Ore Grade Estimation Research Articles

Estimation of Fe Grade at an Ore Deposit Using Extreme Gradient Boosting Trees (XGBoost)

Estimating the spatial distribution of ore grade is one of the most critical and important steps to continue investment decision on the deposit. Kriging is the most widely used method to estimate the ore grade while alternative techniques are being developed. Machine learning algorithms can be used as alternative methods to classical kriging. In this paper, Fe grade of a deposit is estimated with XGBoost algorithm, and results are compared with kriging estimation results. For estimation processes, samples collected from the drillholes are used. To mitigate the effect of varying sampling length, both estimations use composites of these samples. Due to the different nature of the estimation methods, different steps have been taken to perform estimations. Results show that XGBoost estimates produced higher ranged estimates which is a desired result in ore grade estimation while minimum and maximum of the estimates were lower and higher than the kriging estimates, respectively. However, like kriging estimates, estimation results were smoother than composites while variance of the XGBoost estimates were lower than variance of composites. This means that even though estimation with XGBoost mitigates the smoothing effect, estimation results suffer from smoothing effect like kriging.

Evaluation method of ore grade estimation effectiveness.

This study proposes a new method to evaluate the effectiveness of orebody grade estimations, drawing upon the analysis of existing evaluation methods for grade estimation. This new approach addresses factors such as uneven sampling and asymmetric estimation range, which are challenging to overcome with existing evaluation techniques. The core principle of this method involves documenting how frequently individual samples are used during grade estimation and calculating the total distance weights for each sample. Subsequently, the usage frequency and total weight of the samples are standardized, and these standardized values are weighted based on the sample grades. A comparison is made between the weighted sample grades and the estimated grades, with the closeness between the two serving as a metric for assessing the effectiveness of the estimation. This study compares the new evaluation method to the direct comparison and cross-validation methods, examining the effectiveness of grade estimation using the inverse distance weighting (IDW) method. The findings revealed that: (1) The new evaluation method theoretically accounts for the systematic deviation between the statistical measures of estimated and sample grades resulting from uneven sample distribution, offering a fresh approach for enhancing the effectiveness of orebody grade estimation. (2) In the grade estimation of experimental Fe samples, the frequency of usage and the sum of distance weights were unequal. This inequality significantly contributes to the systematic deviation between the estimated and sample grades. (3) Comparing the new evaluation method to others confirms the stability and reliability of the new approach for evaluating the effectiveness of orebody grade estimation. This novel method demonstrates theoretical advantages and practical utility. (4) The deviation between the estimated grades and the statistical results of sample grades is influenced by the distribution pattern of sample grades, the spatial relationship between samples and estimation blocks, and the inherent systematic error associated with the IDW method. This systematic error cannot be overlooked.

A new method for estimating ore grade based on sample length weighting

Estimation of ore grade is very important for the value evaluation of ore deposits, and it directly affects the development of mineral resources. To improve the accuracy of the inverse distance weighting (IDW) method in ore grade estimation and reduce the smoothing effect of the IDW method in grade estimation, the weight calculation method involved in the IDW method was improved. The length parameter of the ore sample was used to calculate the weight of the IDW method. The length of the ore samples was used as a new factor of the weighting calculation. A new method of IDW integrated with sample length weighting (IDWW) was proposed. The grade estimation of Li, Al, and Fe in porcelain clay ore was used as a case study. A comparative protocol for grade estimation via the IDWW method was designed and implemented. The number of samples involved in the estimation, sample combination, sample grade distribution, and other factors affecting the grade estimation were considered in the experimental scheme. The grade estimation results of the IDWW and the IDW methods were used for comparative analysis of grades of the original and combined samples. The estimated results of the IDWW method were also compared with those of the IDW method. The deviation analysis of the estimated grade mainly included the minimum, maximum, mean, and coefficient of variation of the ore grade. The estimation effect of IDWW method was verified. The minimum deviations of the estimated grade of Li, Al, and Fe were between 9.129% and 59.554%. The maximum deviations were between 4.210 and 22.375%. The mean deviations were between − 1.068 and 7.187%. The deviations in the coefficient of variation were between 3.076 and 36.186%. The deviations in the maximum, minimum, mean, and coefficients of variation of the IDWW were consistent with those of the IDW, demonstrating the accuracy and stability of the IDWW method. The more the samples involved in the estimation, the greater the estimation deviations of IDW and IDWW methods. The estimated deviations of Li, Al, and Fe were affected by the shape of the grade distribution, when the same estimation parameters were used. The grade distribution pattern of the samples significantly influenced the grade estimation results. The IDWW method offers significant theoretical advantages and addresses the adverse effects of uneven sample lengths on the estimates. The IDWW method can effectively reduce the smoothing effect and improves the utilization efficiency of the original samples.

An approach based on Machine Learning Algorithms, Geostatistical Technique, and GIS analysis to estimate phosphate ore grade at the Abu Tartur Mine, Western Desert, Egypt

Purpose. This paper aims to estimate phosphate ore grade in the Abu Tartur area, Western Desert, Egypt, using four Machine Learning Algorithms (MLA), Geostatistical Techniques (variogram and kriging models), and GIS-analysis. Methods. Four machine-learning techniques include Optimizable Decision Tree (ODT), Optimizable Support Vector Machine (OSVM), Optimizable Gaussian Process Regression (OGPR), Artificial Neural Network (ANN) are applied in this paper. The constructed variogram and kriging models, as well as GIS-analysis, provide a clear understanding of all the elements distributed in the Abu Tartur phosphate ore and are very useful at the planning and mining stages. Findings. Phosphate content has been estimated with high accuracy based on the results of four machine-learning techniques. The most efficient technique for estimating phosphate content is optimizable (OGPR), which gives correlation coefficients (R) of 0.933 and 0.927 with Mean Absolute Errors (MAE) of 0.983 and 0.933 for the training and validation data, respectively. In addition, geostatistical and GIS methods have shown that percentage of P2O5, thickness, and Fe% are suitable for phosphate mining processes, except for small pockets that require little attention at the mining stage. Originality. This research attempts to develop a quick estimation of phosphate ore grade and to provide a clear understanding about the distribution of different constituents within the ore body using different techniques. Practical implications. Grade estimation is commonly reduced to a function approximation. Artificial intelligence (AI) techniques, and in particular the chosen type of AI techniques, can provide, a valid methodology for estimating grade, and the proposed models can be applied to any other data in the range used in this research.

Error reduction in long-term mine planning estimates using deep learning models

The long-term mine planning model (LTMP) and short-term mine planning model (STMP) are two approaches that describe the ore content in a mine; they are essential intangible resources that determine a mining operation and its feasibility. These models are obtained with geostatistical methods and, given their nature, are prone to discrepancies with one another. To reduce these differences, we studied the performance of deep learning (DL)-based models in ore grade estimation for a copper mine in Chile. Specifically, feedforward neural network (FNN), one-dimensional (1D) convolutional neural network (CNN), and long short-term memory (LSTM) models were analyzed. The experiment consisted of a dataset with 732,870 samples, obtained after data cleaning and selection. The use of spatial information in the samples was also studied, adding contextual information for estimation. This led to a dataset of 545,768 samples that were used to evaluate 1D CNN and LSTM models. Architecture tuning was performed by the k-fold cross-validation (CV) method, and hyperparameters such as the number of layers, number of neurons, activation function, and kernel size were optimized. The resulting hyperparameters were used to perform a final evaluation. Performance was measured based on the mean absolute error (MAE), mean squared error (MSE), and coefficient of determination (R2) metrics. A baseline is created using LTMP and STMP estimates to quantify the improvement in the performance of DL-based models. The experimental results revealed the ability of DL-based models to significantly improve copper grade estimates provided by standard mining industry methods in the context under study. For MSE in the final tests, FNN improved by 21%, CNN by 37%, and LSTM by 39% over baselines.

Challenges with Density-Based Grade Estimation at LKAB’s Underground Iron Ore Mines

Sublevel caving operation relies on the estimation of ore grade at drawpoints, as the mine management uses grade to decide whether the material at a certain ring should be loaded or abandoned. Grade is estimated in various ways, including visual estimation, density-based calculation, and sampling and assay methods. The grade estimation at the world’s two largest underground iron ore mines owned by LKAB in northern Sweden is based on the density difference between ore and waste. The calculations assume a constant swell factor, a theoretical fill of 100%, and a linear relationship between bucket weight and material grade. This study evaluated these assumptions in detail based on the loading data for 12,237 buckets and concluded that the method has some shortcomings which render the assumptions invalid. Further research is required to deal with these shortcomings to improve estimation of the material grade.

Combination of Machine Learning Algorithms with Concentration-Area Fractal Method for Soil Geochemical Anomaly Detection in Sediment-Hosted Irankuh Pb-Zn Deposit, Central Iran

Prediction of geochemical concentration values is essential in mineral exploration as it plays a principal role in the economic section. In this paper, four regression machine learning (ML) algorithms, such as K neighbor regressor (KNN), support vector regressor (SVR), gradient boosting regressor (GBR), and random forest regressor (RFR), have been trained to build our proposed hybrid ML (HML) model. Three metric measurements, including the correlation coefficient, mean absolute error (MAE), and means squared error (MSE), have been selected for model prediction performance. The final prediction of Pb and Zn grades is achieved using the HML model as they outperformed other algorithms by inheriting the advantages of individual regression models. Although the introduced regression algorithms can solve problems as single, non-complex, and robust regression models, the hybrid techniques can be used for the ore grade estimation with better performance. The required data are gathered from in situ soil. The objective of the recent study is to use the ML model’s prediction to classify Pb and Zn anomalies by concentration-area fractal modeling in the study area. Based on this fractal model results, there are five geochemical populations for both cases. These elements’ main anomalous regions were correlated with mining activities and core drilling data. The results indicate that our method is promising for predicting the ore elemental distribution.

Surface Warping Incorporating Machine Learning Assisted Domain Likelihood Estimation: A New Paradigm in Mine Geology Modeling and Automation

This paper illustrates an application of machine learning (ML) within a complex system that performs grade estimation. In surface mining, assay measurements taken from production drilling often provide useful information that allows initially inaccurate surfaces created using sparse exploration data to be revised and subsequently improved. Recently, a Bayesian warping technique has been proposed to reshape modeled surfaces using geochemical and spatial constraints imposed by newly acquired blasthole data. This paper focuses on incorporating machine learning into this warping framework to make the likelihood computation generalizable. The technique works by adjusting the position of vertices on the surface to maximize the integrity of modeled geological boundaries with respect to sparse geochemical observations. Its foundation is laid by a Bayesian derivation in which the geological domain likelihood given the chemistry, p(g|c), plays a similar role to p(y(c)|g). This observation allows a manually calibrated process centered around the latter to be automated since ML techniques may be used to estimate the former in a data-driven way. Machine learning performance is evaluated for gradient boosting, neural network, random forest and other classifiers in a binary and multi-class context using precision and recall rates. Once ML likelihood estimators are integrated in the surface warping framework, surface shaping performance is evaluated using unseen data by examining the categorical distribution of test samples located above and below the warped surface. Large-scale validation experiments are performed to assess the overall efficacy of ML assisted surface warping as a fully integrated component within an ore grade estimation system where the posterior mean is obtained via Gaussian Process inference with a Matern 3/2 kernel.

An advanced uranium ore grade estimation method based on photofission driven by an e-LINAC

A method for evaluating the grade of uranium (U) ores through the analysis of β-delayed neutrons following (γ, fission) is discussed. By measuring β-delayed fission neutrons stimulated from 238U, the U-Ra disequilibrium problem, which limits the accuracy of traditional grade estimation methods that rely on measuring radioactivity, is addressed. In this research, 6 MV bremsstrahlung photons, delivered by a 6 MeV electron linear accelerator (e-LINAC), were used to irradiate U ore samples, and a moderator surrounded thermal neutron detector was designed to register the emitted neutrons after each X-ray pulse. Although the prompt fission neutrons were discarded due to the interference caused by the photoneutrons emitted from the matrix nuclides in the analytical environment, an excellent linear relationship was observed between the counts of β-delayed neutrons and U ore grades, demonstrating that this method is promising for the in-situ analysis of U ores.

Ore grade estimation using the imperialist competitive algorithm (ICA)

In this paper, a hybrid inverse distance weighted (IDW) and the imperialist competitive algorithm (ICA) was proposed for grade estimations in mining projects. Indeed, the coefficients of the IDW equation, power, and the influence distance were modified by applying the ICA algorithm. For this, an example was solved by using IDW, the ordinary kriging, and IDW-ICA. After successfully validating the IDW-ICA, the iron grades were estimated in the Baba Ali iron mine, the most prominent iron mine in the west of Iran. For this, after gathering data from thirty-two boreholes, the grade estimations were conducted using IDW, kriging, and IDW-ICA. Some statistical parameters, including the mean absolute percentage error (MAPE), root-mean-squared error (RMSE), and correlation coefficient, were used to compare the results. The higher value of the R2, 94.41%, the lowest values of MAPE, 17.4%, and RMSE, 4.19, of the proposed algorithm, revealed that the IDW-ICA could be applied as a new-fangled method for grade estimations in the mining projects.

Assessment of Ore Grade Estimation Methods for Structurally Controlled Vein Deposits - A Review

Resource estimation techniques have upgraded over the past couple of years, thereby improving resource estimates. The classical method of estimation is less used in ore grade estimation than geostatistics (kriging) which proved to provide more accurate estimates by its ability to account for the geology of the deposit and assess error. Geostatistics has therefore been said to be superior over the classical methods of estimation. However, due to the complexity of using geostatistics in resource estimation, its time-consuming nature, the susceptibility to errors due to human interference, the difficulty in applying it to deposits with few data points and the difficulty in using it to estimate complicated deposits paved the way for the application of Artificial Intelligence (AI) techniques to be applied in ore grade estimation. AI techniques have been employed in diverse ore deposit types for the past two decades and have proven to provide comparable or better results than those estimated with kriging. This research aimed to review and compare the most commonly used kriging methods and AI techniques in ore grade estimation of complex structurally controlled vein deposits. The review showed that AI techniques outperformed kriging methods in ore grade estimation of vein deposits.
 
 Keywords: Artificial Intelligence, Neural Networks, Geostatistics, Kriging, Mineral Resource, Grade

Evaluating the Performance of Extreme Learning Machine Technique for Ore Grade Estimation

Due to the complex geology of vein deposits and their erratic grade distributions, there is the tendency of overestimating or underestimating the ore grade. These estimated grade results determine the profitability of mining the ore deposit or otherwise. In this study, five Extreme Learning Machine (ELM) variants based on hard limit, sigmoid, triangular basis, sine and radial basis activation functions were applied to predict ore grade. The motive is that the activation function has been identified to play a key role in achieving optimum ELM performance. Therefore, assessing the extent of influence the activation functions will have on the final outputs from the ELM has some scientific value worth investigating. This study therefore applied ELM as ore grade estimator which is yet to be explored in the literature. The obtained results from the five ELM variants were analysed and compared with the state-of-the-art benchmark methods of Backpropagation Neural Network (BPNN) and Ordinary Kriging (OK). The statistical test results revealed that the ELM with sigmoid activation function (ELM-Sigmoid) was the best among all the other investigated methods (ELM-Hard limit, ELM-Triangular basis, ELM-Sine, ELM-Radial Basis, BPNN and OK). This is because the ELM-sigmoid produced the lowest MAE (0.0175), MSE (0.0005) and RMSE (0.0229) with highest R2 (91.93%) and R (95.88%) respectively. It was concluded that ELM-Sigmoid can be used by field practitioners as a reliable alternative ore grade estimation technique.

Optimizing Extreme Learning Machine Algorithm using Particle Swarm Optimization to Estimate Iron Ore Grade

Scientific uncertainties make the grade estimation very complicated and important in the metallic ore deposits. This paper introduces a new hybrid method for estimating the iron ore grade using a combination of two artificial intelligence methods; it is based on the single layer-extreme learning machine and the particle swarm optimization approaches, and is designed based on the location of the boreholes, depth of the boreholes, and drill hole information from an orebody, and applied for the ore grade estimation on the basis of a block model. In this work, the two algorithms of optimization clustering and neural networks are used for the iron grade estimation in the Choghart iron ore north anomaly in the central Iran. The results of the training and testing the algorithms indicate a significant ability of the optimized neural network system in the ore grade estimation.

The influence of distance weight on the inverse distance weighted method for ore-grade estimation

In order to study the influence of distance weight on ore-grade estimation, the inverse distance weighted (IDW) is used to estimate the Ni grade and MgO grade of serpentinite ore based on a three-dimensional ore body model and related block models. Manhattan distance, Euclidean distance, Chebyshev distance, and multiple forms of the Minkowski distance are used to calculate distance weight of IDW. Results show that using the Minkowski distance for the distance weight calculation is feasible. The law of the estimated results along with the distance weight is given. The study expands the distance weight calculation method in the IDW method, and a new method for improving estimation accuracy is given. Researchers can choose different weight calculation methods according to their needs. In this study, the estimated effect is best when the power of the Minkowski distance is 3 for a 10 m × 10 m × 10 m block model. For a 20 m × 20 m × 20 m block model, the estimated effect is best when the power of the Minkowski distance is 9.

Delineation of Alteration Zones Based on Wavelet Neural Network (WNN) and Concentration–Volume (C-V) Fractal Methods in the Hypogene Zone of Porphyry Copper Deposit, Shahr-e-Babak District, SE Iran

In this paper, we aim to achieve two specific objectives. The first one is to examine the applicability of wavelet neural network (WNN) technique in ore grade estimation, which is based on integration between wavelet theory and Artificial Neural Network (ANN). Different wavelets are applied as activation functions to estimate Cu grade of borehole data in the hypogene zone of porphyry ore deposit, Shahr-e-Babak district, SE Iran. WNN parameters such as dilation and translation are fixed and only the weights of the network are optimized during its learning process. The efficacy of this type of network in function learning and estimation is compared with Ordinary Kriging (OK). Secondly, we aim to delineate the potassic and phyllic alteration regions in the hypogene zone of Cu porphyry deposit based on the estimation obtained of WNN and OK methods, and utilize Concentration–Volume (C–V) fractal model. In this regard, at first C–V log–log plots are generated based on the results of OK and WNN. The plots then are used to determine the Cu threshold values of the alteration zones. To investigate the correlation between geological model and C-V fractal results, the log ratio matrix is applied. The results showed that, Cu values less than 1.1% from WNN have more overlapped voxels with phyllic alteration zone by overall accuracy (OA) of 0.74. Spatial correlation between the potassic alteration zones resulted from 3D geological modeling and high concentration zones in C-V fractal model showed that the alteration zone has Cu values between 1.1% and 2.2% with OA of 0.72 and finally have an appropriate overlap with Cu values greater than 2.2% with OA of 0.7. Generally, the results showed that the WNN (Morlet activation function) with OA greater than OK can be can be a suitable and robust tool for quantitative modeling of alteration zones, instead of qualitative methods.

Grade 3D Block Modeling and Reserve Estimation of the C-North Iron Skarn Ore Deposit, Sangan, NE Iran

Estimation of ore grade is a time and cost consuming process that requires laboratory-based and exploratory information to present the shape and the ore grade distribution of ore deposit in three dimensional space. The block size is one of the most important parameters which impacts the quality of grade estimates in a resource model. This study aims at spatial modeling of iron ore deposit using geostatistical estimation methods such as Ordinary Kriging based on error estimation, selection of the appropriate size for mining blocks using Vlse Kriterijumsk Optimizacija Kompromisno Resenje method, and performing a three-dimensional block modeling along a grade estimation study for the resource estimation in the C-North iron ore deposit, NE Iran. The variogram that was used in OK estimation was cross validated. Cross validation results showed that compared with the local model, OK with the global model was the most appropriate model for the ore body. Detailed distribution maps of total iron contents in the C-North ore deposit showed a close relationship between structural features and higher iron contents, relative to other areas of the ore deposit. Structural features included the major faults and fault zones along the axial plane. These structures are interpreted to have played a significant role in (re) mobilisation and concentration of the metals, in agreement with observations made elsewhere in the Sangan iron ore complex. Based on the estimation results, 83 million tons of resource was estimated at an average grade of 41.86 % Fe using OK method. The C-North ore deposit has been classified based on the relative estimation error variance and the Australasian Code for Reporting of Mineral Resources and Ore Reserves. It is hoped that this example, taken from very different application fields, will encourage practitioners in applying an OK method with variety of ore deposits.

Multi-point geostatistics for ore grade estimation

A multi-point geostatistical method for ore grade estimation is introduced in order to fully utilize existing sampling information. A block model is used to construct a new three-dimensional training image instead of a variogram. Data events and pattern matching is improved, and the directionality of the data template is considered in the matching. The inverse distance weighted method is used to make up for the lack of multi-point geostatistics. The research improves the reliability of multi-point geostatistical estimation. Optimal estimation results for Li2O and Ta2O5 come from the inverse distance weighted, ordinary Kriging, and multi-point geostatistical methods. Multi-point geostatistical estimation results are compared with those of the inverse distance weighted and ordinary Kriging methods. Deviation, trend, and variogram analyses are used to assess the effect of multipoint geostatistical estimation. This study shows that reducing the samples participating in the estimation can reduce the maximum and minimum deviation of the estimated grade to a certain extent. The grade distribution pattern is the primary factor affecting minimum and maximum deviation. This study proves the reliability and accuracy of the multi-point geostatistical method for ore grade estimation.

Delineation of alteration zones based on artificial neural networks and concentration-volume fractal methods in the hypogene zone of porphyry copper-gold deposit, Masjed-Daghi, East Azerbaijan Province, Iran

In this paper, we aim to achieve two specific objectives. The first one is to examine the applicability of the Artificial Neural Networks (ANNs) technique in ore grade estimation. Different training algorithms and numbers of hidden neurons are applied to estimate Cu grade of borehole data in the hypogene zone of porphyry copper-gold deposit, Masjed-Daghi, East Azerbaijan Province (Iran). The efficacy of ANNs in function-learning and estimation is compared with ordinary kriging (OK). As the kriging algorithms smooth the data, their applicability in the pre-processing of data for fractal analysis is not conducive. ANNs can be introduced as an alternative for this kind of problem. Secondly, we aim to delineate the potassic and phyllic alteration regions in the hypogene zone of Cu-Au porphyry deposit based on the estimation obtained by the ANNs and OK methods, and utilize the Concentration-Volume (C-V) fractal model. In this regard, at first, C-V log-log is generated based on the ANN results. The plots are then used to determine the Cu threshold values for the alteration zones. To investigate the correlation between the geological model and C-V fractal results, the log ratio matrix is applied. The results obtained show that Cu values less than 0.38% from ANNs have more overlapped voxels with phyllic alteration zone by an overall accuracy of 0.72. Spatial correlation between the potassic alteration zones resulting from 3D geological modeling and high concentration zones in C-V fractal model show that Cu values greater than 0.38% have more voxels overlapped with the potassic alteration zone by an overall accuracy of 0.76. Generally, the results obtained show that a combination of the ANNs and C-V fractal methods can be a suitable and robust tool for quantitative modeling of alteration zones instead of the qualitative methods.

Multi-scale mapping of oil-sands in Anhembi (Brazil) using imaging spectroscopy

In this work, oil-sand outcrops of the Anhembi deposit located in the Paraná Basin, Brazil, were investigated using multi-scale imaging spectroscopy. The study incorporated VNIR–SWIR (400–2500 nm) spectroscopic data from imaging (i.e. sisuCHEMA) and nonimaging (i.e. FieldSpec-4) instruments in the lab, an AisaFENIX hyperspectral system on the ground and from the air, and WorldView-3 multispectral instrument. The aim was to assess the usefulness of emerging remote sensing technologies in characterizing hydrocarbon-bearing targets and understand the spatial variability of oil-sands at different scales using multi-source spectroscopic data. The bitumen content of the sands, estimated to be as high as 12 wt. %, was revealed to be unevenly distributed at all scales. Its distribution was shown to be controlled mainly by the clay proportion and permo-porosity of the strata, with the sand sheet facies corresponding to the highest bitumen contents. The ubiquitous clays, identified to be dominantly montmorillonite, were found to be intimately mixed with bitumen at all studied scales. The mean bitumen content was estimated to decrease from ˜ 6 to 4.5% while moving from small-, to deposit-scale as a consequence of the pixel aggregation effect and incremental clay contribution. The study showed that bitumen determination on the ground requires an imaging system with a high signal-to-noise ratio and good illumination conditions. Spectral denoising is also a crucial prerequisite for the extraction of coherent spectral information from the data. WV-3 data was proved capable of resolving HC’s feature at 1700 nm wavelength by its SWIR band-4 over targets encompassing >30% of the 7.5 m SWIR pixel; albeit it was not successful in determining the total bitumen content of the sands. This work indicated that HC signatures, particularly the one centered at 2300 nm, is consistent and comparable among scales, and upon employing properly calibrated data, could be used to confidently map the bitumen content of oil-sands at all imaging scales. A multi-scale spectroscopic approach can provide a complete picture of the variations in geologic targets and is able to fill the gap in scale differences across scales that when integrated, would add synergy and help reduce the uncertainties associated with ore grade estimation.

A new multiple-point grade estimation method by implicit volterra series

Ore grade estimation plays an important role in recoverable resource calculations and mining projects. Classic geostatistical estimation methods are based on two-point statistics and cannot make use of multiple-point and higher-order statistics of the data. Very few studies have been conducted on determination of the possible effects of these features on the results of ore grade estimation. In view of this, the present study introduced a new multiple-point interpolation method based on the implicit Volterra series. In this regard, least square support vector machines (LS-SVM) were used to implicitly estimate the Volterra series coefficients. Regularized risk minimization in the LS-SVM can increase generalization of the Volterra series and reduce sensitivity of these series to data noise. Also, conjugate gradient iterative algorithm was used to solve the linear equations of the implicit Volterra series estimation problem. This sets the stage to solve large-scale problems for Volterra series. With the use of Volterra series, multiple-point multiplicative interactions of spatial data can be used in the ore grade estimation process. In this study, multiple point spatial templates were used to extract multiplicative features of the input data. Therefore, an algorithm was presented to search the 3D space by these templates. The applicability of the regularized implicit Volterra series in capturing the higher-order features of the spatial data is successfully evaluated in a synthetic example. Also, the generalization ability of the introduced method is successfully examined in a synthetic 2D example and one real 3D mining example at the Sarcheshmeh porphyry copper deposit. The results revealed that the introduced multiple-point method could present better results than the ordinary kriging method.