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Minerals
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Geostatistics in the Life Cycle of Mines
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Geostatistics in the Life Cycle of Mines

A special issue of Minerals (ISSN 2075-163X). This special issue belongs to the section "Mineral Deposits".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 15447

Special Issue Editors

Dr. Nasser Madani

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Guest Editor
School of Mining and Geosciences, Nazarbayev University, Astana 010000, Kazakhstan
Interests: univariate and multivariate geostatistics; resource estimation; stochastic modeling of geological domains
Dr. Mohammad Maleki

E-Mail Website
Guest Editor
Department of Metallurgical and Mining Engineering, Universidad Católica del Norte, Antofagasta 1270709, Chile
Interests: geostatistical modeling; resource estimation; data analysis
Dr. Nadia Mery

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Guest Editor
Department of Mining Engineering, University of Chile, Santiago 8370450, Chile
Interests: geostatistics; machine learning applied to mineral resource quantification; data analysis; resource estimation
Dr. Emmanouil Varouchakis

E-Mail Website
Guest Editor
School of Mineral Resources Engineering, Technical University of Crete, 731 00 Chania, Greece
Interests: space-time geostatistics; gaussian processes; non-Eucledian spatial metrics; risk analysis; groundwater; sustainable development in mining
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The life cycle of a mine can usually be summarized in five main stages. The first step, prospecting, is about finding the anomaly of minerals that can mostly be obtained by geological, geochemical, and geophysical investigations. This step is also accomplished by interpreting satellite/aerial images to narrow the geographical scope of the search. In the exploration stage, geoscientists and mining engineers tend to define the size of the orebody in more detail. This usually includes measuring the ore grade, geological, and geotechnical characteristics of the deposit at the sampling points, where they can later be evaluated/estimated at unsampled locations. The development stage starts with engineering and design studies to construct the optimum plans for ore extraction and beneficiation. This stage is critical in making decisions to exploit the ore deposit through surface, underground mine, or a combination of both. The fourth step, exploitation, is dealing with the extraction of the ore and processing it to meet the market need. The last step, reclamation, aims to restore the mine site to its original condition. On top of these five stages, a complementary stage is of paramount importance in re-mining the waste materials and tailing storage facilities to obtain critical raw materials. These five plus one stages explain the series of actions in contemporary mining business.

Geostatistics is a subdivision of spatial statistics that focuses on the interpretation of spatial characteristics and modeling values of natural phenomena at unsampled locations. Geostatistics quantifies and describes spatial, temporal, and directional behavior of the variables of interest and provides explicable maps and solutions for downstream activities of a mining project. This Special Issue concentrates on publishing high-quality and exclusive contributions that cover all aspects of geostatistics. This includes the development of innovative geostatistical algorithms and their applications that can solve research problems in any of these 5 +1 stages of the life cycle of mines, solving the complexities in modeling the regionalized variables for: compositional geochemical data, geophysical attributes, mineral/ore grades, geotechnical parameters, complex geological features, geometallurgical responses, prediction of imprecise and uncertain data, complex multivariate relationship, non-stationary, mining selectivity and information effect, soft data and Bayesian updating, data imputation, data scarcity, uncertainty quantification, and hydroinformatics.

We welcome works with more emphasis on, but not exclusively, the following subcategories:

  1. Prospecting (e.g., development of geochemical and geophysical maps and integration of GIS data to the subsequent stages);
  2. Exploration (e.g., building geological and mineral grades of block model using cascade/hierarchical or joint modeling);
  3. Development (e.g., resource and reserve modeling and investigating their impacts on long- and short-term mine planning and design);
  4. Exploitation (e.g., model reconciliation, rapid and real-time updating of the block model and computational issues, grade control, mining dilution, and water management);
  5. Reclamation (e.g., estimation and spatial modeling of heavy metals, soil compactness and erodibility or conductivity);
  6. Re-mining of waste and tailings (e.g., resource evaluation of critical raw materials).

Dr. Nasser Madani
Dr. Mohammad Maleki
Dr. Nadia Mery
Dr. Emmanouil Varouchakis
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Minerals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • geostatistics
  • kriging and cokriging
  • simulation and cosimulation
  • truncated and plurigaussian simulation
  • sequential indicator simulation
  • multiple-point statistics
  • object-based simulation
  • simulated annealing
  • ensemble kalman filter
  • combination of machine learning and geostatistics
  • using geostatistics for image analysis
  • non-euclidean spaces
  • spatio-temporal geostatistics
  • spatio-directional geostatistics

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Published Papers (7 papers)

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Research

23 pages, 7549 KiB  
Article
Probabilistic Modelling of Geologically Complex Veins of the Barberton Greenstone Complex at Fairview Mine, South Africa
by Tyson Mutobvu, Hendrik Pretorius, Charles Johannes Muller and Mahlomola Isaac Mabala
Minerals 2024, 14(4), 343; https://doi.org/10.3390/min14040343 - 26 Mar 2024
Viewed by 1267
Abstract
Achieving accurate estimations of recoverable tonnage relies on a robust geological modelling process. To ensure this accuracy, it is crucial to incorporate information from exploration, grade control, and sampling, considering well-identified mineralization controls. However, modelling the geology of complex orebodies, especially veins, poses [...] Read more.
Achieving accurate estimations of recoverable tonnage relies on a robust geological modelling process. To ensure this accuracy, it is crucial to incorporate information from exploration, grade control, and sampling, considering well-identified mineralization controls. However, modelling the geology of complex orebodies, especially veins, poses challenges due to their intricate mineral accumulation processes and variable structural complexities. Fairview Mine’s Main Reef Complex (MRC) reef is highly discontinuous, with most of the valuable mineralized zone concentrated within localized ore shoots that intersect various lithologies, exemplifying these challenges. This study aimed to improve the modelling of veins at the mine, striving for a more accurate representation of the mineralization zones. To achieve this, a hybrid approach was employed, combining a deterministic method based on minimum curvature interpolation with a probabilistic method using anisotropic inverse distance weighting for categorical/discrete variables. The subsequent tonnage estimates showed a robust correlation with actual production output. The initial deterministic model established the large-scale geological trend, providing a foundation for estimating a probabilistic model. The iterative nature of probabilistic modelling allowed for the analysis of various probable options, facilitating the selection of the model that best captured the underlying geology. This approach enabled robust mathematical modelling while incorporating valuable input from geological knowledge and expectations. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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21 pages, 9400 KiB  
Article
Integrated Stochastic Underground Mine Planning with Long-Term Stockpiling: Method and Impacts of Using High-Order Sequential Simulations
by Laura Carelos Andrade and Roussos Dimitrakopoulos
Minerals 2024, 14(2), 123; https://doi.org/10.3390/min14020123 - 24 Jan 2024
Cited by 2 | Viewed by 1546
Abstract
The integrated optimization of stope design and underground mine production scheduling is an approach that has been shown to effectively leverage the synergies among these two underground mine planning components to generate truly optimal stope layouts and extraction sequences. The existing stochastic integrated [...] Read more.
The integrated optimization of stope design and underground mine production scheduling is an approach that has been shown to effectively leverage the synergies among these two underground mine planning components to generate truly optimal stope layouts and extraction sequences. The existing stochastic integrated methods, however, do not include several elements of a mining complex, such as stockpiles, due to the computational complexity and non-linearity that they might add to the optimization of the long-term mine plan. Additionally, sequential simulation methods that rely on two-point statistics and Gaussian distribution assumptions are commonly used to generate the input realizations of the mineral deposit. These methods, however, are not able to properly characterize complex spatial geometries or the high-grade connectivity of non-Gaussian and non-linear natural phenomena. The present work proposes an extension of previous developments on the integrated stope design and underground mine scheduling optimization through an expanded stochastic integer programming formulation that incorporates long-term stockpiling decisions. An application of the proposed method at an operating underground copper mine compares the cases in which the geological simulated orebody models are based on high-order and Gaussian sequential simulation methods. The extraction sequence and related final stope design are shown to be physically different. It is seen that the optimization process takes advantage of the better representation of high-grade connectivity when high-order sequential simulations are used, by targeting the areas with grades that follow the mill’s blending requirements and by making less use of the stockpiles. Overall, a 4% higher copper metal production and a resultant 6% higher net present value are observed when high-order sequential simulations are used. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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13 pages, 2169 KiB  
Article
The Place of Geostatistical Simulation through the Life Cycle of a Mineral Deposit
by Clayton V. Deutsch
Minerals 2023, 13(11), 1400; https://doi.org/10.3390/min13111400 - 31 Oct 2023
Viewed by 1454
Abstract
Geostatistical techniques are applied to examine the life cycle of a mineral deposit. There are two main classes of geostatistical techniques: (1) deterministic techniques that include kriging and cokriging for a single best estimate, and (2) probabilistic techniques that include simulation, which infer [...] Read more.
Geostatistical techniques are applied to examine the life cycle of a mineral deposit. There are two main classes of geostatistical techniques: (1) deterministic techniques that include kriging and cokriging for a single best estimate, and (2) probabilistic techniques that include simulation, which infer probability distributions and simulate realizations to transfer multivariable and multilocation uncertainty through to larger-scale resource and reserve uncertainty. Probabilistic techniques are newer and more powerful in that they provide access to quantitative measures of uncertainty and models with correct spatial variability; however, they have not seen widespread application in all aspects of the life cycle of mines. Workflows and methodologies for the appropriate use of deterministic and probabilistic techniques have been discussed. Software, engineering practices and management expectations limit some applications. Applications have been reviewed, and enhancements are required to realize the full potential of geostatistical techniques, which have been discussed with examples. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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29 pages, 13074 KiB  
Article
Addressing Geological Challenges in Mineral Resource Estimation: A Comparative Study of Deep Learning and Traditional Techniques
by Nurassyl Battalgazy, Rick Valenta, Paul Gow, Carlos Spier and Gordon Forbes
Minerals 2023, 13(7), 982; https://doi.org/10.3390/min13070982 - 24 Jul 2023
Cited by 1 | Viewed by 3623
Abstract
Spatial prediction of orebody characteristics can often be challenging given the commonly complex geological structure of mineral deposits. For example, a high nugget effect can strongly impact variogram modelling. Geological complexity can be caused by the presence of structural geological discontinuities combined with [...] Read more.
Spatial prediction of orebody characteristics can often be challenging given the commonly complex geological structure of mineral deposits. For example, a high nugget effect can strongly impact variogram modelling. Geological complexity can be caused by the presence of structural geological discontinuities combined with numerous lithotypes, which may lead to underperformance of grade estimation with traditional kriging. Deep learning algorithms can be a practical alternative in addressing these issues since, in the neural network, calculation of experimental variograms is not necessary and nonlinearity can be captured globally by learning the underlying interrelationships present in the dataset. Five different methods are used to estimate an unsampled 2D dataset. The methods include the machine learning techniques Support Vector Regression (SVR) and Multi-Layer Perceptron (MLP) neural network; the conventional geostatistical methods Simple Kriging (SK) and Nearest Neighbourhood (NN); and a deep learning technique, Convolutional Neural Network (CNN). A comparison of geologic features such as discontinuities, faults, and domain boundaries present in the results from the different methods shows that the CNN technique leads in terms of capturing the inherent geological characteristics of given data and possesses high potential to outperform other techniques for various datasets. The CNN model learns from training images and captures important features of each training image based on thousands of calculations and analyses and has good ability to define the borders of domains and to construct its discontinuities. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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35 pages, 21772 KiB  
Article
Geometallurgical Responses on Lithological Domains Modelled by a Hybrid Domaining Framework
by Yerniyaz Abildin, Chaoshui Xu, Peter Dowd and Amir Adeli
Minerals 2023, 13(7), 918; https://doi.org/10.3390/min13070918 - 7 Jul 2023
Cited by 1 | Viewed by 1781
Abstract
Identifying mineralization zones is a critical component of quantifying the distribution of target minerals using well-established mineral resource estimation techniques. Domains are used to define these zones and can be modelled using techniques such as manual interpretation, implicit modelling, and advanced geostatistical methods. [...] Read more.
Identifying mineralization zones is a critical component of quantifying the distribution of target minerals using well-established mineral resource estimation techniques. Domains are used to define these zones and can be modelled using techniques such as manual interpretation, implicit modelling, and advanced geostatistical methods. In practise, domaining is commonly a manual exercise that is labour-intensive and prone to subjective judgement errors, resulting in a largely deterministic output that ignores the significant uncertainty associated with manual domain interpretation and boundary definitions. Addressing these issues requires an objective framework that can automatically define mineral domains and quantify the associated uncertainty. This paper presents a comparative study of PluriGaussian Simulation (PGS) and a Hybrid Domaining Framework (HDF) based on simulated assay grades and XGBoost, a machine-learning classification technique trained on lithological properties. The two domaining approaches are assessed on the basis of the domain boundaries produced using data from an Iron Oxide Copper Gold deposit. The results show that the proposed HDF domaining framework can quantify the uncertainty of domain boundaries and accommodate complex multiclass problems with imbalanced features. Geometallurgical models of the Net Smelter Return and grinding time are used to demonstrate the effectiveness of HDF. In addition, a preprocessing step involving a noise filtering method is used to improve the performance of the ML classification, especially in cases where domain boundaries are difficult to predict due to the similarity in geological characteristics and the inherent noise in the data. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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15 pages, 6362 KiB  
Article
Geostatistical Evaluation of a Porphyry Copper Deposit Using Copulas
by Babak Sohrabian, Saeed Soltani-Mohammadi, Rashed Pourmirzaee and Emmanuel John M. Carranza
Minerals 2023, 13(6), 732; https://doi.org/10.3390/min13060732 - 29 May 2023
Cited by 4 | Viewed by 1815
Abstract
Kriging has some problems such as ignoring sample values in giving weights to them, reducing dependence structure to a single covariance function, and facing negative confidence bounds. In view to these problems of kriging in this study to estimate Cu in the Iju [...] Read more.
Kriging has some problems such as ignoring sample values in giving weights to them, reducing dependence structure to a single covariance function, and facing negative confidence bounds. In view to these problems of kriging in this study to estimate Cu in the Iju porphyry Cu deposit in Iran, we used a convex linear combination of Archimedean copulas. To delineate the spatial dependence structure of Cu, the best Frank, Gumbel, and Clayton copula models were determined at different lags to fit with higher-order polynomials. The resulting Archimedean copulas were able to describe all kinds of spatial dependence structures, including asymmetric lower and upper tails. The copula and kriging methods were compared through a split-sample cross-validation test whereby the drill-hole data were divided into modeling and validation sets. The cross-validation showed better results for geostatistical estimation through copula than through kriging in terms of accuracy and precision. The mean of the validation set, which was 0.1218%, was estimated as 0.1278% and 0.1369% by the copula and kriging methods, respectively. The correlation coefficient between the estimated and measured values was higher for the copula method than for the kriging method. With 0.0143%2 and 0.0162%2 values, the mean square error was substantially smaller for copula than for kriging. A boxplot of the results demonstrated that the copula method was better in reproducing the Cu distribution and had fewer smoothing problems. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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16 pages, 3940 KiB  
Article
Resource Estimation in Multi-Unit Mineral Deposits Using a Multivariate Matérn Correlation Model: An Application in an Iron Ore Deposit of Nkout, Cameroon
by Franklin Ekolle-Essoh, Arsène Meying, Alain Zanga-Amougou and Xavier Emery
Minerals 2022, 12(12), 1599; https://doi.org/10.3390/min12121599 - 12 Dec 2022
Cited by 2 | Viewed by 2265
Abstract
Modeling the spatial dependence structure of metal grades in the presence of soft boundaries between geological domains is challenging in any mineral resource estimation strategy. The aim of this work was to propose a structural model adapted to this type of geological boundary, [...] Read more.
Modeling the spatial dependence structure of metal grades in the presence of soft boundaries between geological domains is challenging in any mineral resource estimation strategy. The aim of this work was to propose a structural model adapted to this type of geological boundary, based on a multivariate Matérn model that fits the observed direct (within domain) and cross (between domains) correlation structures of metal grades. The methodology was applied to a case study of an iron deposit located in southern Cameroon. Cross-validation scores show that accounting for the grade correlation across domain boundaries improved the traditional workflow, where the grade was estimated in each domain separately. The scores were significantly better when we also ensured that the mean grade was locally invariant from one domain to another to reflect the grade continuity across the domain boundary. Full article
(This article belongs to the Special Issue Geostatistics in the Life Cycle of Mines)
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