Search Results (245)

Rockfalls are natural slope-instability phenomena that pose a significant hazard to infrastructure and human activity. In recent years, the increasing availability of high-resolution three-dimensional (3D) models acquired through photogrammetric techniques has enabled detailed pre-/post-event analyses of rock slopes. However, in this domain, the availability of accurate ground truth for the quantitative evaluation of 3D change detection methods and for training machine-learning approaches aimed at recognising and volumetrically quantifying detachments on rock faces remains very limited. This work presents a simulator that, starting from a 3D model of a rock face, generates pre-/post-failure scenarios through controlled removal of rock blocks and produces photogrammetric acquisitions affected by realistic measurement noise. The pipeline emulates the main processing stages of the reconstruction workflow. Noise realism is validated and calibrated by comparing real and simulated data through a multi-indicator framework (marginal distribution, variogram, power spectrum, and multiscale roughness), integrated into a Mahalanobis-distance-based acceptance test with empirical thresholds derived from real measurements. Results from two pilot sites show that, after site-specific tuning of the simulator noise levels, the calibrated configurations reproduce the main magnitude and spatial-structure characteristics of the real noise, with stronger agreement for the fixed stereo-pair configuration and partial but still informative agreement for the more complex UAV-based case. Moreover, the simulator provides a controlled environment for benchmarking and sensitivity analyses of change detection methods. Full article

When comparing soil water sensors installed in close proximity, observed differences in readings may reflect spatial heterogeneity in soil hydraulic properties, intrinsic sensor variability, or both. Partitioning sources of variability is essential for informed sensor selection and placement. This study used variogram analysis to quantify small-scale (9 m) soil water variability at three irrigated corn sites in southeastern North Dakota during the 2022 and 2023 growing seasons. Volumetric water content (θ_v) was measured along transects parallel and perpendicular to the crop rows using an Acclima TDR-310H sensor and contrasted with previously deployed sets of different types of soil water sensors. Descriptive statistics of the collected θ_v data revealed variability within transects, with mean θ_v ranging from 0.19 to 0.24 cm³ cm⁻³. Directional variograms showed anisotropic spatial structures, where perpendicular transects exhibited a higher nugget effect than parallel transects (square roots of nugget 0.019–0.030 cm³ cm⁻³ vs. 0.012–0.022 cm³ cm⁻³, respectively), likely due to stem flow patterns along corn rows. Similarly, sill and range parameters were also higher for perpendicular than for parallel transects. Comparison of variogram-derived variances with sensor-to-sensor differences indicated that the observed variability arises from both spatial heterogeneity and sensor type. For sensor comparison studies, these results demonstrate that sensors installed parallel to crop rows are less affected by spatial variability compared with sensors installed perpendicular to crop rows and that such installation minimizes confounding factors of spatial heterogeneities, while demonstrating the broader use of variogram analysis for partitioning measurement variability. Full article

Ammonium nitrogen (NH₄⁺-N) contamination in groundwater beneath chemical industrial parks exhibits extreme spatial heterogeneity, yet the comparative effectiveness of spatial prediction methods under such conditions remains poorly understood. At a chemical industrial park in a region of Shanxi Province, northern China, we analyzed 133 monitoring wells sampled across four campaigns (April–October 2024) at two aquifer depths. Global Moran’s I (0.040–0.118) and variogram nugget ratios (>75%) indicated weak spatial autocorrelation. Consequently, on the raw concentration scale, all six geostatistical methods yielded near-zero or negative leave-one-out cross-validation (LOO-CV) R². Evaluated on the log₁₀ scale, machine learning (ML) models achieved positive predictive skills, with Extreme Gradient Boosting (XGBoost) performing best (R² ≈ 0.75). Three hybrid ML–kriging methods produced physically coherent plume surfaces while retaining their predictive skills; the April upper-layer result (R² ≈ 0.67)—the only campaign without retained within-well information—best represents spatial generalization, whereas the higher later-campaign values (R² > 0.97) are optimistic. Exceedance probability mapping based on XGBoost (area under the ROC curve, AUC = 0.959) revealed a persistent high-risk zone. Because the geostatistical and ML metrics span different response scales and validation schemes, their comparison is indicative rather than a direct ranking. Spatial autocorrelation diagnostics should precede method selection at point-source-dominated industrial sites. Full article

Evaluating joint predictive performance for multivariate hydroclimatic models requires metrics that simultaneously assess marginal accuracy and cross-variable dependence recovery. Existing metricsthe Energy Score, Variogram Score, and their derivativesdo not adapt to the structural complexity of the residual correlation matrix, treating a single correlated pair identically to a fully dense dependence structure. We propose two novel metric families: Metric E (E-CVWMD: Enhanced Coefficient-of-Variation Weighted Marginal-Dependence) and Metric E2 (E-CVWMD-Pairwise), which are designed for mixed-type multivariate responses combining continuous and binary outcomes within a cross-validation framework. We position Metrics E and E2 as diagnostic ranking tools for comparing competing models rather than as strictly proper scoring rules, and we provide a strictly proper Log-Loss variant (E-LL/E2-LL) for applications that require the full properness guarantee. Metric E assigns variable-level weights proportional to the coefficient of variation (CV) of each outcome on the training partition and adaptively calibrates the marginal-dependence trade-off parameter ${\alpha }^{\ast }$ via a global distance-correlation test. Metric E2 refines this by replacing the global test with a pairwise Spearman screening index $\widehat{\pi }$, the proportion of variable pairs with significant residual correlationwhich maps linearly to ${\alpha }^{\ast }\left(\widehat{\pi }\right)=1-\widehat{\pi }/2\in [0.5,1]$. Applied to the validation of a Generalized Multivariate Functional Additive Mixed Model (GMFAMM) on 62 Valle del Cauca meteorological stations ($N_{\mathrm{test}}\approx$ 31,663), the naive significance-based index saturates ($\widehat{\pi }=1.0$) at this large sample sizeevery pair, including correlations as small as $|{\widehat{\rho }}_s| \approx 0.01$, is flagged “significant”which is precisely the sample-size sensitivity we address. Under the effect-size screening ($|{\widehat{\rho }}_s| \ge 0.05$), three negligibly correlated pairs are excluded, yielding $\widehat{\pi }=0.70$ and ${\alpha }_{E2}^{\ast }=0.65$, a better-calibrated weight than Metric E’s ${\alpha }_E^{\ast }\approx 0.797$ under the same data. A large-scale simulation study with 37,440 model evaluations confirms that Metric E inverts the correct ranking at correlation levels $\rho \ge 0.40$ (CDR = 0%), while E2 maintains correct discrimination in 14 of 15 simulation conditions (M1 vs. M3). We also delimit the metrics’ scope: E2 degrades under near-saturated uniform dependencea regime in which the strictly proper Energy Score remains preferableand the pairwise index is sensitive to sample size, for which we provide an effect-size-based variant. An R package (mvmetrics v0.2.0) implementing both metrics, the Log-Loss variant, alternative weighting schemes, and the effect-size screening is publicly available. Full article

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