Geostatistical Methods Research Articles

GeosPIn: A MATLAB library for geostatistical petrophysical inversion

The petrophysical inversion of seismic data is one of the key components of seismic reservoir characterization. The goal of petrophysical inversion is to estimate the petrophysical properties of reservoir rocks, such as porosity, volumes of minerals or lithologies, and water and hydrocarbon saturations, from seismic data. This process can be performed by combining seismic amplitude-variation-with-offset (AVO) modeling and rock-physics relations with deterministic or probabilistic inverse theory methods, either in a two-step approach based on seismic AVO inversion and rock-physics inverse mapping or in a single-loop step that includes both. We present a comprehensive MATLAB library named Geostatistical Petrophysical Inversion. The novelty of the library lies in a single-loop geostatistical inversion method based on probability field simulation and ensemble smoother multiple data assimilation, as well as its implementation for applications to 3D data sets. The library also includes a Bayesian petrophysical inversion based on the two-step approach for comparison. We illustrate the main algorithms, explain the structure of the source codes, and demonstrate the library applications through 1D and 3D examples.

Machine learning and genetic algorithm for mapping soil available phosphorus in coastal provinces in Southeast China

Soil available phosphorus (SAP) is a crucial nutrient for sustaining plant growth, and accurate prediction of its spatial distribution is vital for agricultural production and environmental management. Here, we comprehensively integrate multiple environmental variables impacting the phosphorus cycle, including climate, remote sensing imagery, vegetation indices, topography, and anthropogenic factors. Employing two geostatistical methods, three machine learning algorithms, and incorporating genetic algorithm (GA), the research aims to precisely forecast SAP content and generate spatial distribution maps. The GA successfully identifies the optimal indices of environmental variables, comprising Band3, Brightness Index, land use type, distance to water, and mean annual precipitation. In performance evaluation, the combination of GA with Gradient Boosting Decision Tree exhibits the best results (R2 = 0.60, MAE = 2.79, RMSE = 3.64). High-value SAP areas are predominantly located in the western region, demonstrating a correlation with land use patterns. Validating the model’s applicability in coastal provinces in Southeast China, covering Fujian, Zhejiang, and Guangdong, underscores the profound insights of this study into the dynamics and geographical correlations of SAP. Our findings demonstrate that GA exhibit outstanding stability and performance in mapping SAP, contributing to a better understanding of SAP dynamics, supporting improved soil management practices and sustainable agriculture.

Gold content determination in small core-samples by instrumental neutron activation analysis

Application of instrumental neutron activation analysis (INAA) based on the relative method of concentration standardization was considered to determine Au content in small solid core-samples of the gold-bearing ores and rocks up to 10 g of the mass. The small core-samples about 10 mm in diameter and 22-23 mm in length were cut from the previously collected ore lumps or in-situ using a handheld drilling rig. The studied small core-samples and the polyethylene capsules of the same dimensions filled up with the corresponding certified reference material (CRM) were irradiated for 2 min by a lower density neutron flux with the help of the automated pneumatic transport system (PTS). Maximum mass and dimensions of the core-samples corresponded to the PTS design and to the conditions of its safe operation. A special device was made to fix the transport capsules in the stable counting geometry making possible to eliminate the influence of the neutron flux gradient during irradiation. Due to the substantial differences in CRM and solid sample densities, corrections for neutron self-shielding and for gamma-ray self-absorption by the core-samples were applied. The method was tried to analyze Au content in 170 small core-samples presenting different gold-bearing ores and country rocks from the Kazakhstan’s gold-barite-polymetallic deposit Maikain. This approach, rather simple methodically and requiring no unique equipment, can be used to assess gold resources together with the methods of geostatistics.

Prediction of geothermal temperature field by multi-attribute neural network

Hot dry rock (HDR) resources are gaining increasing attention as a significant renewable resource due to their low carbon footprint and stable nature. When assessing the potential of a conventional geothermal resource, a temperature field distribution is a crucial factor. However, the available geostatistical and numerical simulations methods are often influenced by data coverage and human factors. In this study, the Convolution Block Attention Module (CBAM) and Bottleneck Architecture were integrated into UNet (CBAM-B-UNet) for simulating the geothermal temperature field. The proposed CBAM-B-UNet takes in a geological model containing parameters such as density, thermal conductivity, and specific heat capacity as input, and it simulates the temperature field by dynamically blending these multiple parameters through the neural network. The bottleneck architectures and CBAM can reduce the computational cost while ensuring accuracy in the simulation. The CBAM-B-UNet was trained using thousands of geological models with various real structures and their corresponding temperature fields. The method’s applicability was verified by employing a complex geological model of hot dry rock. In the final analysis, the simulated temperature field results are compared with the theoretical steady-state crustal ground temperature model of Gonghe Basin. The results indicated a small error between them, further validating the method's superiority. During the temperature field simulation, the thermal evolution law of a symmetrical cooling front formed by low thermal conductivity and high specific heat capacity in the center of the fault zone and on both sides of granite was revealed. The temperature gradually decreases from the center towards the edges.

Spatial analysis and mapping of intensity and types of agricultural salt-affected soils around Abaya and Chamo Lakes, South Ethiopia Rift Valley

PurposeSalt-affected soils have significant enough salt concentrations to impact other land and soil resource uses, plant health, soil characteristics, and water quality. Consequently, a study was carried out in the South Ethiopian Rift Valley area around the lakes of Abaya and Chamo to determine the intensity and the types of salt-affected soil and map their spatial distributions. MethodsAt 0–20 cm depths, a grid soil sampling scheme was employed to gather data from agricultural soils affected by salt. An adequately spaced grid cell of 200 m*200 m or seven transects, with seven samples collected every 200 m on each sampling site, was generated by the QGIS software's Fishnet tool, and an auger collected 226 soil samples from the proposed 245 soil sampling points. The analysis and interpretation of the data were done using both statistical and geostatistical methods. The un-sampled surface was predicted and mapped from laboratory point data using the standard Kriging algorithm in QGIS. ResultsAccording to the results, the soil in the study area was rated as strongly alkaline and moderately alkaline in the reaction. The coefficient of variation (CV) was the lowest for soil pH. Except for the Ganta Kanchama site, low CV (<10 %) confirmed the similarity of pH values throughout all research areas. The EC values depicted that the study area is slightly saline except for the Ganta Kanchame site, which rated moderately saline to strongly saline. The variability of soil EC rated moderate to strong variation for the studied area. The exchangeable sodium percentage (ESP) values distribution between the study sites demonstrates considerable variability and difference. The area is dominated by low to high-risk rate soil sodicity, as evidenced by the soil ESP CV of the studied area, which was >100 % and showed significant variability among the samples. Out of 2274.65ha of the studied area, the type of salt 62.28 %, 26.09 %, 10.99 %, and 0.63 % were categorized as non-saline non-sodic, saline-sodic, sodic, and saline, respectively. Following saline-sodic, sodic, and saline soils, respectively, non-saline and non-sodic soils comprise most of the investigated areas. ConclusionsThe result indicates almost all the salt-affected areas were situated in relatively lower slope areas exhibiting a flat to almost flat slope (0–2%). The study's findings are that the studied area needs specific soil management strategies to boost the salinity and sodicity problems around the study area and recommended reclamation techniques as the extent of the problems.

On the extension and deflection of bayhead river-mouth shoal within a tide-dominated embayment, pearl river estuary

Based on chart data from the 1900s to the 2020s, it is evident that the western bayhead river-mouth shoal in Lingding Bay, Pearl River Estuary, has extended and deflected. This study uses geostatistical methods and numerical simulation experiments to investigate the dynamics of western river-mouth shoals in tide-dominated estuarine embayments. The results show that these shoals extend and deflect between two channels in a clockwise pattern, with their eastward expansion constrained by the adjacent channel. The semi-variogram and anisotropic model effectively describe changes in shoal orientation. Based on numerical experiments, we found that tides contribute to eastward lateral residual sediment transport and deposition, which is the primary sedimentary process for river-mouth shoal extension. Moreover, residual sediment transport at nearby channels or troughs induces this clockwise deflection of river-mouth shoals, with secondary effects from Coriolis forces. Future studies should consider three-dimensional processes to better understand sedimentary processes under intensive human activities in Lingding Bay, Pearl River Estuary.

Prediction Model of Groundwater Sulphate Based on Combined Multi-source Spatio-temporal Data

The accurate prediction of spatial variation trends in groundwater SO42- is of great significance for improving groundwater quality and regional groundwater management level. The multi-source spatio-temporal data such as land cover data, soil parameter data, digital elevation data, and groundwater pH value in the plain area of the Yarkant River Basin in 2011, 2014, 2017, and 2020 were used as characteristic variables to analyze their correlation with groundwater SO42- concentration. To enhance the prediction accuracy, the Bayesian optimization algorithm (BOA) was used to optimize the random forest regression (RFR). Based on the BOA-RFR model, the importance of the characteristic variables was analyzed, the prediction accuracy of the model was evaluated, and the groundwater SO42- prediction map was generated. The results showed that pH value, ground elevation (GE), and percentage of bare land (BAR) in the contribution area were important parameters influencing groundwater hydrochemical composition, which were significantly negatively correlated with groundwater SO42- concentration, and the importance of impact factors for predicting groundwater SO42- concentration exceeded 25 %. The geostatistical interpolation method was used as an auxiliary tool for the predictive modeling of spatial distribution. After adding auxiliary samples, the R2 of groundwater SO42- concentration prediction of the BOA-RFR model was greater than 0.96, and the maximum values of RMSE and MAE were reduced by 4.7 % and 23.8 %, respectively, compared with the minimum values of the model with fewer samples. The SO42- concentration prediction map showed that high SO42- groundwater was enriched in the northeast of the plain area of the Yarkand River Basin, an area that was expanding.

The Interconnection between Climate Cycles and Geohazards in Urban Areas of the Tourist Island of Mallorca, Spain

The island of Mallorca has experienced major interventions and transformations of the territory, with unprecedented urban development related to growing tourism activity. In this paper, we present a spatio-temporal analysis—by using spectral analysis techniques—of climate cycles on the island of Mallorca (Spain) and their correlation with the occurrences of landslides and flash floods. Both geohazards are closely related to wet periods, which are controlled by different, well-known natural cycles: ENSO, the NAO, sunspot, etc. Geostatistical methods are used to map the distribution of rainfall, as well as a spatial representation of the spectral confidence of the different natural cycles, to define the hazardous areas on the island. The cycles with the greatest influence on rainfall in Mallorca are El Niño–Southern Oscillation (ENSO) (5.6 y and 3.5 y), the North Atlantic Oscillation (NAO) (7.5 y), and Quasi-Biennial Oscillation (QBO). Recorded events of both rockfalls and flash floods exhibit a strong correlation with the climate indices of QBO, ENSO, the NAO, and sunspot activity. This correlation is particularly pronounced with QBO, as this cycle has a higher frequency than the others, and QBO is observed as part of the other cycles in the form of increases and decreases during periods of higher ENSO, NAO, and sunspot values. However, the impact of flash floods is also significant in the southeast part of the island, despite its lower levels of rainfall. The most dangerous episodes are related to ENSO (6.4 y) and the NAO. The validation of the methodology employed is strengthened by incorporating information from the flash flood data, as it offers comprehensive coverage of the entire island, compared to the landslide database, which is confined to the Serra de Tramuntana region. The study reveals that the city of Palma and the municipality of Calvià, as well as the central and eastern urban areas of the island, are the most vulnerable regions to intense rainfall and its consequences.

Groundwater quality evaluation for drinking and agricultural purposes. A case study in semi-arid region (Zab El-gharbi SE-Algeria)

The current research delved into the geochemical attributes of groundwater and assessed compliance with drinking water standards. 35 samples of Zab El Gharbi region groundwater in the province of Biskra were analyzed to evaluate the physico-chemical quality. The obtained results were compared to World Health Organization drinking water standards as well as Algerian Standards. It appears that nitrate concentrations in all samples were acceptable since they were less than 50 mg/L. The results of the WQI classification showed that WQI values ranged from 95 to 269; only 3 % of samples had good quality, 80 % had poor quality, and 17.14 % had very poor water, indicating the need for treatment before use for human consumption. Two main hydrochemical facies were dominated and predominated, Ca-SO4 type and Mixed Ca–Mg–Cl-SO4 type, respectively. Q mode hierarchical cluster analysis (HCA) was employed for partitioning the water samples into hydrochemical facies, revealed the presence of two distinct water types based on principal ion concentrations. Hydrochemically, group 1 was characterized by two primary facies, with 90.32 % categorized as Ca-SO4 type and 9.67 % as Mixed Ca-Mg-Cl-SO4 type. While group 2 was characterized by a Ca-SO4 type. The estimated values of sodium adsorption ratio (SAR), percent sodium (Na%), permeability index (PI), Kelly's ratio (KR) and Magnesium hazard (MH), averages for the study area is reported to be in the range of 0.90 to 5.60, 4.46 % to 41.26 %, 12.50 % to 44.47 %, 0.10 to 0.73 % and 9.69 % to 75.06 % respectively. Parameters such as Permeability Index (PI), Kelly's Ratio (KR), and Magnesium Hazard (MH) indicated that 37.14 % of groundwater samples were in the excellent category, while the remaining 62.85 % were in the good category, making them suitable for irrigation across various soil types. They indicated that the considered water exhibits favorable characteristics for agricultural irrigation applications, ranging from excellent to good. These findings are encouraging for agriculture and land-use planning. This study lies in addressing the water quality in this promontory area, where no prior research has been published. We assessed water quality using statistical, geostatistical, and cartographic methods to estimate quality in unsampled areas. Additionally, we examined how climatic conditions, particularly high evapotranspiration during the festive season, affect water and soil quality. This study will help farmers and scientists in the region make informed decisions to protect natural resources. This work is meant to highlight the issues and also provide practical solutions to optimize the management of natural resources.

Spatial prediction of plant invasion using a hybrid of machine learning and geostatistical method.

Modeling ecological patterns and processes often involve large-scale and complex high-dimensional spatial data. Due to the nonlinearity and multicollinearity of ecological data, traditional geostatistical methods have faced great challenges in model accuracy. As machine learning has increased our ability to construct models on big data, the main focus of the study is to propose the use of statistical models that hybridize machine learning and spatial interpolation methods to cope with increasingly large-scale and complex ecological data. Here, two machine learning algorithms, boosted regression tree (BRT) and least absolute shrinkage and selection operator (LASSO), were combined with ordinary kriging (OK) to model plant invasions across the eastern United States. The accuracies of the hybrid models and conventional models were evaluated by 10-fold cross-validation. Based on an invasive plants dataset of 15 ecoregions across the eastern United States, the results showed that the hybrid algorithms were significantly better at predicting plant invasion when compared to commonly used algorithms in terms of RMSE and paired-samples t-test (with the p-value < .0001). Besides, the additional aspect of the combined algorithms is to have the ability to select influential variables associated with the establishment of invasive cover, which cannot be achieved by conventional geostatistics. Higher accuracy in the prediction of large-scale biological invasions improves our understanding of the ecological conditions that lead to the establishment and spread of plants into novel habitats across spatial scales. The results demonstrate the effectiveness and robustness of the hybrid BRTOK and LASOK that can be used to analyze large-scale and high-dimensional spatial datasets, and it has offered an optional source of models for spatial interpolation of ecology properties. It will also provide a better basis for management decisions in early-detection modeling of invasive species.

A spatial analysis of one of the regional logistics clusters in central Poland using GIS

Abstract Logistics services are a consequence of increasingly rapid economic development and globalisation. More and more facilities with adequate transport accessibility are being created for the storage of goods, which form logistics clusters. They emerged later in Central and Eastern Europe than in the United States and Western Europe. Investment in Poland's first logistics parks can be linked to the political and economic transformation in 1989, Poland's accession to the European Union in 2004, the development of motorways, and Poland's integration into the global economy. In the second decade of the 21st century, there are more than a dozen places in Poland that can be called logistics clusters. The purpose of this research was to geographically analyse a selected regional cluster located in Lodz voivodeship, as well as its links to the transport network of Poland and Europe. Geostatistical and GIS methods were used for spatial analysis. It was shown that its spatial distribution is strongly related to the A1 highway, the intersection of the A1 and A2 highways and the voivodeship city of Lodz. The characteristics of the geographic environment give reason to suggest that it has great development potential and is worthy of further observation and comparative studies.

Borehole‐Based Interval Kriging for 3D Lithofacies Modeling

AbstractDeveloping a three‐dimensional (3D) lithofacies model from boreholes is critical for providing a coherent understanding of complex subsurface geology, which is essential for groundwater studies. This study aims to introduce a new geostatistical method—interval kriging—to efficiently conduct 3D borehole‐based lithological modeling with sand/non‐sand binary indicators. Interval kriging is a best linear unbiased estimator for irregular interval supports. Interval kriging considers 3D anisotropies between two orthogonal components—a horizontal plane and a vertical axis. A new 3D interval semivariogram is developed. To cope with the nonconvexity of estimation variance, the minimization of estimation variance is regulated with an additional regularization term. The minimization problem is solved by a global‐local genetic algorithm embedded with quadratic programming and Brent's method to obtain kriging weights and kriging length. Four numerical and real‐world case studies demonstrate that interval kriging is more computationally efficient than 3D kriging because the covariance matrix is largely reduced without sacrificing borehole data. Moreover, interval kriging produces more realistic geologic characteristics than 2.5D kriging, while conditional to spatial borehole data. Compared to the multiple‐point statistics (MPS) algorithm—SNESIM, interval kriging can reproduce the geological architecture and spatial connectivity of channel‐type features, meanwhile producing tabular‐type features with better connectivity. Because the regularization term constrains kriged value toward 0 or 1, interval kriging produces more certainty in sand/non‐sand classification than 2.5D kriging, 3D kriging, and SNESIM. In conclusion, interval kriging is an effective and efficient 3D geostatistical algorithm that can capture the 3D structural complexity while significantly reducing computational time.

Quantifying land change dynamics, resilience and feedback: A comparative analysis of the lake Chad basin in Africa and Aral Sea basin in Central Asia

The intricate interaction of natural and anthropogenic factors drives changes in land and water in response to societal demands and climate change. However, there has been insufficient information on the feedback effects in dryland hotspots altered by land change dynamics. This research compared two transboundary inland lakes, the Lake Chad basin (LCB) in Africa and the Aral Sea basin (ASB) in Central Asia, using remote sensing and geographic information system techniques to analyze and quantify present and future land cover dynamics, resilience, and their feedback effects. The study integrated Cellular Automata, Markov Chain, and Multilayer Perceptron models to predict LULC changes up to 2030. Descriptive statistics, ordinary least squares regression, hotspot Gi-Bin, trend analysis, and advanced geostatistical methods were utilized to identify relationships, patterns, magnitudes, and directions of observed changes in the feedback effects. From 2000 to 2030, the analysis unveils intriguing trends, including an increase in cropland from 48% to 51% and a decrease in shrubland from 18% to 15% in the LCB. The grassland increased from 21% to 22%, and the settlement expanded from 0.10 to 0.60% in the ASB. Water bodies remained stable at 1.60 % in LCB, while in ASB, it declined from 3% to 2%. These changes were significantly influenced by population, elevation, and temperature in both basins, with irrigation also playing a significant role in the ASB and slope in LCB. The study further revealed discernible shifts in normalized difference vegetation index, temperature, and precipitation linked to specific land cover conversions, suggesting alterations in surface properties and vegetation health. This study underscores the complex interplay between land cover dynamics, resilience, climate variability, and feedback mechanisms in LCB and ASB.

A U-Net architecture as a surrogate model combined with a geostatistical spectral algorithm for transient groundwater flow inverse problems

Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems, and inverse techniques play a fundamental role in modeling hydrogeological parameters and assessing their uncertainties. Nonetheless, the use of a forward model in these methods can be highly time-consuming, especially with an increasing number of model parameters. To address this issue, we propose a surrogate model based on a U-Net architecture that replaces the transient groundwater flow model, reducing runtime and enabling a fast quantification of uncertainties related to key parameters, including heterogeneous hydraulic conductivity, boundary conditions, specific storage, and pumping rate. The surrogate is trained using limited evaluations of the forward model to learn the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. The physical principles of the studied problem, including boundary conditions, specific storage, and source terms, are also mapped and introduced as inputs to the model to enhance its understanding of the governing equation of transient groundwater flow. To speed up learning using image–image regression, the previously predicted transient hydraulic heads also serve as an input to predict the transient heads at the current time step. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem, a pumping test of 12 h, using the surrogate model in place of the forward model. Our study demonstrates that the trained U-Net accurately reproduces the state variables corresponding to a specific parameter field, and in terms of computational demand, using U-Net as a surrogate model reduces the required computational time by approximately an order of magnitude for the defined problem. The proposed approach offers an efficient and accurate method for groundwater flow parameter characterization and uncertainty quantification in complex aquifer systems.

METHOD OF ACCOUNTING SOIL-AGROCHEMICAL POTENTIAL FOR OPTIMIZING THE STRUCTURE OF LAND USE OF THE VOLOZHINSK DISTRICT OF THE REPUBLIC OF BELARUS

The article discusses one of the ways to assess the condition of soil cover to improve the efficiency of land management using the example of the Volozhin region of the Republic of Belarus. A comprehensive assessment of the agrochemical and natural potential of the soil is proposed by means of typing the soil cover depending on agrochemical indicators (pHKCl, humus content, mobile compounds of phosphorus and potassium) and a quality score reflecting the natural state of the soil. Using geostatistical methods, the values of agrochemical indicators were interpolated from elementary areas into areas of soil varieties of agricultural lands and classified according to the degree of content of agrochemical elements that made up the agrochemical potential (AP). After crossing the AP with the bonitet score, 9 groups of soils were identified according to soil-agrochemical potential (SAP), of which the largest share (58,2 %) is occupied by soils with average potential (61,950 ha). Based on the results of a spatial assessment of the PAP, it was determined that sod-podzolic and sod-podzolic swampy soils developing on light loams and cohesive sandy loams have the greatest potential. It was also revealed that areas with low PAP gravitate towards the most dissected areas of the terrain with sandy and cohesive sandy soils. Based on the typification carried out, the main types of preferred land use in the Volozhin region were determined: more than half of the agricultural land can be used for intensive agricultural use for arable land (52,1 %) and meadows (12,5 %), traditional land use is possible for 29,3 % territories and only 6,2 % of lands require the use of soil protection farming systems, primarily focused on erosion-hazardous areas of the area.

Derivation of Landslide Rainfall Thresholds by Geostatistical Methods in Southwest China

Derivation of Landslide Rainfall Thresholds by Geostatistical Methods in Southwest China

Hybrid Machine Learning and Geostatistical Methods for Gap Filling and Predicting Solar-Induced Fluorescence Values

Sun-induced chlorophyll fluorescence (SIF) has proven to be advantageous in estimating gross primary production, despite the lack of a stable relationship. Satellite-based SIF measurements at Level 2 offer comprehensive global coverage and are available in near real time. However, these measurements are often limited by spatial and temporal sparsity, as well as discontinuities. These limitations primarily arise from incomplete satellite trajectories. Additionally, variability in cloud cover and periodic issues specific to the instruments can compromise data quality. Two families of methods have been developed to address data discontinuity: (1) machine learning-based gap-filling techniques and (2) geostatistical techniques (various forms of kriging). The former techniques utilize the relationships between ancillary data and SIF, while the latter usually rely on the available SIF data recordings and their covariance structure to provide estimates at unsampled locations. In this study, we create a synthetic approach for SIF gap filling by hybridizing the two approaches under the umbrella of kriging with external drift. We performed leave-one-out cross-validation of the OCO-2 SIF retrieval aggregates for the entire year of 2019, comparing three methods: ordinary kriging, ML-based estimation using ancillary data, and kriging with external drift. The Mean Absolute Error (MAE) for ML, ordinary kriging, and the hybrid approach was found to be 0.1399, 0.1318, and 0.1183 mW m2 sr−1 nm−1, respectively. We demonstrate that the performance of the hybrid approach exceeds both parent techniques due to the incorporation of information from multiple resources. This use of multiple datasets enriches the hybrid model, making it more robust and accurate in handling the spatio-temporal variability and discontinuity of SIF data. The developed framework is portable and can be applied to SIF retrievals at various resolutions and from various sources (satellites), as well as extended to other satellite-measured variables.

Geotechnical correlation field-informed and data-driven prediction of spatially varying geotechnical properties

Geotechnical measurements are often limited, leading to the use of interpolation techniques for interpreting spatial variations in geotechnical properties from sparse geo-data. Traditional geostatistical methods suffer from significant computational complexity. On the other hand, data-driven approaches often lack integration with geotechnical domain knowledge, potentially oversimplifying or complicating predictions related to the spatial variability of geotechnical properties. This study introduces a novel framework that combines geotechnical knowledge with data-driven methods to model inherent soil spatial variability incorporating Geotechnical Correlation Field (GCF) that reflects domain knowledge. The GCF, influenced by Autocorrelation Function (ACF) types and Scale of Fluctuation (SOF), provides a flexible basis for accurately representing spatially varying geotechnical properties. Using a large synthetic database comprising known ACF types and SOFs, we constructed a series of specialized neural networks. These networks identify random field parameters at different sites based on sparse data, and the estimated parameters can be directly used to calculate GCFs for a given site. The performance of the proposed method is validated using a set of synthetic data and a real case history in New Zealand. The results demonstrate the model can accurately predict random field parameters for irregularly spaced geo-data, even with limited information. Significantly, the GCFs offer improved physical interpretations and enhance the performance of subsurface modeling. The computational complexity of this method is independent of the number of soil cells, making it highly efficient and scalable.

A Stepwise Cosimulation Framework for Modeling Critical Elements in Copper Porphyry Deposits

The increased attention given to batteries has given rise to apprehensions regarding their availability; they have thus been categorized as essential commodities. Cobalt (Co), copper (Cu), lithium (Li), nickel (Ni), and molybdenum (Mo) are frequently selected as the primary metallic elements in lithium-ion batteries. The principal aim of this study was to develop a computational algorithm that integrates geostatistical methods and machine learning techniques to assess the resources of critical battery elements within a copper porphyry deposit. By employing a hierarchical/stepwise cosimulation methodology, the algorithm detailed in this research paper successfully represents both soft and hard boundaries in the simulation results. The methodology is evaluated using several global and local statistical studies. The findings indicate that the proposed algorithm outperforms the conventional approach in estimating these five elements, specifically when utilizing a stepwise estimation strategy known as cascade modeling. The proposed algorithm is also validated against true values by using a jackknife method, and it is shown that the method is precise and unbiased in the prediction of critical battery elements.

DESARROLLO DE MÉTODOS BASADOS EN REDES NEURONALES EN LA ESTIMACIÓN DE RECURSOS MINERALES

Due to economic and physical limitations, our understanding of mineral resources in a specific area of interest is limited and fragmented. Traditionally, this problem has been solved using the Kriging geostatistical method, where the ore grade is estimated at unmeasured locations using known values of the grade at surrounding points. The advantage of this method lies in the calculation of weights through a spatial variability model known as a variogram. However, the method is imperfect, as it is based on the assumption of stationarity, aditivity, linearity and potential subjectivity in variographic modelling. This study proposes to approach the mineral resource estimation problem as a regression problem using neural networks, which are not subject to the restrictions of stationarity, aditivity, linearity and spatial modelling of geostatistics methods. Kriging and a radial basis function neural network and a multilayer perceptron have been compared using different validation metrics. The results show that a properly trained neural network model, with appropriate labelling of the mineral grade and its input characteristics, achieves similar results to the geostatistical approach, with a significant reduction in time, while avoiding all the aforementioned assumptions. However, neural networks do not consider the spatial correlation of ore grade or reproduce it at the locations where it was measured, characteristics that have marked distrust in its industrial implementation and that are discussed in this article, finally proposing an adjustment between both approaches at a minimum sacrifice of time and labor costs. Keywords Neural networks; machine learning; geostatistics.