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The construction of a high-precision geomagnetic map is a prerequisite for geomagnetic navigation and magnetic target-detection technology. The Kriging interpolation algorithm makes use of the variogram to perform linear unbiased and optimal estimation of unknown sample points. It has strong spatial autocorrelation and is one of the important methods for geomagnetic map construction. However, in a region with a complex geomagnetic field, the sparse geomagnetic survey lines make the ratio of line-spacing resolution to in-line resolution larger, and the survey line direction differs from the geomagnetic trend, which leads to a serious effect of geometric anisotropy and thus, reduces the interpolation accuracy of the geomagnetic maps. Therefore, this paper focuses on the problem of geometric anisotropy in the process of constructing a geomagnetic map with sparse data, analyzes the influence of sparse data on geometric anisotropy, deduces the formula of geometric anisotropy correction, and proposes a modified interpolation algorithm accounting for geometric anisotropy correction of variogram for sparse geomagnetic data. The results of several sets of simulations and measured data show that the proposed method has higher interpolation accuracy than the conventional spherical variogram model in a region where the geomagnetic anomaly gradient changes sharply, which provides an effective way to build a high-precision magnetic map of the complex geomagnetic field under the condition of sparse survey lines.

In seismic exploration, establishing a reliable parameter model (such as velocity, density, impedance) is crucial for seismic migration imaging and reservoir characterization. The interpolation of well data to obtain a complete spatial model is an important aspect of parameter modeling. However, in practical applications, well data are often sparse and irregularly distributed, which complicates the accurate construction of subsurface parameter models. The Kriging method is an effective interpolation method based on discrete well data, but its theoretical assumptions do not meet the practical requirements in seismic exploration, resulting in low modeling accuracy. This article introduces seismic facies information into the Kriging method and proposes a novel parameter modeling method named the facies-constrained Kriging (FC-Kriging) method. The FC-Kriging method modifies the Euclidean distance metric used in Kriging so that the distance between two points depends not only on their spatial coordinates but also on their associated facies categories. The proposed method is a multi-information fusion method that integrates facies information based on well data, enabling good interpolation results even with a limited number of wells. The parameter modeling results based on the FC-Kriging method are more consistent with geological logic, exhibiting clearer boundary features and higher resolution. Furthermore, the FC-Kriging method does not introduce additional computational complexity, making it convenient to implement in a 3D situation. The FC-Kriging method is applied to the 2D Sigsbee model, the 3D Standford V reservoir model and F3 block field data. The results demonstrate its accuracy and effectiveness.

A detailed analysis of natural frequencies of laminated composite plates using the meshfree moving Kriging interpolation method is presented. The present formulation is based on the classical plate theory while the moving Kriging interpolation satisfying the delta property is employed to construct the shape functions. Since the advantage of the interpolation functions, the method is more convenient and no special techniques are needed in enforcing the essential boundary conditions. Numerical examples with different shapes of plates are presented and the achieved results are compared with reference solutions available in the literature. Several aspects of the model involving relevant parameters, fiber orientations, lay-up number, length-to-length, stiffness ratios, etc. affected on frequency are analyzed numerically in details. The convergence of the method on the natural frequency is also given. As a consequence, the applicability and the effectiveness of the present method for accurately computing natural frequencies of generally shaped laminates are demonstrated.

The geoid is the equipotential surface of the Earth's gravity field that best approximates mean sea level. In many applications of geomatics the availability of a geoid model is fundamental as it allows to transform the ellipsoidal heights provided by the GNSS (Global Navigation Satellite System) survey into orthometric heights, i.e. referred to the mean sea level. There are global-scale geoid models, while others exist on a regional scale and are more accurate than the former. Global geoids are generally obtained from measurements of the terrestrial geopotential carried out from space, appropriately integrated with data obtained in situ. This article focuses on the possibility of improving the accuracy of the global model GOCO06s (GOCO is the acronym of Gravity Observation Combination) in a local area, Sardinia Island (Italy), through two operations carried out in Geographic Information System (GIS) and based on the comparison with the local model (at national scale) ITALGEO2005: the removal of the bias found between the two (global and local) models, and the application of the Ordinary Kriging interpolator on the residuals that still remain between the two surfaces compared. The first operation determines a considerable improvement, demonstrated by the RMS value dropping from 1.000 m to 0.365 m. The second operation further increases the accuracy of the model since, with the use of 60 Ground Control Points, an RMS equal to 0.140 m is reached.

Aim: Many taxa, especially invertebrates, remain biogeographically highly understudied and even baseline assessments are missing, with too limited and heterogeneous sampling being key reasons. Here we set out to assess the human geographic and associated environmental factors behind inventory completeness for the hawkmoths of Africa. We aim to separate the causes of differential sampling from those affecting gradients of species richness to illustrate a potential general avenue for advancing knowledge about diversity in understudied groups. Location: Sub-Saharan Africa. Methods: Using a database of distributional records of hawkmoths, we computed rarefaction curves and estimated total species richness across 200 km × 200 km grid cells. We fitted multivariate models to identify environmental predictors of species richness and used environmental co-kriging to map region-wide diversity patterns. We estimated cell-wide inventory completeness from observed and estimated data, and related these to human geographic factors. Results: Observed patterns of hawkmoths species richness are strongly determined by the number of available records in grid cells. Both show spatially structured distributions. Variables describing vegetation type, emerge as important predictors of estimated total richness, and variables capturing heat, energy availability and topographic heterogeneity all show a strong positive relationship. Patterns of interpolated richness identify three centres of diversity: Cameroon coastal mountains, and the northern and southern East African montane areas. Inventory completeness is positively influenced by population density, accessibility, protected areas and colonial history. Species richness is still under-recorded in the western Congo Basin and southern Tanzania/Mozambique. Main conclusions: Sampling effort is highly biased and controlling for it in large-scale compilations of presence-only data is critical for drawing inferences from our still limited knowledge of invertebrate distributions. Our study shows that a baseline of estimate of broad-scale diversity patterns in understudied taxa can be derived from combining numerical estimators of richness, models of main environmental effects and spatial interpolation. Inventory completeness can be partly predicted from human geographic features and such models may offer fruitful guidance for prioritization of future sampling to further refine and validate estimated patterns of species richness.

In view of the urgent need for high coverage and high-resolution atmospheric CO2 data in the study of carbon neutralization and global CO2 change research, this study combines the Kriging interpolation and the Triple Collision (TC) algorithm to fuse three XCO2 datasets, OCO-2, GOSAT, and CarbonTracker, to obtain a 1° × 1° half-monthly average XCO2 dataset. Through a sub division of the Kriging interpolation, the average coverages of the OCO-2 and GOSAT XCO2 interpolating datasets are increased by 53.65% and 48.5%, respectively. In order to evaluate the accuracy of the TC fusion dataset, this study used a reliable reference dataset, TCCON data, as the verification data. Through comparative analysis, the MAE of the fusion dataset is 0.6273 ppm, RMSE is 0.7683 ppm, and R2 is 0.8279. It can be seen that the combination of Kriging interpolation and TC algorithm can effectively improve the coverage and accuracy of the XCO2 dataset.

In order to determine the distribution area and amount of Artemisia annua Linn. (A. annua) in China, this study estimated the current amount of A. annua specimens based on the field survey sample data obtained from the Fourth National Census of Chinese Medicinal Resources. The amount was calculated using the maximum entropy model (MaxEnt model) and spatio-temporal kriging interpolation. The influencing factors affecting spatial variations in the amount were studied using geographic probes. The results indicated that the amount of A. annua in China was about 700 billion in 2019. A. annua was mainly distributed in the circular coastal belt of Shandong Peninsula, central Hebei, Tianjin, western Liaoning, and along the Yangtze River and in the middle and lower reaches of Jiangsu, Anhui, and the northern Chongqing provinces. The main factors affecting the amount are the precipitation in the wettest and the warmest seasons, the average annual precipitation, and the average temperature in the coldest and the driest seasons. The results show that the amount of A. annua is strongly influenced by precipitation and temperature.

With the rapid development of economy, the process of urbanization in China has become more and more rapid, and the municipal solid waste (MSW) generation has also increased year by year. The MSW generation prediction is an important prerequisite for MSW management. Considering the uncertainty of MSW generation and the unbalanced economic development in different districts, first, the fuzzy information granulation (FIG) method is used to granulate and predict the three explanatory variables (annual disposable income per capita, GDP and total retail sales of consumer goods) in different districts. Second, the prediction results are substituted into the support vector regression model optimized by genetic algorithm (GA-SVR) to predict the MSW generation per capita. Then, ARIMA model is applied to predict population of each community. After that, the predicted MSW generation per capita is combined with the predicted population of each community to obtain the MSW generation distribution. Finally, the Kriging interpolation method is used to present the MSW generation distribution. The MSW generation distribution prediction in Huangshi, a city of Hubei province in China, is chosen as the case to test the feasibility and effect of the model. The prediction results of Huangshi presented as interval value suggest that the accuracy of MSW distribution prediction can meet the identification requirements of MSW management system. Therefore, the FIG–GA-SVR prediction model proposed in this paper is suitable for interval prediction and has good generalization ability. This model can not only be applied to the prediction of MSW generation, but also can be applied for prediction in other fields.

The accurate prediction of static formation temperature (SFT) is essential for ensuring safety and efficiency in ultra-deep well drilling operations. Excessive downhole temperatures (>150 °C) can degrade drilling fluids, damage temperature-sensitive tools, and pose serious operational risks. Conventional methods for SFT determination—including direct measurement, temperature recovery inversion, and artificial intelligence models—are often limited by post-drilling data dependency, insufficient spatial resolution, high computational costs, or a lack of adaptability to complex wellbore geometries. In this study, we propose a new pseudo-3D Kriging interpolation framework that explicitly incorporates real wellbore trajectories to improve the spatial accuracy and applicability of pre-drilling SFT predictions. By systematically optimizing key hyperparameters (θ = [10, 10], lob = [0.1, 0.1], upb = [20, 200]) and applying a grid resolution of 100 × 100, the model demonstrates high predictive fidelity. Validation using over 5.1 million temperature data points from 113 wells in the Shunbei Oilfield reveals a relative error consistently below 5% and spatial interpolation deviations within 5 °C. The proposed approach enables high-resolution, trajectory-integrated SFT forecasting before drilling with practical computational requirements, thereby supporting proactive thermal risk mitigation and significantly enhancing operational decision-making on ultra-deep wells.

Groundwater is a crucial natural resource in the state of Florida. since it supports to environmental, social, and economic aspects of the country. Groundwater will not be contaminated easily but it is difficult to restore once it is contaminated. Since its extensive usage in agricultural activities in the state of Florida, groundwater has degraded in recent years, resulting in many direct and indirect impacts, particularly nitrogen content in the form of nitrates using Geographical Information System (GIS) technology, the researchers investigated the effects of groundwater on Nitrogen (NO3) content in the study area by creating a spatial distribution of NO3 contamination, which was then analyzed using GIS, Kriging Interpolation, and the DRASTIC model to determine the susceptibility of groundwater to NO3 contamination. The final result depicts the model’s performance as vulnerability groups, which are based on natural breaks showing places that are more susceptible to nitrogen pollution. The map highlighted that the south zone of Florida was more vulnerable to nitrogen contamination, necessitating more careful wastewater disposal system planning.