogenic Belt, China

Efficient and high-precision methods for magnetic field modeling are crucial for the accurate inversion and interpretation of magnetic survey data. In response, an efficient magnetic field forward modeling algorithm using Quadratic Finite Element Continuous Fourier Transform (QFE-CFT), leveraging CPU/GPU parallel computing, has been proposed to meet these demands. By applying a two-dimensional Fourier transform in the horizontal directions, the three-dimensional partial differential equation is reduced to a set of independent one-dimensional ordinary differential equations in the vertical direction, significantly improving computational efficiency and enabling parallel acceleration. The finite element method is then employed to form a five-diagonal linear system, which is efficiently solved using the chasing method. Finally, the magnetic field in the spatial domain is obtained using the Quadratic Finite Element Continuous Inverse Fourier Transform (QFE-CIFT). A model with anomalous spheres near the boundary of the considered computation area was designed to validate the accuracy and effectiveness of the algorithm. Comparisons with the standard-FFT, Gauss-FFT, and NUFFT algorithms demonstrated that the proposed method is unaffected by boundary effects. By utilizing OpenMP for equation solving and GPU acceleration for the QFE-CFT, the computational efficiency of the CPU/GPU parallel algorithm is significantly enhanced compared to the CPU serial algorithm, achieving an acceleration ratio of up to 86 times under the given hardware conditions. This approach provides a powerful tool for high-precision magnetic data inversion and geological interpretation.

Summary Inversion of geomagnetic anomaly data poses an ill-posed problem, and extremal models such as equivalent source layers or point-source distributions can explain observations to the same degree as volumetric magnetisation distributions. However, the spectral characteristics of magnetic anomalies provide fundamental constraints for magnetic source-depth estimation. Specifically, the maximum detectable depth of crustal magnetic sources is dictated by the longest wavelengths present in the field, which correspond to the low-wavenumber bands of the spectrum. This relationship is often analysed through the log power spectrum versus wave number plot, using the slopes of the linear segment for depth estimation. Methods aiming at reconstructing the depth to the bottom of magnetisation from spectral field characteristics are commonly referred to as spectral methods. However, these methods are based on assumptions about the statistical properties of the source distribution and are prone to misinterpretations. Here, we apply sparsity-constrained 3D inversion of magnetic data using an elastic net regularisation to recover the susceptibility distribution and the bottom of magnetisation. We claim that the elastic net (ℓ2ℓ1 norm) regularisation, when properly tuned to balance the solution’s smoothness with sparsity, stabilises the inversion, avoiding extremal magnetisation distributions and generating a geologically plausible source depth distribution that is consistent with the expected source distribution. The ℓ1 norm brings sparsity and high resolution, while the ℓ2 norm brings inversion stability and structural continuity to the final model. From the recovered 3D elastic net sparse inversion model, we extract the depths of all the deepest non-zero susceptibility values and suggest this to be an alternative estimate to the base of magnetisation. Moreover, we suggest that the resulting 3D model has a value in itself and may aid geological interpretation.

The late Silurian to early Devonian Cobar Supergroup hosts a variety of poly-metallic mineral systems and is one of the most prospective regions in Australia for gold and base metal exploration. Early research on its geology and geophysical characteristics produced numerous insights into the mineral system. However, the region has not yet benefited from many modern approaches, including integrated geological and geophysical modelling, and prospective areas undercover remain underexplored. The aim of this paper is to test the current understanding of geology and mineralisation processes, particularly structural control, in the central Cobar District, and propose a new approach based on these new technologies to identify prospective areas within the underexplored southern Cobar District. 3D geophysical inversion of magnetic data was undertaken in key areas of the central and southern Cobar Basin to identify the location and geometry of potential magnetised mineral deposits. The inversion results were then incorporated into 3D fault models to identify connections between the regional architecture and localisation of the mineral deposits. Magnetic inversion was performed using VOXI Magnetic Vector Inversion (MVI) software, which solves the 3D inverse problem mathematically using magnetisation vectors. VOXI MVI results are also compared with traditional voxel inversions and VPmg inversions, both of which assume that all magnetisation is induced. The unconstrained magnetic inversion produced magnetised bodies coincident with some major deposits in the area. Furthermore, it identified new areas of interest within the underexplored areas of the Cobar District. Inversion results suggest that major N- to NNW-trending faults might control the location of the known mineral occurrences and potentially prospective rocks at the regional scale. The latter are frequently localised on or next to NE- and NW-trending strike-slip faults that crosscut the major structures at the camp scale. This suggests that in the south Cobar District, dilation zones might have focused ore-fluid flux and subsequent mineral deposition, which is a main mechanism already invoked for mineralisation in the central Cobar District. VOXI MVI results suggest that remanent magnetisation is significant in some of these deposits, highlighting that remanent magnetisation should be incorporated into models to maximise the likelihood of successful geophysical targeting of Cobar-type systems.

Abstract Magnetic and gravity inversion has long attracted attention and research. A recent topic in such inversion studies is the magnetic and gravity joint inversion with the constraint that the derived magnetization and density models are correlated. The purpose of this approach is to reduce the non-uniqueness of the individual models, which is an inherent problem of potential-field data inversion, by using the constraints of multiple data. Another point of interest is the introduction of sparse regularization in the magnetic and gravity inversion. If the conventional smoothness-promoting inversion is used, the derived model is likely to be blurred. The aim of introducing sparse regularization is to reduce the blurred feature and improve the resolution of the derived model. In this paper, we proposed and developed a new magnetic and gravity joint inversion method by introducing the group lasso regularization. The group lasso is a kind of sparseness-promoting regularization method, an extension of the $$L_1$$ L 1 norm regularization. By introducing the group lasso into the magnetic and gravity joint inversion, the derived magnetization and density models are constrained to have a high correlation with each other and at the same time the sparseness of the derived model is promoted. In this way, the incorporation of the group lasso has the advantage that the two recent research trends, the introduction of structural similarity and sparseness in the derived model, can be implemented at once. However, the $$L_1$$ L 1 norm and other sparse regularization methods are known to have a drawback of deriving an over-concentrated model, and this property is carried over to the group lasso, which is confirmed by the synthetic test. Therefore, to overcome this problem, this paper proposes the use of $$L_2$$ L 2 norm and group lasso combined regularization, which leads to derive a correlated magnetic and density model that is not overly concentrated and not too blurred. The implementation of the inversion with this combined penalty can be easily completed by using the Alternating Direction Method of Multiplier (ADMM), a family of Lagrange multiplier methods. The proposed method is applied to synthetic data and magnetic and gravity anomalies observed on the Hiraniwa pluton, Kitakami Belt, North-east Japan, and the validity of our proposed method is confirmed. Graphic Abstract

This study applies unconstrained 3D inversion of high-resolution airborne magnetic data to model subsurface susceptibility distribution in the Southwestern Basement Complex of Nigeria. Total magnetic intensity (TMI) data were processed to residual magnetic anomalies, first vertical derivative (FVD), and analytical signal maps, followed by inversion using GM-SYS 3D in Oasis Montaj software (cell size: 250 × 250 × 100 m). The model converged after 50 iterations, achieving an RMS misfit of and . High-susceptibility anomalies (>0.05 cgs) extend laterally over 5–20 km and to depths exceeding 1.5 km, aligning with major NE–SW and NW–SE structural corridors. Integration of magnetic depth estimates, structural trends, and inversion results highlights prospective targets for iron oxide–copper–gold (IOCG), skarn-type, and gold-bearing systems. These targets coincide with structurally complex zones near the boundaries of high and low magnetic domains. The results provide a framework for prioritizing mineral exploration in the region.

SUMMARY The Xiangshan volcanic basin locates in southeast China hosts the world's third-largest volcanogenic uranium deposit. However, the structure of the volcanic system remains poorly resolved, limiting insights into the uranium mineralization. To address this, we conducted a joint inversion of gravity and magnetic data collected in the basin. Our inversion results reveal a southeast-dipping porphyroclastic lava conduit beneath the peak of Mount Xiangshan, characterized by low density and high magnetic susceptibility. A southwest-dipping volcanic conduit has also been identified beneath the rhyodacite crater in the Shutang area of the western basin. It connects to the porphyroclastic lava conduit in the deep. Both of these volcanic conduits are controlled by an EW-trending, low-density basement fault zone. This spatial relationship indicates that the volcanic eruptions in the western basin share a common subvolcanic plumbing system, which collectively acted as principal pathways for ore–forming hydrothermal fluids and uranium enrichment. These results underscore the role of volcanic-intrusive architecture in controlling the mineralization processes in the Xiangshan volcanic basin.

Accurate estimation of subsurface parameters is a critical objective in geophysical exploration. This study introduces an innovative hybrid algorithm integrating the Bat Algorithm (BA) with the Fourth Horizontal Gradient (FHG) to optimize the estimation of geometric parameters (depth, amplitude coefficient, shape factor, source origin, and magnetization angle) from magnetic field data. The FHG enhances the resolution of magnetic anomalies by mitigating regional field effects, while the BA efficiently navigates the parameter space to accurately delineate subsurface structures modeled as simplified geometric. This approach prioritize geometric parameters to define the spatial configuration of magnetic sources, assuming constant petrophysical properties (e.g., magnetization intensity, susceptibility contrast) to simplify the inversion process. The algorithm's robustness and effectiveness were extensively evaluated using synthetic magnetic datasets under both noise-free and with 10% Gaussian noise conditions. The findings demonstrate the method's capability to achieve accurate parameter estimation even in noisy environments. The proposed approach was further assessed using real magnetic profile data acquired from the Faro Mine Complex in Yukon, Canada. The estimated subsurface parameters closely match with well data and prior studies, emphasizing the algorithm's practical effectiveness. This integrated approach significantly advances the interpretation of magnetic datasets by improving both the accuracy and resolution of subsurface parameters estimation within the framework of idealized geometric models.

The article presents the application results of a set of geophysical methods to study the Kaspinsky ore cluster in the Krasnoyarsk Krai. The purpose of the study was to evaluate the efficiency of various modern methods when solving the problem of identifying the boundaries of intrusive massifs and analyzing tectonic disturbances that play a key role in the formation of gold-sulfide-quartz mineralization. The geophysical complex included unmanned magnetic exploration (SibGIS UAS complex), non-contact electric field measurement (BIKS non-contact measurement of electric field hardware complex) and electromagnetic sensing with induced polarization (Mars hardware and software complex). Magnetic exploration allowed to identify small diorite massifs of the Olkhovsky complex and their contacts with carbonate deposits, as well as to identify tectonic faults. Electrical exploration contributed to the analysis of small faults and distribution of induced polarization, which is important when searching for mineralization zones. Also, the study included a three-dimensional cascade inversion of magnetic exploration data for intrusive body localization. Conducted work resulted in the conclusion that the presented methodology is not optimal and the complex of geophysical methods is redundant. It is proposed to exclude the method of non-contact measurement of electric fields in further researches due to the small amount of useful information and interpretation problems as compared with the method of electromagnetic sensing and induced polarization. In addition, the main change in the methodology is the sequence of work stages. The data obtained as a result of the conducted research served as one of the bases for setting up drilling operations at the exploration stage.

3D inversion and modelling of geophysical magnetic data for Cu-Au exploration in Gomrokan area, Kerman, Iran

Abstract Collapse of hydrothermally weakened rock on the flanks of volcanic islands is a recognized cause of tsunamis generated by volcanoes. Here we use a multiphysics clustering method to derive a volcanic facies model for Whakaari/White Island, an andesite arc volcanic island in New Zealand. Through probabilistic inversion of magnetic and gravity data, combined with airborne electromagnetic data inversion we derive density, susceptibility, resistivity and saturation models of the island. Petrophysical relationships between density, P‐wave velocity and mean effective stress extends the range of physical properties mapped. A clustering algorithm identifies four clusters, that is facies, related to rock volumes characterized by varying degrees of hydrothermal alteration and saturation that occupy specific spatial locations in the edifice. Two volumes of rock (0.05–0.1 km3) in the west and north of the island, with contrasting facies properties are identified as the most hydrothermally altered or fractured parts of the island. Saturation models derived from resistivity models show the upper flanks are at low saturation, reducing their likelihood of failure. The submerged flanks become progressively more saturated with depth, in line with existing models of the hydrothermal system that show significant seawater input. The gravity and magnetic models delineate subcrater boundaries and highlight regions with different styles of alteration, including pore filling that increases rock density, and rock dissolution that decreases density. The model identifies new areas of potential slope instability, context for interpreting volcano monitoring data and quantified rock volumes for generation of scenarios which simulate tsunamis caused by volcanic landslides.

Abstract The Antarctic Peninsula is a unique sector of the circum‐Pacific continental margin arc where subduction ceased due to a series of ridge‐trench collisions, preserving a relatively un‐deformed magmatic arc. This region, therefore, has the potential to provide key insights into how subduction systems behave during their final stages. However, the remote nature of the region means that both geological and geophysical data coverage is often sparse, limiting the ability to interpret its tectonic evolution. Here we present a new analysis of gravity and magnetic data collected from a Windracers Ultra Uncrewed Aerial Vehicle (UAV). The survey targeted a 75 × 25 km region where the Antarctic Peninsula bends and magnetic signatures change, which has been attributed to the onshore influence of adjacent oceanic transform faults running approximately orthogonal to the Peninsula. Using joint inversion of magnetic and gravity data based on a “Variation of Information” approach, we show the region is dominated by two large intrusions, of likely granodiorite composition. Our data indicate little evidence for structural control on magma emplacement, however, coincident imagery suggests that after magma emplacement the region was subject to significant deformation approximately parallel to the Peninsula margin. We interpret these features in terms of the processes occurring as subduction ceased.

The main objective of this research is to get a comprehensive view on the subsurface geological data on the Esh El Mellaha area and environs, Red Sea, Egypt. This includes determining the depth and structural characteristics of the basement surface beneath the region, as well as identifying additional gravity and magnetic sources and potential structures within the sedimentary cover. To achieve this goal, Bouguer gravity and aeromagnetic data were used, processed and analyzed. Various depth estimation techniques were employed to analyze subsurface structures, each offering distinct advantages. Euler Deconvolution effectively delineates structural discontinuities and fault systems, while the Source Parameter Imaging (SPI) method improves depth accuracy through wavenumber analysis. The Analytical Signal method enhances resolution, providing detailed depth variations. Across these methods, the estimated depth ranges from 300 to 5000 m, with an average depth of approximately 2380 m, offering critical insights into the subsurface geological framework. Two-dimensional (2.5D) modeling was conducted on two selected gravity and magnetic profiles to estimate the depth, dip, density, and magnetic susceptibility of the source bodies. Additionally, three-dimensional (3D) modeling was applied to Bouguer gravity and Reduced-to-the-Pole (RTP) magnetic profiles, providing a detailed representation of the causative source structures. The results of the 3D inversion of gravity and magnetic data reveal the subsurface distribution of density and magnetic susceptibility, aiding in the identification of major geological structures. The sectional maps and 3D models illustrate the vertical and horizontal variations in subsurface formations, highlighting distinct anomaly zones that may correspond to faults and lithological changes. The obtained results indicate that the sedimentary succession thickness is ranging from 1.0 to 2.2 km, a finding corroborated by the borehole data. Positive structural features identified in these models suggest promising targets for potential hydrocarbon reservoirs.