ABSTRACT Seismic data interpolation is crucial for improving data quality and ensuring reliable subsurface interpretation. While deep learning methods have shown strong potential for this task, they often struggle to preserve the spatial continuity and global consistency of seismic data under complex missing conditions, leading to amplitude distortion and reduced accuracy in subsequent geological interpretation and reservoir evaluation. To address this issue, we propose Meta‐Interpolation, a novel adaptive framework that explicitly models spatial continuity by leveraging prior knowledge from complete seismic data. Specifically, we design a dual‐branch architecture comprising an auxiliary network (AN) and an interpolation network (IN). The AN is pre‐trained on complete seismic data to capture spatially continuous feature representations. Rather than relying solely on a direct mapping from incomplete data during training, our framework employs a knowledge distillation strategy where the AN acts as a teacher to guide the IN. To ensure this guidance is optimal and adaptive to varying missing patterns, we introduce a meta‐network (MN). The MN dynamically generates channel‐wise weights and regulates the distillation process, effectively guiding the IN to capture both global consistency and local spatial continuity. Extensive experiments conducted under random missing, consecutive missing and noisy data missing scenarios demonstrate that the proposed framework significantly improves the quality, efficiency and generalization of seismic interpolation.
ABSTRACT Magnetic surveying is widely used for unexploded ordnance (UXO) detection. However, reliable target localization and characterization remain challenging because of noise, orientation‐dependent magnetic responses, elongated target geometries and inversion non‐uniqueness. In this context, we present an enhancement‐constrained stochastic magnetic inversion workflow that uses anomaly‐enhancement results as spatial prior information to restrict the admissible model space before optimization. First, magnetic anomalies are denoised using a modified non‐local means approach to suppress high‐frequency noise that would otherwise be amplified during derivative‐based processing. Modified local‐phase filters are then used to delineate laterally confined target zones, whereas approximate depth estimates constrain the vertical search range. The resulting spatial bounds are incorporated into a parsimonious stochastic inversion based on the Hunger Games Search algorithm, in which UXO responses are approximated by uniformly magnetized equivalent spheres for computational efficiency. The workflow is tested using noisy synthetic data generated from elongated UXO‐like sphero‐cylinders. The intentional mismatch between the forward‐model geometry and the equivalent‐sphere inversion model provides a more demanding assessment of robustness to geometric simplification. Normalized source strength (NSS)‐based Euler deconvolution (NSS‐Euler) is evaluated as an independent localization benchmark and is not incorporated into the proposed inversion workflow. The proposed framework is then applied to magnetic data acquired over targets with known positions and orientations at a controlled test site in Slovakia. Compared with otherwise identical unconstrained inversions, the derived spatial constraints improve target localization, reduce solution ambiguity and increase the consistency of the recovered models. NSS‐Euler provides an independent estimate of target location and depth, whereas the constrained stochastic inversion yields more accurate localization and depth estimates while additionally recovering effective‐magnetization and other source‐related parameters. Although this simplified representation cannot reproduce all geometric details of real UXO bodies, it offers a practical and computationally efficient framework for localization‐oriented interpretation. The proposed strategy may also be applicable to other compact‐target‐detection problems in which enhancement‐derived spatial information can guide inversion.
ABSTRACT We present a workflow for three‐dimensional probabilistic inversion of controlled‐source electromagnetic data that effectively balances accuracy and computational efficiency. The approach mitigates the high computational cost of forward modelling by employing a surrogate model derived from a mesh coarsening strategy. To account for the modelling errors inherent to this approximation, we implement a deep‐learning–based parametric correction, enabling the joint inversion of correction and subsurface physical parameters. We use a synthetic marine experiment to verify that the proposed method recovers the true subsurface parameters. The inclusion of an error correction improves the predictive accuracy of the coarse mesh strategy and significantly reduces computation time compared to fine meshing forward modelling. Application to real‐world marine data acquisition further illustrates the capability of the method to estimate the geometry and location of an oil reservoir. Our results highlight the potential of deep‐learning–assisted surrogate modelling as a practical tool for accelerating the probabilistic inversion.
ABSTRACT On the basis of real ray path and the newly developed g *‐Hamiltonian method of ray‐velocity vectors, we theoretically investigate three homogeneous body waves (qP, qSV and qSH) in viscoelastic transversely isotropic media and distinguish them from their inhomogeneous situations. We demonstrate theoretical conditions of the Q ‐factors of medium for the three homogeneous body waves and conduct computational experiments with rock samples to validate the analytic derivations and characterizations of the homogenous and inhomogeneous body waves. The theoretical analysis and computational experiments reveal that in a viscoelastic isotropic medium P‐ and S‐wave are always homogeneous; in a viscoelastic transversely isotropic medium, the qP‐ and qSV‐wave are homogeneous only when four Q ‐factors , share a same value, and qSH‐wave becomes homogeneous only when equals These theoretical predictions may significantly simplify the computations of the slowness and ray‐velocity vectors and the complex Snell's law of these body waves at an interface and break the bottleneck of seismic ray tracing in viscoelastic transversely isotropic media, which holds crucial practical significance in enhancing the computational efficiency.
ABSTRACT Real earth media cause absorption attenuation and anisotropy. Ignoring these effects leads to amplitude and imaging‐position errors in migration profiles. The classical Born approximation generates large errors under the strong forward accumulative effect of visco‐acoustic VTI (Transversely Isotropic media with a Vertical symmetry axis) media. Therefore, this article integrates the De Wolf approximation with visco‐acoustic VTI media for the first time. We renormalize the Born series using the De Wolf approximation and establish its integral representation for visco‐acoustic VTI media, thereby improving the accuracy of the Born approximation. Following the thin‐slab approximation, the velocity model is divided into several thin slabs, each containing background parameters (velocity, quality factor and anisotropy) and perturbation parameters. Dual‐domain screen approximation migration operators (frequency‐wavenumber and frequency‐space domains) are then constructed for visco‐acoustic VTI media, leading to a prestack migration imaging method based on the De Wolf approximation. Algorithm tests on the Overthrust and Hess models show that the proposed migration operator effectively compensates for amplitude attenuation and corrects anisotropic effects, producing migration results with higher signal‐to‐noise ratio and resolution. The specific effects of viscosity and anisotropy on imaging are explicitly analysed based on comparative data of migration profiles, waveforms and amplitude spectra, further validating the algorithm's effectiveness.
ABSTRACT In situ stress characterisation is crucial for the exploration and development of coal resources. Conventional methods based on well‐log data offer high‐accuracy point measurements but are limited to wellbore locations, whereas traditional seismic‐based predictions provide extensive spatial coverage but have lower accuracy and often fail to capture the complex, non‐linear relationships between seismic attributes and the stress field. To bridge this gap, we introduce a data‐driven approach that integrates the strengths of both data types using a random forest (RF) model. In our approach, geomechanical attributes (Young's modulus and Poisson's ratio) and geometric attributes (curvature), derived from pre‐stack inversion, serve as the model's input features. High‐resolution stress values calculated from well logs using the combined spring model serve as the training labels. The RF model, optimised via grid search and cross‐validation, demonstrates high predictive accuracy. We apply the proposed RF‐based method to a field dataset from the Daji area in Shanxi Province, North China, successfully generating a continuous three‐dimensional (3D) in situ stress volume. The resulting stress field exhibits strong spatial consistency with regional tectonic features, validating the model's accuracy and geological applicability. This study demonstrates that a machine learning framework can effectively link seismic data with well‐log‐derived reference stress labels, extending sparse reference stress information into a continuous 3D volume that reliably characterises the inter‐well stress heterogeneity. This provides a practical and effective framework for in situ stress analysis in complex geological settings.
ABSTRACT Elastic full waveform inversion (EFWI) aims to reconstruct high‐resolution elastic properties by minimizing the waveform misfit between observed and simulated multicomponent seismic data, yet its practical performance is often limited by cycle skipping and modelling errors that conventional misfit‐based methods cannot fully resolve. We propose a deep‐learning‐based matching‐filtering framework, in which a lightweight neural network is trained to learn adaptive, data‐driven matching filters that map synthetic elastic wavefields towards the observed data. Instead of directly enforcing waveform agreement, the learned filters absorb phase, amplitude and dispersion discrepancies arising from inaccurate initial models, elastic‐parameter trade‐offs and imperfect physics. The matching filters are optimized jointly with elastic parameters within an AD framework, enabling seamless gradient propagation through both the wave‐equation solver and the neural components. Numerical experiments on synthetic elastic models and field data demonstrate that the proposed approach significantly reduces cycle skipping and improves the recovery of P‐ and S‐wave velocities compared to conventional EFWI, particularly when the initial model is strongly biased. The results suggest that deep learning–based matching filtering provides a physically interpretable and computationally efficient pathway for robust elastic waveform inversion under realistic modelling uncertainties.
ABSTRACT Integrated earth modelling aims to combine all available geoscientific information to derive one common earth model. However, combining multiple parameters in a meaningful way remains challenging. In this study, we aim to improve mineral exploration workflows through the integration of new magnetotelluric data with other geophysical and petrophysical data to enhance local geological understanding of the northern Kiruna mining district, Norrbotten, Sweden. The area is economically important and geoscientifically interesting. We derived three‐dimensional (3D) geophysical models based on new magnetotelluric data and previously collected gravity and magnetic data. The magnetotelluric data and the resulting 3D electrical‐resistivity model are described in detail. Additionally, a new petrophysical dataset containing surface and subsurface samples and their density, electrical resistivity and magnetic susceptibility is presented and linked to the 3D geophysical models. The geophysical 3D models are interpreted using information gained from the measured rock properties, allowing for correlation and cross‐validation between models and geology. Integration of a clustering approach into the mineral exploration workflow allows for a holistic interpretation of all information available in the area. These interpretations and models improve understanding of the Per Geijer mineral system, its immediate surroundings and the relationships between local rock types and their geophysical and mineralogical signatures.
ABSTRACT For geotechnical applications, surface‐wave methods are one of the most important techniques for gathering information about the strength of the near surface, but these methods are sensitive to noise. Often only the fundamental mode is considered, but higher modes can also provide more information on deeper parts of the subsurface. We investigate the use of iterative supervirtual interferometry (SVI) to increase the signal‐to‐noise ratio and to extract more information about the higher modes. A big advantage is that the method results in data in the same domain as the original data, such that similar multichannel analysis of surface waves–based procedures can be used afterwards. SVI utilises seismic interferometry to extract the extra information in consecutive folds. Generally, the strongest event in the data is boosted the most. Although surface waves are usually the strongest, they consist of sub‐events (the modes) with different amplitudes. Previously, iterative SVI has been applied to further boost the result of SVI. For surface waves, this would further diminish the presence of weaker modes. Instead, we subtract the results of SVI from the original data and use the remainder as input for the next iteration, which gives potential for highlighting different modes. We apply our methodology to three different datasets to show different properties of the iterative SVI. When the level of random noise is high, further iterations retrieve mostly the dominant event and no extra information on different modes is gained. When the level of noise is relatively low, we show that higher modes can be found in a wider frequency band in the results of each separate iteration. In both cases, the combination of all iterations provides a more complete description of the surface waves. The presence of strong random noise or spikes in the data can have negative effects on the methodology in the form of spurious events originating from the spikes.
The effective processing of seismic data contaminated by high-amplitude erratic noise presents a problem in geophysical signal processing, particularly within onshore surveys where noise distributions are complex, non-stationary and largely unknown. Traditional denoising algorithms, including standard prediction error filters and projection filters, primarily rely on minimising the error norm. While computationally efficient, these methods operate under the assumption of Gaussian noise, causing them to disproportionately penalise large residuals and inadvertently smear outlier energy across valid seismic events. This sensitivity to non-Gaussian contamination compromises the fidelity of signal preservation and can introduce artefacts into the denoised data. This work addresses these limitations by incorporating an adaptive robust loss function directly into the optimisation framework of three-dimensional (3D) projection filtering in the frequency-space domain. By allowing the loss function to dynamically adapt its shape parameter , which is found by minimising the Negative Log Likelihood (NLL) of the adaptive loss function, to the statistical properties of the noise, interpolating between Gaussian and heavy-tailed distributions, we develop a filtering methodology that robustly suppresses erratic outliers without degrading the underlying signals. Using synthetic and real datasets, we verified the performance of the proposed approach and found that the 3D robust projection filter can outperform the conventional least-squares projection filter when the data are contaminated by erratic noise.
Electrical resistivity has been shown to offer significant insights into post-seismic changes in geothermal reservoirs; however, its interpretation is complicated by the fact that it is controlled not only by temperature, but also by porosity and clay content. In this study, we used a post-seismic electrical resistivity-depth model from magnetotelluric data to estimate the temperature changes following a seismic swarm in the vicinity of the Tuzla Geothermal Field in the Biga Peninsula of northwestern Anatolia. In the absence of pre-seismic resistivity data for the field, we attribute the characteristic part of the post-seismic model to the seismic swarm. Temperature changes were then evaluated using pre- and post-seismic wellhead temperature observations together with the post-seismic resistivity-depth model. In order to address the relationships between resistivity and petrophysical parameters, the present study combined the established equations for temperature, porosity and clay-related effects. The estimation of petrophysical parameters from combined equations was then conducted using the differential evolution algorithm (DEA), a method that has gained popularity due to its effectiveness in solving non-linear optimization problems. The main contribution of this study lies in the integrated use of a unified petrophysical framework and the DEA to jointly estimate post-seismic changes in temperature, porosity and clay content from the resistivity model. Furthermore, an estimation was made of the reduction in stored heat within the defined reservoir zone. The results indicate that the observed increase in resistivity is primarily associated with a decrease in reservoir temperature, which is consistent with the observed decrease in wellhead temperatures. In addition, changes in clay content and porosity contribute significantly to the resistivity response. The findings demonstrate the efficacy of models of resistivity-depth, obtained following seismic activities, in facilitating the inference of changes in petrophysical parameters and thermal state in geothermal systems.
Coal electrical conductivity is a key physical parameter during the coalbed resources exploration and development. Conventional petrophysical experiments face challenges in studying coal electrical conductivity due to its insufficient resolution and coal's brittle nature. The recently developed digital core technology provides a novel approach to characterize coal resistivity by coupling with various influencing factors. In this study, a multi-modal data fusion strategy was first developed to construct a three-dimensional (3D) digital coal-rock model by integrating micro-computed tomography (micro-CT) imaging, MaipSCAN mineral analysis data and laboratory porosity measurements. The lattice Boltzmann method was subsequently employed to characterize the distributions of movable hydrocarbons and water within coal pores. Using finite element simulations coupled with a controlled variable method, we systematically investigated the effects of intrinsic and extrinsic factors on coal resistivity. Furthermore, the sensitivity of each factor was quantitatively evaluated using the Morris screening method. Our study reveals that under the same metamorphic grade, the effects of different factors on coal resistivity exhibit significant variations depending on pore structure development and fluid occurrence states. The relationship between coal resistivity and variations in matrix porosity and water saturation demonstrates a staged correlation in coal seams with underdeveloped cleat fractures. Formation water salinity and clay CEC follow power-exponential relationships with resistivity reduction, whereas clay content and temperature exhibit linear dependencies. Clay minerals and pore fluids exhibit a dynamic competitive relationship in their contributions to coal conductivity, which conforms to parallel conduction principles. Sensitivity analysis revealed that the descending order of influencing factors is water saturation, matrix porosity, clay mineral content, clay CEC, temperature and formation water salinity, indicating that the coal resistivity is more significantly influenced by intrinsic factors than by extrinsic factors. These results can provide essential theoretical insights for optimizing coal resource exploration strategies and reservoir evaluation protocols.
We present an approach for seismic characterization of a deep supercritical geothermal reservoir in the direct vicinity of an exploration well. Our investigation area is the Larderello geothermal field in Tuscany (Italy) where we focus on the K-horizon, which is represented by a strong reflector at a depth of 3-6 km marking the geothermal reservoir hosting fluids at a supercritical state. We used a low-cost piggyback vertical seismic profiling experiment with two surface seismic profiles crossing each other at the borehole location to obtain seismic images of the K-horizon and to improve the migration velocity model. The rather sparse seismic data set was imaged using coherency migration, and the tomographic models were derived using non-linear first-arrival-traveltime tomography. The velocity field was extended towards depth by incorporating supplementary borehole and laboratory data. A more precise definition of the top of the K-horizon was achieved using borehole seismic data. The resulting images show the potential of such additional low-cost experiments for geothermal reservoir characterization. They supplement larger scale images from legacy surface seismic data and reveal more details, especially along and below the existing exploration well.
The genetic origin of the antimony deposits in the D & uacute;rico-Beir & atilde;o mining district has been studied for a long time, and this study intends to bring more knowledge to this subject. Currently, two main hypotheses are proposed for this: (1) They are genetically connected to non-outcropping granites; (2) they are connected to mafic intrusions at depth. For this study, a gravimetric campaign was performed on the entire D & uacute;rico-Beir & atilde; area. The Bouguer residual anomaly (RA) map (obtained from the removal of a regional anomaly from the complete Bouguer anomaly [CBA]) shows positive anomalies that appear associated with the Palaeozoic metasediments of the Valongo Anticline flanks, as well as some positive anomalies to the west and in the centre of the anticline. The spatial statistical analyses performed with the gravimetry values and the location of the antimony deposits show that these mineralisations are mainly associated with the positive anomalies on the CBA and the Bouguer RA. The same thing happens for the dolerite veins that outcrop in the studied area, although with some of the veins appearing on the negative anomalies. The results from this study are not enough to prove one of these two hypotheses, although we believe they will be very useful in future studies on this matter.
Seismic data reconstruction is crucial in seismic exploration, enabling cost-effective data acquisition and enhanced seismic imaging and reservoir characterization. Denoising diffusion probabilistic models (DDPMs) have emerged as powerful tools for capturing complex data distributions, demonstrating their growing popularity in recent years. However, DDPMs purely generate data distributions from the latent space with reliance on random noise, which may be suboptimal for deterministic seismic reconstruction tasks. In this work, interpretability refers to the ability to associate the diffusion variable with a physically meaningful quantity in seismic reconstruction, namely the residual related to missing information rather than a variable governed only by artificially injected Gaussian noise. In addition, the reverse process that starts from noise is inefficient for seismic data reconstruction. To address these limitations, a condition-constrained residual diffusion model (CRDM) is proposed, which incorporates residual diffusion and conditional constraints from observed data, thereby enhancing constraint-guided reconstruction stability and interpretability. CRDM employs a shallow U-Net with multi-head self-attention to increase the receptive field, thereby improving information gathering. Experimental results on seven independent synthetic and real datasets indicate that CRDM achieves competitive or superior performance relative to DDPM and several traditional and data-driven methods while requiring only a few timesteps during inference. In this work, generalization capability refers to the ability of a trained model to maintain stable reconstruction performance on independent unseen datasets that differ from the training data in geological structures, acquisition geometries, dimensionality or data domains.
ABSTRACT As a crucial method in seismic interpretation, acoustic impedance (AI) inversion is an ill‐posed inverse problem and requires regularization to obtain stable results. Total variation (TV) regularization and a series of its non‐convex variants are commonly used to recover models with piecewise‐constant characteristics, but they suffer from two key issues. First is the scale‐variant property, which prevents them from accurately separating sparsity structure from amplitude information and thus fails to preserve stratigraphic boundaries. Second, they do not consider the complex structure of the subsurface, limiting their ability to represent inclined geological structures effectively. To address these limitations, we propose a structural‐guided ratio total variation (SGRTV) regularized AI inversion method, which employs the ratio of L 1 and L 2 ( L 1 / L 2 ) norms to penalize the directional derivatives of the AI model. Specifically, the scale‐invariant L 1 / L 2 norm effectively approximates the L 0 norm to enhance sparsity and delineate stratigraphic edges. Additionally, the directional derivatives incorporate geological structural information, enhancing the geological representation capability of the inversion. To ensure the stability of the solution, we impose a box constraint on the AI model and adopt a specific optimization scheme that features a doubly nested alternating direction method of multipliers (DN‐ADMM) structure. Tests on synthetic and field data demonstrate that the proposed method can accurately recover the AI of inclined strata while preserving geological edges, showing significant improvement compared to traditional methods.
In contexts such as mineral prospecting based on gravitational and magnetic surveys, common pre-processing steps bring the data to equispaced two-dimensional (2D) grid locations. The region with data is often of a highly irregular shape and may contain internal voids. Given the power of Fourier-based data processing, a key task becomes to extend such data to become periodic over a larger 2D rectangular region, in a way that artefacts caused by the extension process become minimized. We describe here a new and computationally fast numerical technique for this task. Numerical illustrations include magnetic recordings from the McFaulds Lake area (Ontario, Canada).
ABSTRACT Accurate seismic traveltime modelling in geologically complex media is fundamental to seismic imaging and inversion. While physics‐informed neural networks (PINNs) have emerged as a promising mesh‐free alternative to traditional eikonal solvers, they often suffer from low accuracy near sharp velocity contrasts and slow convergence in complex models. In this study, we develop SARAS‐PINN, a structure‐aware and residual‐gradient‐adaptive sampling framework designed to enhance PINN‐based traveltime modelling. Our method integrates two key innovations: (1) structure‐aware initialization using elliptical exclusion zones, where axes are dynamically scaled by local velocity and directional gradients to prioritize structural features; and (2) residual‐and‐gradient‐based adaptive sampling, which leverages both the local partial differential equation residual and its spatial gradient to refine the training set iteratively. Numerical experiments on layered, Marmousi and BP models demonstrate significant improvements. In the layered model, SARAS‐PINN reduces the mean absolute error (MAE) from 0.1274 to 0.0086 ms, a 15‐fold improvement in precision. For the Marmousi model, our approach achieves a 3.6‐fold computational speedup in reaching the target MAE ( ms) compared to standard PINN. Furthermore, the inclusion of the residual gradient allows for the precise capture of sharp interfaces and salt bodies that are typically undersampled by traditional residual‐only methods (e.g., residual‐based adaptive refinement with distribution). These results confirm that SARAS‐PINN provides a robust and efficient tool for high‐precision seismic simulations.
ABSTRACT Quantifying dynamic reservoir properties, such as pressure and saturation from 4D seismic data, is crucial for improving reservoir management, increasing hydrocarbon recovery and maximizing economic returns. Although data‐driven approaches, particularly deep neural networks (DNNs), have shown promise in mapping seismic attributes to reservoir properties, they are often deterministic and lack robust uncertainty quantification. This limitation is critical in geosciences, where decisions must be made despite inherent data noise and model limitations. We propose a Bayesian Neural Network (BNN) framework to comprehensively quantify both aleatoric (data‐related) and epistemic (model‐related) uncertainty in 4D seismic inversion. Our method extends a deterministic autoencoder architecture into a probabilistic one by treating network weights as distributions. Furthermore, we leverage data from multiple repeated 4D seismic surveys, rather than a single baseline‐monitor pair, to capture spatio‐temporal trends. Synthetic validation demonstrates the model's ability to provide well‐calibrated uncertainty estimates. Application to the Schiehallion field shows that the BNN successfully estimates pressure and saturation changes, with uncertainty maps highlighting areas affected by noise, data sparsity or competing geophysical effects. The results provide reservoir engineers with critical confidence intervals for dynamic property estimates, enabling more informed and risk‐aware decision‐making.
ABSTRACT In conventional three‐dimensional gravity forward modelling, the vertical gravitational field is obtained either from closed‐form analytical expressions or by numerically solving the boundary value problem (BVP) for the gravitational potential and then applying numerical differentiation. Closed‐form solutions may exhibit singularities in certain cases, whereas traditional numerical techniques require additional computational expense to compute the first‐ or second‐order partial derivatives. To address these limitations, we introduce a forward modelling scheme that evaluates the vertical gravitational field directly from Poisson's equation, thereby establishing a formal link between the gravitational field and the spatial distribution of density. We initially employed a finite‐difference ghost‐point strategy to solve the problem under Robin boundary conditions. For efficiency, the resulting large, sparse and non‐symmetric linear system is handled with the quasi‐minimal residual (QMR) iterative solver combined with incomplete LU (ILU) preconditioning. The method's accuracy is assessed using two synthetic test cases and by comparison with closed‐form analytical results and Fourier spectral solutions. Additionally, the large‐scale modelling performance of the proposed forward algorithm is evaluated by the three‐dimensional SEG/EAGE salt dome model.
