Radial Basis Function Network for Ore Grade Estimation

This paper highlights the performance of a radial basis function (RBF) network for ore grade estimation in an offshore placer gold deposit. Several pertinent issues including RBF model construction, data division for model training, calibration and validation, and efficacy of the RBF network over the kriging and the multilayer perceptron models have been addressed in this study. For the construction of the RBF model, an orthogonal least-square algorithm (OLS) was used. The efficacy of this algorithm was testified against the random selection algorithm. It was found that OLS algorithm performed substantially better than the random selection algorithm. The model was trained using training data set, calibrated using calibration data set, and finally validated on the validation data set. However, for accurate performance measurement of the model, these three data sets should have similar statistical properties. To achieve the statistical similarity properties, an approach utilizing data segmentation and genetic algorithm was applied. A comparative evaluation of the RBF model against the kriging and the multilayer perceptron was then performed. It was seen that the RBF model produced estimates with the R ² (coefficient of determination) value of 0.39 as against of 0.19 for the kriging and of 0.18 for the multilayer perceptron.     

Evaluation of Diverse Geometric and Geostatistical Estimation Methods Applied to Annual Precipitation in Asturias (NW Spain)

Several alternative estimation and interpolation methods for making annual precipitation maps of Asturias are analysed. The data series in this study corresponds to the year 2003. There exists an evident relationship between precipitation and altitude, with a high correlation coefficient of 0.70, that reflects the hillside effect; that is, the increase in the amount of precipitation in more mountainous areas. The direct spatial variability of precipitation and of altitude and the cross variability of precipitation–altitude are defined by two exponential variogram models: one with a short-range structure (15–30 km) that reflects the control exerted by the lesser, local mountain ranges over the amount of precipitation; and another with a long-range structure (80 km) that supposes the influence over precipitation of the major mountainous alignments of the inland areas of the Cantabrian Mountain Range (Cordillera Cantábrica) situated between 60 and 90 km from the coastline. These variogram models had to be validated for coregionalization by the Pardo-Igúzquiza and Dowd method so as to be able to make the cokriging map. The geometric estimation methods employed were triangulation and inverse distance. The geostatistical estimation methods developed were simple kriging, ordinary kriging, kriging with a trend model (universal kriging), lognormal kriging, and cokriging. In all of these methods, a 3 × 3 km² grid was selected with a total of 2580 points to estimate, a circular search window of 60 km, and a relatively small number of samples with the aim of highlighting the local features and variations on isohyet maps. The kriging methods were implemented using the WinGslib software, incorporating two specific programs, Prog2 and Fichsurf, so as to be able then to make isohyet maps using the Surfer software. All the methods employed, apart from triangulation, rendered realistic maps with good fits to the values of the original data (precipitation) of the sample maps. The problem with triangulation lies not in the reliability of the estimates but in the fact that it gives rise to contrived maps because of the tendency of isohyets to present abundant triangular facets. The reliability of the methods was based on cross-validation analysis and on evaluation of the different types of errors, both in their values and in their graphical representations. Substantial differences were not found in the values of the errors that might discriminate some methods from others in an evident way. Bearing the aforesaid in mind, should we have to make an evaluation of the different estimation methods in decreasing order of acceptance, this would be: kriging with a trend model, inverse distance, cokriging, lognormal kriging, ordinary kriging, simple kriging, and triangulation. The application of other estimation methods such as colocated cokriging, kriging with an external drift, and kriging of variable local means (residual kriging) is dependent on the availability of a digital model of the terrain with an altitude grid of the region.     

Spatial Prediction of Lateral Variability of a Laterite-Type Bauxite Horizon Using Ancillary Ground-Penetrating Radar Data

Tropical laterite-type bauxite deposits often pose a unique challenge for resource modelling and mine planning due to the extreme lateral variability at the base of the bauxite ore unit within the regolith profile. An economically viable drilling grid is often rather sparse for traditional prediction techniques to precisely account for the lateral variability in the lower contact of a bauxite ore unit. However, ground-penetrating radar (GPR) offers an inexpensive and rapid method for delineating laterite profiles by acquiring fine-scale data from the ground. These numerous data (secondary variable) can be merged with sparsely spaced borehole data (primary variable) through various statistical and geostatistical techniques, provided that there is a linear relation between the primary and secondary variables. Four prediction techniques, including standard linear regression, simple kriging with varying local means, co-located cokriging and kriging with an external drift, were used in this study to incorporate exhaustive GPR data in predictive estimation the base of a bauxite ore unit within a lateritic bauxite deposit in Australia. Cross-validation was used to assess the performance of each technique. The most robust estimates are produced using ordinary co-located cokriging in accordance with the cross-validation analysis. Comparison of the estimates against the actual mine floor indicates that the inclusion of ancillary GPR data substantially improves the quality of the estimates representing the bauxite base surface.     

Sparse Data Division Using Data Segmentation and Kohonen Network for Neural Network and Geostatistical Ore Grade Modeling in Nome Offshore Placer Deposit

In this paper, sparse data problem in neural network and geostatistical modeling for ore-grade estimation was addressed in the Nome offshore placer gold deposit. The problem of sparse data arises because of the random data division into training, validation, and test subsets during ore-grade modeling. In this regard, the possibility of generating statistically dissimilar data subsets by random data division was also explored through a simulation exercise. A combined approach of data segmentation and application of a Kohonen network then was used to solve the data division problem. Two neural networks and five kriging models were applied for grade modeling. The neural network was trained using an early stopping method. Performance evaluation of the models was carried out on the test data set. The study results indicated that all the models that were investigated in this study performed almost equally. It was also revealed that by using the secondary variable watertable depth the neural network and the kriging models slightly improved their prediction precision. Further, the overall R ² of the models was poor as a result of high nugget (noisy) component in ore-grade variation.     

Comparison Between Kriging Variance and Interpolation Variance as Uncertainty Measurements in the Capanema Iron Mine, State of Minas Gerais—Brazil

The Capanema Mine, an iron ore deposit, is located in the central portion of the Quadrilátero Ferrífero, State of Minas Gerais, southeastern Brazil. Mine development data from approximately 7000 drillholes were used for a comparative study between kriging variance and interpolation variance as uncertainty measurements associated with ordinary kriging estimates. As known, the traditional kriging variance does not depend on local data and, therefore, does not measure the actual dispersion of data. On the other hand, the interpolation variance measures adequately the local dispersion of data used for an ordinary kriging estimate. This paper presents an application of the concept of interpolation variance for measuring uncertainties associated with ordinary kriging estimates of Fe and silica grades. These data were selected for their distinct statistical characteristics with Fe presenting a negatively skewed distribution and, consequently, a low dispersion, and silica a positively skewed distribution and, therefore, a high variability. Comparative studies between the two uncertainty measurements associated with ordinary kriging estimates of Fe and silica proved the superiority of the interpolation variance as a reliable and precise alternative to the kriging variance.     

基于遥感和机器学习的内陆水体水深反演技术

文章主要根据机器学习算法（随机森林算法和极端梯度提升算法）和遥感水深反演的原理,利用Sentinel_2多光谱卫星数据和无人船实测水深数据,对内陆水体——梅州水库建立了随机森林（RF）、极端梯度提升（XGBoost）和支持向量机（SVM）水深反演模型,并对反演结果进行对比分析。结果表明：1）RF的训练精度为97%,测试精度为0.80;XGBoost模型的训练精度为97%,测试精度为0.79;SVM的训练精度为90%,测试精度为0.78。说明了在水深预测方面RF模型和XGBoost模型比SVM模型表现更好,对各个区段的水深值较为敏感。2）根据运行时间考察各个模型的效率,其中RF模型从读取数据至输出结果耗时3.92 s;XGBoost模型4.26 s;SVM模型6.66 s。因此,在反演精度和效率上RF模型优于XGBoost模型优于SVM模型,且RF模型的预测结果图细节更加丰富,轮廓更加分明;XGBoost模型次之,但总体效果也较好;SVM模型表现最差。由此可知,机器学习水深反演模型获得的水深结果精度明显提高,解决了传统水深反演模型精度不高的问题。     

Unbiased Resource Evaluations with Kriging and Stochastic Models of Heterogeneous Rock Properties

This paper revisits the computation of product combinations for quantification of resources (e.g., pore volume for hydrocarbon reservoir formations). The explanations have been simplified by considering the exhaustive numerical model for properties that are multiplied first and then added or averaged for evaluation. The analysis starts without any probabilistic considerations. Abbreviated (up-scaled) computations in the sum of multiplications are proposed by substituting the individual values by averages for each rock property in the coarser cell resolution model. A result found is that averaged properties can be utilized for estimation at non-sampled locations, instead of individual values; however, covariances and cumulants must also be included in the abbreviated computations. The smoothing effect of kriging is found to be irrelevant if the kriging variance is also included in the up-scaled abbreviated pore volume computations. Thus, the equivalence between computation of resource volumes from kriging estimates and conditional stochastic simulations is established, with the condition that numerical estimation must incorporate the complete covariance and cumulant information as well. An example shows pore volume prediction from a kriging model matches the unbiased result from stochastic simulations.     

Machine learning predictions of passive microwave brightness temperature over snow-covered land using the special sensor microwave imager (SSM/I)

Abstract

Two different forms of machine learning – an artificial neural network (ANN) and a support vector machine (SVM) – are used to estimate passive microwave (PMW) brightness temperatures (Tb) as observed by the special sensor microwave imager (SSM/I) satellite sensor over snow- covered land in North America. Both techniques reasonably reproduce unbiased estimates of SSM/I observations at 19.35 and 37.0 GHz for both vertically- and horizontally-polarized channels. When compared against SSM/I observations not used during training, domain-averaged statistics from 1 September 1987 to 1 September 2002 yielded a root mean squared error (RMSE) of less than 9 K for all frequency and polarization combinations examined in this study. Even though both ML techniques reasonably reproduced SSM/I Tb observations, the SVM outperformed the ANN because the SVM: (1) better captured the high-frequency (i.e. day-to-day) temporal characteristics in the Tb observations across the majority of the study domain, (2) better reproduced the spatial variability as a function of snow classification, and (3) yielded greater sensitivity to snow-related input variables during the estimation of PMW Tb. These findings reinforce previous research of SVM-based estimation of PMW Tb employing observations from the advanced microwave scanning radiometer.     

Strength of Stacking Technique of Ensemble Learning in Rockburst Prediction with Imbalanced Data: Comparison of Eight Single and Ensemble Models

Rockburst is a common dynamic geological hazard, severely restricting the development and utilization of underground space and resources. As the depth of excavation and mining increases, rockburst tends to occur frequently. Hence, it is necessary to carry out a study on rockburst prediction. Due to the nonlinear relationship between rockburst and its influencing factors, artificial intelligence was introduced. However, the collected data were typically imbalanced. Single algorithms trained by such data have low recognition for minority classes. In order to handle the problem, this paper employed stacking technique of ensemble learning to establish rockburst prediction models. In total, 246 sets of data were collected. In the preprocessing stage, three data mining techniques including principal component analysis, local outlier factor and expectation maximization algorithm were used for dimension reduction, outlier detection and outlier substitution, respectively. Then, the pre-processed data were split into a training set (75%) and a test set (25%) with stratified sampling. Based on the four classical single intelligent algorithms, namely k-nearest neighbors (KNN), support vector machine (SVM), deep neural network (DNN) and recurrent neural network (RNN), four ensemble models (KNN–RNN, SVM–RNN, DNN–RNN and KNN–SVM–DNN–RNN) were built by stacking technique of ensemble learning. The prediction performance of eight models was evaluated, and the differences between single models and ensemble models were analyzed. Additionally, a sensitivity analysis was conducted, revealing the importance of input variables on the models. Finally, the impact of class imbalance on the prediction accuracy and fitting effect of models was quantitatively discussed. The results showed that stacking technique of ensemble learning provides a new and promising way for rockburst prediction, which exhibits unique advantages especially when using imbalanced data.

     

Landslide susceptibility mapping based on Support Vector Machine: A case study on natural slopes of Hong Kong, China

The Support Vector Machine (SVM) is an increasingly popular learning procedure based on statistical learning theory, and involves a training phase in which the model is trained by a training dataset of associated input and target output values. The trained model is then used to evaluate a separate set of testing data. There are two main ideas underlying the SVM for discriminant-type problems. The first is an optimum linear separating hyperplane that separates the data patterns. The second is the use of kernel functions to convert the original non-linear data patterns into the format that is linearly separable in a high-dimensional feature space. In this paper, an overview of the SVM, both one-class and two-class SVM methods, is first presented followed by its use in landslide susceptibility mapping. A study area was selected from the natural terrain of Hong Kong, and slope angle, slope aspect, elevation, profile curvature of slope, lithology, vegetation cover and topographic wetness index (TWI) were used as environmental parameters which influence the occurrence of landslides. One-class and two-class SVM models were trained and then used to map landslide susceptibility respectively. The resulting susceptibility maps obtained by the methods were compared to that obtained by the logistic regression (LR) method. It is concluded that two-class SVM possesses better prediction efficiency than logistic regression and one-class SVM. However, one-class SVM, which only requires failed cases, has an advantage over the other two methods as only “failed” case information is usually available in landslide susceptibility mapping.     

Selection of Optimal Thresholds for Estimation and Simulation Based on Indicator Values of Highly Skewed Distributions of Ore Data

This study strives to outline a geostatistics model for estimation and simulation of the Qolqoleh gold ore deposit located in Saqqez, NW of Iran. Considering that this gold deposit contains high-grade values, accurate evaluation of such values is of high importance, and therefore different methods based on indicator values, such as full indicator kriging (FIK) and sequential indicator simulation (SIS), have been employed to improve the accuracy of estimation and simulation of high-grade values. FIK and SIS cover the full range of grades based on several thresholds on the indicator data. The cumulative distribution function (CDF) is typically used for selection of threshold values. Given the highly skewed distribution of gold grade and its intense fluctuations, the number of thresholds is increased using CDF, which in turn results in a whole lot of calculations. To reduce the volume of calculations, the number–size (N–S) fractal model has been used to select thresholds. From such a model, all optimal thresholds are chosen with respect to geology and the unnecessary thresholds are excluded from selection. Thus, a study of the selection of optimal thresholds for estimation and simulation of a gold ore resource by means of FIK and SIS, respectively, based on thresholds selected using the N–S fractal model is presented. Finally, it is proved that results of these geostatistical methods based on thresholds selection from the N–S model appear to be better-positioned to explain ore grade variability compared to thresholds selected from the CDF and threshold selection from the N–S model is more effective for reducing the volume of required calculations.     

Application of Discriminant Analysis and Support Vector Machine in Mapping Gold Potential Areas for Further Drilling in the Sari-Gunay Gold Deposit,NW Iran

In this contribution, we used discriminant analysis (DA) and support vector machine (SVM) to model subsurface gold mineralization by using a combination of the surface soil geochemical anomalies and earlier bore data for further drilling at the Sari-Gunay gold deposit, NW Iran. Seventy percent of the data were used as the training data and the remaining 30 % were used as the testing data. Sum of the block grades, obtained by kriging, above the cutoff grade (0.5 g/t) was multiplied by the thickness of the blocks and used as productivity index (PI). Then, the PI variable was classified into three classes of background, medium, and high by using fractal method. Four classification functions of SVM and DA methods were calculated by the training soil geochemical data. Also, by using all the geochemical data and classification functions, the general extension of the gold mineralized zones was predicted. The mineral prediction models at the Sari-Gunay hill were used to locate high and moderate potential areas for further infill systematic and reconnaissance drilling, respectively. These models at Agh-Dagh hill and the area between Sari-Gunay and Agh-Dagh hills were used to define the moderate and high potential areas for further reconnaissance drilling. The results showed that the nu-SVM method with 73.8 % accuracy and c-SVM with 72.3 % accuracy worked better than DA methods.     

The Precision of C Stock Estimation in the Ludhikola Watershed Using Model-Based and Design-Based Approaches

In this study, two sampling protocols using a model-based and a design-based framework were juxtaposed to evaluate their precision in the estimation of C stock in the Ludikhola watershed, Nepal. The model-based approach exploits the spatial dependencies in the sampled variable and may therefore be attractive over the design-based approach as it reduces the substantial costs of survey and effort required in the latter. Scales of spatial variability for C stock which resulted in a grid resolution of 10,000 m² were determined using a reconnaissance variogram. Akaike information criterion was used for the selection of the best linear model of feature space for use in kriging with external drift (KED). Among the five tested covariates, distance, elevation, and aspect were statistically significant, with the best model of feature space accounting for 87.7% variability of C stock. An ANOVA established significance differences in mean C stocks (P = 0.00017). KED using the best model of feature space was found to be more precise, (9.89 ± 0.17) sqrt mg C/ha, than a pure-based approach of ordinary kriging and the design-based approach, (9.91 ± 0.8) sqrt mg C/ha. The confidence bounds of the two estimators showed that their confidence intervals will overlap 99.7% of the time, with both confidence intervals falling within the 95% confidence bounds of each other. There is less uncertainty around the mean C stock estimated using the model-based approach than the mean C stock estimated using the design-based approach. The model-based approach is a prospective option for the REDD framework.     

Bayesian and Neural Network Approaches to Estimate Deep Temperature Distribution for Assessing a Supercritical Geothermal System: Evaluation Using a Numerical Model

The temperature distribution at depth is a key variable when assessing the potential of a supercritical geothermal resource as well as a conventional geothermal resource. Data-driven estimation by a machine-learning approach is a promising way to estimate temperature distributions at depth in geothermal fields. In this study, we developed two methodologies—one based on Bayesian estimation and the other on neural networks—to estimate temperature distributions in geothermal fields. These methodologies can be used to supplement existing temperature logs, by estimating temperature distributions in unexplored regions of the subsurface, based on electrical resistivity data, observed geological/mineralogical boundaries, and microseismic observations. We evaluated the accuracy and characteristics of these methodologies using a numerical model of the Kakkonda geothermal field, Japan, where a temperature above 500 °C was observed below a depth of about 3.7 km. When using geological and geophysical knowledge as prior information for the machine learning methods, the results demonstrate that the approaches can provide subsurface temperature estimates that are consistent with the temperature distribution given by the numerical model. Using a numerical model as a benchmark helps to understand the characteristics of the machine learning approaches and may help to identify ways of improving these methods.

     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Prediction of Arsenic in Bedrock Derived Stream Sediments at a Gold Mine Site Under Conditions of Sparse Data

Arsenic is often present in gold mining areas. The high sensitivity of arsenic to biogeochemical conditions may lead to catastrophic consequences through contamination of resources such as ground water. Therefore, it is critical to understand the spatial occurrence of arsenic across a given site. Previous studies using traditional pattern recognition techniques such as neural networks and kriging have not been entirely successful in predicting arsenic concentrations across a gold mining area. The methods used in this paper are the support vector machines (SVM) and robust least-square support vector machines (robust LS-SVM). The two techniques were used to predict arsenic concentrations in the sediments of Circle City, Alaska, using the gold concentration distribution present within the sediments. The analysis of the results shows an improved performance and better predictive capabilities of SVM and robust LS-SVM than that of the neural networks and kriging techniques. The robust LS-SVM performed better than the SVM. The performance of the SVM was affected by outliers. The removal of the outliers from the data set and application of SVM showed improved results.     

喀斯特地区春季土壤水分空间插值方法对比

以杨眉河小流域为研究区,通过土壤水分采样,选取辅助变量,采用普通克里金、协同克里金、回归克里金3种地统计学方法对土壤水分数据进行空间插值。结果表明：1）回归克里金对研究区土壤水分估算误差最小,其次为协克里金,普通克里金的误差最大;2）普通克里金生成的土壤水分表面最为平滑,而回归克里金最大程度反映了研究区实际的土壤水分空间变化;3）对于协同克里金,以湿度指数（WI）样点数据作为辅助变量的估算误差小于将WI栅格数据作为辅助变量的估算误差。总之,在可获得有效辅助变量的条件下,回归克里金对研究区土壤水分估算的效果优于协同克里金与普通克里金。     

Grade and Tonnage Uncertainty Analysis of an African Copper Deposit Using Multiple-Point Geostatistics and Sequential Gaussian Simulation

Spatial uncertainty analysis is a complex and difficult task for orebody estimation in the mining industry. Conventional models (kriging and its variants) with variogram-based statistics fail to capture the spatial complexity of an orebody. Due to this, the grade and tonnage are incorrectly estimated resulting in inaccurate mine plans, which lead to costly financial decision. Multiple-point geostatistical simulation model can overcome the limitations of the conventional two-point spatial models. In this study, a multiple-point geostatistical method, namely SNESIM, was applied to generate multiple equiprobable orebody models for a copper deposit in Africa, and it helped to analyze the uncertainty of ore tonnage of the deposit. The grade uncertainty was evaluated by sequential Gaussian simulation within each equiprobable orebody models. The results were validated by reproducing the marginal distribution and two- and three-point statistics. The results show that deviations of volume of the simulated orebody models vary from ? 3 to 5% compared to the training image. The grade simulation results demonstrated that the average grades from the different simulation are varied from 3.77 to 4.92% and average grade 4.33%. The results also show that the volume and grade uncertainty model overestimates the orebody volume as compared to the conventional orebody. This study demonstrates that incorporating grade and volume uncertainty leads to significant changes in resource estimates.     

Improving Coal Quality Estimations with Geostatistics and Geophysical Logs

In most modern coal mines, there are many coal quality parameters that are measured on samples taken from boreholes. These data are used to generate spatial models of the coal quality parameters, typically using inverse distance as an interpolation method. At the same time, downhole geophysical logging of numerous additional boreholes is used to measure various physical properties but no coal quality samples are taken. The work presented in this paper uses two of the most important coal quality variables—ash and volatile matter—and assesses the efficacy of using a number of geostatistical interpolation methods to improve the accuracy of the interpolated models, including the use of auxiliary variables from geophysical logs. A multivariate spatial statistical analysis of ash, volatile matter and several auxiliary variables is used to establish a co-regionalization model that relates all of the variables as manifestations of an underlying geological characteristic. A case study of a coal mine in Queensland, Australia, is used to compare the interpolation methods of inverse distance to ordinary kriging, universal kriging, co-kriging, regression kriging and kriging with an external drift. The relative merits of these six methods are compared using the mean error and the root mean square error as measures of bias and accuracy. The study demonstrates that there is significant opportunity to improve the estimations of coal quality when using kriging with an external drift. The results show that when using the depth of a sample as an external drift variable there is a significant improvement in the accuracy of estimation for volatile matter, and when using wireline density logs as the drift variable there is improvement in the estimation of the in situ ash. The economic benefit of these findings is that cheaper proxies for coal quality parameters can significantly increase data density and the quality of estimations.