Search Results (241)

A new fractional Brownian vector field (FBVF) is created for modeling multidimensional and multivariate fractal data. It is shown that the FBVF is a multidimensional and multivariate generalization of the classical Kolmogorov–Wiener process, allowing the distribution of field increments to be defined solely through fractal Euclidean distances between observation points. Conditions are established under which the family of field distributions satisfies the Kolmogorov consistency theorem. Maximum likelihood and variogram-based methods are developed to analytically estimate the mean and covariance of the FBVF, while the Hurst parameter is computed using an one-variable optimization algorithm. A kriging method is constructed for solving prediction problems using observations of fractal data. For computer simulation of field realizations, recursive and kriging-based algorithms are applied. A computational Monte Carlo experiment confirms the reliability of the proposed methods, particularly in accurately estimating the Hurst parameter. Applications to heavy metal concentrations in soil and climate data analysis demonstrate the effectiveness of the model in representing and analyzing multifractal, multidimensional processes. Full article

Early stage mineral exploration requires the reliable identification of anomalous gold zones from drillhole geochemistry in data-limited environments. This study applies a machine learning (ML) classification framework to detect anomalous gold zones (Au ≥ 0.68 ppm; 90th percentile) from bulk XRF multielement drillhole geochemistry in a Paleoproterozoic Birimian greenstone belt sulphide-hosted orogenic gold system, West African Craton. A total of 53,126 one-metre diamond core samples from 301 drillholes were preprocessed within a compositional data analysis (CoDA) framework, with Au being explicitly excluded from the centred log-ratio (CLR) transformation to eliminate target–predictor circularity. After Minimum Covariance Determinant (MCD) outlier filtering, 40,385 samples were retained to construct a 19-feature matrix of 10 CLR-transformed elements, 1 rock-type feature, and 8 sulphide–lithology interaction features. Drillhole-based block cross-validation (DH-block CV), validated by an experimental along-hole variogram (practical autocorrelation range ≈ 20 m), ensured spatially honest performance estimates. Four nonlinear classifiers—Random Forest (RF), XGBoost, LightGBM, and Multi-Layer Perceptron (MLP)—were benchmarked against a Logistic Regression (LR) linear baseline. All nonlinear classifiers achieved validation AUC of 0.936–0.938, outperforming LR (AUC = 0.931) with F1-score improvements of +0.09 to +0.11 and precision gains of up to +35 percentage points—directly reducing wasted drill holes in applied exploration. MLP recorded the highest F1-score (0.666) and precision (0.765), and XGBoost the highest recall (0.787). Permutation importance identified S-Ti (ΔAUC = 0.028), S-Fe (0.021), and S-Al (0.013) as the top-ranked features, confirming that sulphide enrichment relative to lithological background is the primary discriminating signal. Partial dependence analysis revealed a threshold-driven non-monotonic Fe dependence at CLR(Fe) ≈ 3, marking the transition from lithological dilutant to sulphide co-indicator—a nonlinear pattern inaccessible to linear classifiers. Full article

High-resolution spatiotemporal sea ice concentration (SIC) estimates are essential for Arctic navigation and ice analysis, but existing observational products are often too coarse, and physics-based models are computationally expensive. This study proposes a data-driven framework that couples Light Gradient Boosting Machine (LightGBM) temporal prediction with Kriging-based spatial interpolation to reconstruct SIC fields over the Northern Sea Route sector. LightGBM is trained on a grid-based SIC time series with engineered features representing persistence, seasonality, and short-term variability, enabling multi-horizon forecasting across large spatial grids. The predicted SIC fields are then refined using Ordinary Kriging (OK) and Co-Kriging (CK) with Gaussian and spherical semi-variogram models. Prediction performance is evaluated using root mean square error, and interpolation accuracy is assessed through cross-validation. Results show that, for high-latitude regions and resolutions finer than 0.25° × 0.25°, OK with a spherical semi-variogram achieves lower interpolation errors than CK and Gaussian-based alternatives. By sequentially coupling temporal learning and spatial refinement, the proposed framework improves temporal continuity, spatial structure, and error quantification, providing high-resolution SIC information suitable for large-scale Arctic ice analysis and navigation support. Full article

A geometry-aware deep learning framework for the reduction of atmospheric noise in SAR (Synthetic Aperture Radar) interferograms has been proposed and validated in this study. Our model has obvious advantages over existing ones in the following three aspects: (1) our objective is to reconstruct the original SAR imagery using an autoencoder and then eliminate noise by subtracting the reconstructed data from the raw data. However, our network architecture is not symmetric, and we choose to employ HRNet-w32 to preserve the details of the input dataset. (2) A deep supervision module equipped with diverse feature-unleashing mechanisms (including geometric, multispectral, and sematic features) is also developed to enhance the model’s predictive capability and interpretability. (3) We emphasize the significance of fractal geometry and variogram inference in the loss function, given that atmospheric disturbances, specifically humidity, clouds, and fogs, often exhibit statistically fractal characteristics. Compared with existing methods and ablation studies, our framework achieves relatively robust APS suppression performance across multiple quantitative metrics, including the Mean Squared Error (MSE), Nash–Sutcliffe Efficiency (NSE), Mean Absolute Error (MAE), Structural Similarity Index (SSIM), and Coefficient of Correlation (CoC), with improvements of at least 5.0% over the baselines. Full article

This article represents part of a broader research project aimed at developing predictive technologies for identifying prospective mineralized zones based on the analysis of data from an integrated subsurface use platform. The study presents a predictive modeling framework for lithium mineralization within the Kalba–Narym metallogenic zone using machine learning and geostatistical methods. The scientific novelty of the research lies in the integration of geochemical, radiometric, and geophysical data extracted from a cloud-based geospatial platform into a unified mineral prospectivity prediction system. Random Forest (RF), Gaussian Process Regression (GPR), and Empirical Bayesian Kriging (EBK) were applied to predict lithium concentration and analyze spatial patterns. The input data included geochemical indicators, radiometric data, magnetic anomalies, and gravity data. Prior to modeling, all datasets were harmonized into a unified spatial and numerical format. The calculated anisotropy ratio (AR) values revealed the presence of direction-dependent spatial continuity and directional asymmetry within the studied fields. At the same time, the overall similarity of variogram shapes across different directions indicates coherent and structured spatial organization rather than completely random variability. The RF model demonstrated greater effectiveness in identifying localized lithium enrichment anomalies, whereas EBK and GPR better represented regional spatial trends and continuity. The resulting prospectivity maps show spatial correspondence between elevated lithium concentrations and gravity, magnetic, and radiometric anomalies. Five prospective lithium mineralization zones were identified within the study area: East Kalba, Central Kalba, Yeser, Proletarsky, and Kovalevsky. The obtained results confirm the effectiveness of integrating machine learning and geostatistical approaches for rare-metal prospectivity mapping and may support future mineral exploration planning. Full article

Coalbed methane (CBM) is an important unconventional natural gas resource, and coal seam gas content is a key parameter for CBM resource evaluation and favorable-zone prediction. Taking the Jiulongchuan exploration area in Gansu Province as the study area, this study integrated drilling, well-logging, and measured gas content data to establish a multivariate regression model for coal seam gas content prediction. On this basis, three-dimensional geological modeling and variogram analysis were applied to characterize the spatial distribution of gas content in the main mineable coal seams (Nos. 5, 6, and 8). The results indicate that the regression model constructed using acoustic transit time, natural gamma-ray values, density logging parameters, and burial depth shows generally reasonable predictive capability for coal seam gas content. Cross-validation results suggest that the predicted gas contents are generally consistent with measured values. Spatial modeling results show that gas content in Seam No. 8 is generally higher than that in Seams No. 5 and No. 6, and gas content tends to increase with burial depth and coal seam thickness. In addition, relatively high gas contents are commonly observed along synclinal zones, whereas lower values occur near anticlinal areas. The integrated application of well-log interpretation and three-dimensional geological modeling provides a reasonable characterization of the spatial variation in coal seam gas content in the study area. The results may provide useful references for CBM resource evaluation and favorable-zone prediction in the Jiulongchuan exploration area. Full article

Cross-sectional imaging of two-phase oil–water flow in horizontal wells is essential for optimising production, yet conventional deterministic interpolation cannot adapt to varying flow regimes: Kriging smooths chaotic textures while stochastic simulation introduces spurious noise into stable flows. This paper proposes a Flow-Regime-driven Framework for Adaptive Cross-sectional Imaging (FR-FACI) that couples flow-regime identification with image reconstruction. Six physically meaningful features extracted from capacitance (CAT) and turbine (SAT) array signals feed a support vector machine (SVM) classifier that assigns each sampling window to one of three regimes: stratified (SF), stratified-froth (SFF), or froth (FR). A chaos weight derived from the calibrated classifier probability continuously blends detrended ordinary kriging with sequential Gaussian simulation, eliminating hard-switching artefacts. Experiments covering 12 operating conditions yield 95.83% classification accuracy under leave-one-condition-out validation. Variogram ranges differ by more than 26-fold across regimes, confirming the physical necessity of dual-path design. FR-FACI achieves an overall MAE of 0.105 and RMSE of 0.160, matching Kriging in stable flows while recovering chaotic textures that all single-model methods miss. Directions for future work, including uncertainty propagation, field-scale validation, and real-time monitoring integration, are discussed. Full article

“Laws” of geography such as Tobler’s First Law (spatial autocorrelation) and Zhu’s Third Law (environmental similarity) offer fundamental principles for spatial prediction and mapping, yet their implications for digital soil mapping (DSM) are often opaque because the underlying principles and mechanisms of DSM models are rarely inspectable in typical DSM workflows. This study presents an interactive geovisualization portal that demystifies Tobler’s Law, Zhu’s Law, and a combined formulation in spatial prediction processes, using soil organic matter (SOM) concentration prediction in Xuancheng, China, as a case study. The portal integrates multiple DSM frameworks that operationalize two geographic laws—inverse distance weighting (IDW), individual predictive soil mapping (iPSM), an iPSM-IDW hybrid, ordinary kriging (OK), and regression kriging (RK)—and couples them with user-configurable parameters such as neighborhood size, distance-decay factor, and variogram model. The portal provides coordinated, interactive views that link SOM predictions to dynamic map and diagnostic statistical charts for explaining location-level predictions, visualizing the manifestation of geographic laws in constructing local predictions, examining weight allocation patterns, and assessing overall prediction accuracy. Additionally, a built-in sensitivity analysis enables users to investigate and understand the effects of varying the geographic law, modeling framework, and modeling parameters on prediction results. This geovisualization portal advances interpretable DSM by rendering its underlying geographic principles, model mechanics, and parameter influences visually inspectable. Full article

Yield monitoring in forage production is typically limited to chopping or baling operations, where spatial resolution is often reduced by windrow merging. This study evaluated the feasibility of estimating mass flow rate (MFR) and generating spatial yield maps at the mowing stage using sensors integrated into a windrower. Conditioning roll speed, swath shield impact force, and the displacement of spring-loaded vanes (fingers) in the crop flow were evaluated during alfalfa harvest and calibrated against measured MFR. Model performance was assessed using cross-validation, and spatial fidelity was evaluated using experimental variograms and kriged yield maps. The average MFR was 19 kg·s⁻¹ with a range of 4 to 55 kg·s⁻¹. Conditioning roll speed provided the most robust and transferable predictor of MFR (R² = 0.89, RMSE = 3.4 kg·s⁻¹), consistently outperforming impact force (R² = 0.70, RMSE = 1.9 kg·s⁻¹) and finger displacement (R² = 0.82, RMSE = 4.3 kg·s⁻¹), which were more sensitive to machine dynamics and sensor placement. Validation of the roll-speed model using an independent dataset resulted in an R² = 0.87 and RMSE of 2.62 kg·s⁻¹. Yield maps derived from roll-speed-based models exhibited clear spatial structure with correlation lengths of approximately 25–40 m, whereas the finger displacement model exhibited higher nugget effects. Yield mapping with the forage harvester showed reduced spatial fidelity compared to mowing stage estimates, as windrow merging prior to chopping caused spatial averaging that diminished recoverable fine-scale yield variability. These results demonstrate that yield monitoring at the mowing stage enabled yield estimates to complement downstream harvest data and improve characterization of within-field yield variability. Full article

Estimating ground motion parameters at an unsampled site is challenging for seismologists and engineers alike. An attempt is made to apply Kriging interpolation to estimate peak ground accelerations at specific nuclear power plant sites. However, issues such as data quality and Kriging assumptions pose challenges to how practical and reasonable Kriging interpolation results may be in terms of estimating ground motion parameters. Peak ground acceleration data from the 2016 Gyeongju and 2017 Pohang earthquakes were taken from a local seismological agency. Peak ground acceleration, logarithms of the peak ground acceleration, and residuals between the recorded data and global and local ground motion models were used to select and derive empirical variogram models. The leave-one-out cross-validation process suggested estimating peak ground acceleration residuals from a locally developed ground motion model using an Exponential variogram model. Kriging estimates were compared to a site-specific ground motion model. These estimates appeared reasonable at one site but were significantly off at the other site. On the whole, Kriging estimates were lower than ground motion model predictions. When viewed relative to the nearest recordings, Kriging estimates appeared inconsistent across the two earthquake events. A nearest neighbor approach to computing Kriging estimates suggested a minimum of five data points but much more for modeling an empirical variogram. Results also suggest focusing on validation processes more than variogram selection. This suggests caution when applying Kriging for ground motion-related assessments in South Korea. Full article

Atmospheric refractivity governs the propagation behavior of electromagnetic waves in the lower troposphere. Accurate spatial characterization of this parameter is essential for optimizing communication, radar, and navigation systems. This study presents a geostatistical framework for generating high-resolution refractivity maps using Universal Kriging (UK) applied to meteorological observations from a dense network of automatic weather stations in the Galician region (NW Spain). The methodology explicitly models the non-stationary vertical structure of the atmosphere by decomposing the refractivity field into a deterministic altitude-dependent drift and a stochastic residual component characterized by an exponential variogram. Validation, performed using independent test stations bounding the regional vertical profile, demonstrates that the UK approach significantly outperforms Ordinary Kriging (OK). UK not only reduces mean errors and improves linear agreement, but critically minimizes systematic bias and extreme outlier occurrences ($P_{95}$). Beyond accurate spatial interpolation, the dynamically estimated vertical drift retrieves the macroscopic refractivity gradient, serving as a direct, real-time diagnostic tool to classify anomalous radio-frequency (RF) propagation regimes (e.g., super-refraction and ducting) and supporting robust decision-making in complex topographies. Full article

Accurate building roof classification from airborne LiDAR point clouds is fundamental to reliable three-dimensional (3D) urban reconstruction. While supervoxel-based methods offer efficiency and resilience to uneven point density, their performance is critically undermined by cross-boundary segmentation errors—a direct consequence of random seed initialization that merges geometrically similar yet semantically distinct objects. To address this root cause, this study proposes Interior-Anchored Mean-Shift (IAMS), a novel supervoxel segmentation framework that rethinks seed placement as a geometry-aware interior localization problem. By integrating local geometric consistency point density, and spatial correlation into a unified kernel density estimator, supplemented by density-adaptive voxel weighting and a semi-variogram-driven bandwidth, IAMS reliably anchors seeds within object interiors, yielding highly homogeneous supervoxels without post-processing. Extensive experiments on three diverse airborne LiDAR datasets demonstrated that IAMS consistently outperformed state-of-the-art baselines. On the International Society for Photogrammetry and Remote Sensing (ISPRS) Vaihingen benchmark, our approach improved roof classification completeness, correctness, and quality by up to 7.1% (per-object) over the conventional Voxel Cloud Connectivity Segmentation (VCCS) algorithm while being significantly faster than recent boundary-preserving alternatives. Critically, IAMS maintains robust performance under challenging conditions, including sparse sampling and dense vegetation occlusion, making it a practical solution for real-world urban remote sensing. Full article

Urban air quality assessment increasingly relies on spatial interpolation to complement fixed monitoring networks; however, the reliability of geostatistical methods depends strongly on temporal conditions and pollutant characteristics. Despite extensive application, limited attention has been paid to how kriging performance varies across hours of the day and months of the year, particularly when contrasting primary pollutants driven by local emissions with secondary pollutants formed through atmospheric chemistry. This study evaluates the temporal sensitivity of Ordinary Kriging (OK) for mapping urban air pollutants in the Mexico City Metropolitan Area. Using hourly observations from the official air quality monitoring network (2021), we analyze ozone (O₃), a secondary pollutant, and sulfur dioxide (SO₂), a primary pollutant, under representative diurnal and monthly scenarios. Variogram model selection and predictive performance are assessed through leave-one-out cross-validation and external hold-out validation across multiple temporal blocks and months. Results indicate that kriging performance is highly sensitive to both hour of day and month. For O₃, smoother Gaussian variogram structures perform best during peak photochemical conditions, producing coherent regional concentration fields with gradual spatial gradients. In contrast, SO₂ exhibits stronger local variability and sharper spatial gradients, favoring exponential variogram models, particularly under stable morning atmospheric conditions associated with primary emission accumulation. Sensitivity analyses further reveal that no single variogram model is universally optimal and that interpolation accuracy depends more on temporal stratification and pollutant behavior than on variogram form alone. These findings demonstrate that geostatistical interpolation is a valuable tool for urban air quality assessment only when temporal sensitivity and pollutant-specific dynamics are explicitly incorporated. The proposed framework provides practical guidance for the responsible use of interpolated air quality maps, supports sustainable urban monitoring strategies, and contributes to more reliable exposure assessment in megacities with limited sensor coverage. Full article

When snow is present, the snow surface is the interface between the atmosphere and the Earth’s surface. The snowpack energy balance is dictated in part by snow surface roughness, which can be quite dynamic. At the Sierra Nevada ski resort in Spain, we measured several snow surface forms: natural, with the presence of dust, with the presence of sun cups, and groomed snow (tracked and between tracks). The snow surface was assessed in 2-dimensions from snow roughness boards and in 3-dimensions from iPad surface scanning to measure across resolutions. Both data collection methods yielded similar roughness estimates via random roughness (RR) and variogram analysis (scale break, SB, and fractal dimension, D) for each distinct surface, yet the roughness differences between the surfaces were substantial. The geometry-based aerodynamic roughness length ($z_0$) was computed for the iPad-scanned surfaces, yielding an order-of-magnitude variability in $z_0$. This produced an order-of-magnitude difference in modelled sublimation. This work can inform snow management at ski areas and reflects some of the snow-surface conditions encountered in a natural snowpack. Full article

In many environmental applications, high-quality measurements are too sparse to resolve the small-scale patterns required for process understanding and management. We investigate a Bayesian kriging (BK) framework that densifies sparse coastal observations into high-resolution gridded fields with calibrated uncertainty. Two pilot sites are considered: (i) sea surface temperature (SST) in the Algarve (Portugal), where point measurements (~10 km spacing) are reconstructed on a 500 m grid, and (ii) chlorophyll (Chl) in the La Spezia embayment (Italy), where in situ supported fields are reconstructed at 30 m. The variogram parameters are treated as random variables with weakly informative priors and inferred via MCMC, so that both measurement noise and structural (variogram) uncertainty are propagated to predictions, yielding posterior means and 95% prediction intervals per grid cell. Independent repeated 80/20 cross validation demonstrates robust out-of-sample skill in both sites. For Algarve, the BK maps recover fine-scale thermal structure while preserving defensible uncertainty under severe sparsity. For La Spezia, the same framework resolves estuarine gradients at 30 m. Credible intervals widen away from observations yet remain sufficiently narrow elsewhere to guide interpretation. Satellite products are used strictly for validation on a common grid (MUR SST at 1 km resampled to 500 m, Landsat OC3 Chl at 30 m), confirming spatial fidelity and clarifying seasonal differences. Overall, the approach produces uncertainty-aware, high-resolution coastal fields from heterogeneous, sparse records, supporting reproducible EO analyses and risk-aware coastal monitoring. Full article