Classification of mineral deposits into types using mineralogy with a probabilistic neural network

In order to determine whether it is desirable to quantify mineral-deposit models further, a test of the ability of a probabilistic neural network to classify deposits into types based on mineralogy was conducted. Presence or absence of ore and alteration mineralogy in well-typed deposits were used to train the network. To reduce the number of minerals considered, the analyzed data were restricted to minerals present in at least 20% of at least one deposit type. An advantage of this restriction is that single or rare occurrences of minerals did not dominate the results. Probabilistic neural networks can provide mathematically sound confidence measures based on Bayes theorem and are relatively insensitive to outliers. Founded on Parzen density estimation, they require no assumptions about distributions of random variables used for classification, even handling multimodal distributions. They train quickly and work as well as, or better than, multiple-layer feedforward networks. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class and each variable. The training set was reduced to the presence or absence of 58 reported minerals in eight deposit types. The training set included: 49 Cyprus massive sulfide deposits; 200 kuroko massive sulfide deposits; 59 Comstock epithermal vein gold districts; 17 quartzalunite epithermal gold deposits; 25 Creede epithermal gold deposits; 28 sedimentary-exhalative zinc-lead deposits; 28 Sado epithermal vein gold deposits; and 100 porphyry copper deposits. The most common training problem was the error of classifying about 27% of Cyprus-type deposits in the training set as kuroko. In independent tests with deposits not used in the training set, 88% of 224 kuroko massive sulfide deposits were classed correctly, 92% of 25 porphyry copper deposits, 78% of 9 Comstock epithermal gold-silver districts, and 83% of six quartzalunite epithermal gold deposits were classed correctly. Across all deposit types, 88% of deposits in the validation dataset were correctly classed. Misclassifications were most common if a deposit was characterized by only a few minerals, e.g., pyrite, chalcopyrite,and sphalerite. The success rate jumped to 98% correctly classed deposits when just two rock types were added. Such a high success rate of the probabilistic neural network suggests that not only should this preliminary test be expanded to include other deposit types, but that other deposit features should be added     

Monte Carlo Simulations of Product Distributions and Contained Metal Estimates

Estimation of product distributions of two factors was simulated by conventional Monte Carlo techniques using factor distributions that were independent (uncorrelated). Several simulations using uniform distributions of factors show that the product distribution has a central peak approximately centered at the product of the medians of the factor distributions. Factor distributions that are peaked, such as Gaussian (normal) produce an even more peaked product distribution. Piecewise analytic solutions can be obtained for independent factor distributions and yield insight into the properties of the product distribution. As an example, porphyry copper grades and tonnages are now available in at least one public database and their distributions were analyzed. Although both grade and tonnage can be approximated with lognormal distributions, they are not exactly fit by them. The grade shows some nonlinear correlation with tonnage for the published database. Sampling by deposit from available databases of grade, tonnage, and geological details of each deposit specifies both grade and tonnage for that deposit. Any correlation between grade and tonnage is then preserved and the observed distribution of grades and tonnages can be used with no assumption of distribution form.     

Enrichment Ratio-Tonnage Diagrams for Resource Assessment

The enrichment ratio (ER), defined as the ratio of grade of a metal element in a deposit to the crustal abundance of the metal, is proposed for assessing mineral resources. According to the definition, the enrichment ratio of a polymetallic deposit is given as a sum of enrichment ratios of all metals. The relation between ER and the cumulative tonnage integrated from the high ER side of about 4750 deposits in the world is approximated by the combination of three exponential functions crossing at ER values of 16 · 10³ and 600. High ER deposits are expected for the commodities Ag, Pb, and Au+Ag, and for epithermal, mesothermal, unconformity-related and vein types. In contrast, low ER deposits are typical for the commodities Cu, Mn, Mo, Ni, and U, and for chemically precipitated, Cyprus, laterite, orthomagmatic, pegmatite, placer, porphyry, and sandstone deposits. The critical ER value of the low ER class (the differential metal amount decreases with decreasing ER in the regions lower than the value) is 250 in all deposits, 610 in W+Mo, 2800 in Pb+Zn and 360 in Au+Ag, 530 in massive sulfides, 160 in the orthomagmatic type, 170 in placers, 220 in the porphyry type, 1900 in the replacement type, 580 in the stratabound type, 3400 in the unconformity-related type, and 1700 in vein type deposits. The frequency proportion determined by a keyword and a commodity provides valuable suggestions for mineral exploration: for example, the exploration target for chromite is a deposit characterized as orthomagmatic, whereas the expected commodity of a newly developed orthomagmatic deposit is chromite.     

Ore value-tonnage diagrams for resource assessment

An ore value-tonnage diagram has been proposed for assessing mineral resources. Diagrams of W+Mo, and Pb+Zn deposits show a good linearity between ore value and logarithms of cumulative ore tonnage. Diagrams of the massive sulfide, orthomagmatic, placer, porphyry, replacement, and stratabound types are also linear. It is assumed, therefore, that deposits of each of these commodities and these types belong to a single population. In contrast, the ore value-tonnage relations of all the deposits analyzed here is approximated by the combination of two exponential functions. The same feature is seen for deposits of the Cu+W+Mo, Cu+Pb+Zn, and Au+Ag commodities, and of the vein and unconformity-related types. This suggests that deposits belonging to each of such categories are divided into the high and low value groups. We can expect, accordingly, to find high value deposits of such categories.     

Computer Monte Carlo simulation in quantitative resource estimation

The method of making quantitative assessments of mineral resources sufficiently detailed for economic analysis is outlined in three steps. The steps are (1) determination of types of deposits that may be present in an area, (2) estimation of the numbers of deposits of the permissible deposit types, and (3) combination by Monte Carlo simulation of the estimated numbers of deposits with the historical grades and tonnages of these deposits to produce a probability distribution of the quantities of contained metal.Two examples of the estimation of the number of deposits (step 2) are given. The first example is for mercury deposits in southwestern Alaska and the second is for lode tin deposits in the Seward Peninsula.The flow of the Monte Carlo simulation program is presented with particular attention to the dependencies between grades and tonnages of deposits and between grades of different metals in the same deposit.     

On a proposed plutonic porphyry gold deposit model

A plutonic porphyry gold deposit model is proposed that is imilar to the plutonic porphyry copper deposit model. However, unlike the plutonic porphyry copper deposit model, the proposed model is deficient in copper and contains less than 1 percent total sulfides. In the proposed model, gold is accompanied by scheelite, molybdenite, arsenopyrite, a variety of bismuth sulfides, tellurides, and native bismuth. The host rock varies from granite to granodiorite stock. Most of the ore is in the pluton. Deposits cited as examples of the proposed model are the Mokrsko deposit in Czechoslovakia, the Fort Knox deposit in the United States, and the Dublin Gulch deposit in Canada. In each of these deposits, pervasive potassic or phyllic alteration zones accompany the gold ore, which is disseminated in quartz-rich stockworks, veinlet swarms, and veins. Tonnages of gold-bearing material are large, but grades are low in the cited deposits. The proposed model is distinct from other gold deposit models because of the low Cu to Au ratio and the association of Au, Bi, W, and Mo.     

Examining Risk in Mineral Exploration

Successful mineral exploration strategy requires identification of some of the risk sources and considering them in the decision-making process so that controllable risk can be reduced. Risk is defined as chance of failure or loss. Exploration is an economic activity involving risk and uncertainty, so risk also must be defined in an economic context. Risk reduction can be addressed in three fundamental ways: (1) increasing the number of examinations; (2) increasing success probabilities; and (3) changing success probabilities per test by learning. These provide the framework for examining exploration risk. First, the number of prospects examined is increased, such as by joint venturing, thereby reducing chance of gambler's ruin. Second, success probability is increased by exploring for deposit types more likely to be economic, such as those with a high proportion of world-class deposits. For example, in looking for 100+ ton (>3 million oz) Au deposits, porphyry Cu-Au, or epithermal quartz alunite Au types require examining fewer deposits than Comstock epithermal vein and most other deposit types. For porphyry copper exploration, a strong positive relationship between area of sulfide minerals and deposits' contained Cu can be used to reduce exploration risk by only examining large sulfide systems. In some situations, success probabilities can be increased by examining certain geologic environments. Only 8% of kuroko massive sulfide deposits are world class, but success chances can be increased to about 15% by looking in settings containing sediments and rhyolitic rocks. It is possible to reduce risk of loss during mining by sequentially developing and expanding a mine—thus reducing capital exposed at early stages and reducing present value of risked capital. Because this strategy is easier to apply in some deposit types than in others, the strategy can affect deposit types sought. Third, risk is reduced by using prior information and by changing the independence of trials assumption, that is, by learning. Bayes' formula is used to change the probability of existence of the deposit sought on the basis of successive exploration stages. Perhaps the most important way to reduce exploration risk is to employ personnel with the appropriate experience and yet who are learning.     

Sensitivity Analysis of a Feedforward Neural Network for Considering Genetic Mechanisms of Kuroko Deposits

Exploration for volcanogenic massive sulfide deposits of the kuroko-type is underway in many places. Clarifying the spatial patterns of the metals in kuroko deposits will be useful for understanding their genetic mechanisms and for future exploration of such types of deposits. This study represents a spatial distribution analysis on the contents of principal metals of kuroko deposits: Cu, Pb, and Zn, in the Hokuroku district, northern Japan, by a feedforward neural network and 1917 sample data at 143 drillhole sites. The network, which consists of three layers, was trained by the principle of SLANS in which the numbers of neurons in the middle layer and training data are changed to improve estimation accuracy. Using the weight coefficients connecting adjacent neurons, sensitivity analysis of the neural network was carried out to identify factors influencing spatial distributions of the three metals. The coordinates depth (z) direction, Bouguer gravity, and specific lithology such as dacite were determined to be influencing factors. The high frequency of the z coordinate signifies that the metal contents differ to a large extent by depth. The sensitivity vector was defined using sensitivity coefficients for x, y, and z coordinates of an estimation point. We determined that the directions of large vectors were different inside and outside of the Hanawa-Ohdate area. This characteristic is considered to originate from the differences in the permeability of fractures that became the paths for rising ore solutions, and the depths that the solutions mixed with sea water.     

Probabilistic Estimates of Number of Undiscovered Deposits and Their Total Tonnages in Permissive Tracts Using Deposit Densities

Empirical evidence indicates that processes affecting number and quantity of resources in geologic settings are very general across deposit types. Sizes of permissive tracts that geologically could contain the deposits are excellent predictors of numbers of deposits. In addition, total ore tonnage of mineral deposits of a particular type in a tract is proportional to the type’s median tonnage in a tract. Regressions using size of permissive tracts and median tonnage allow estimation of number of deposits and of total tonnage of mineralization. These powerful estimators, based on 10 different deposit types from 109 permissive worldwide control tracts, generalize across deposit types. Estimates of number of deposits and of total tonnage of mineral deposits are made by regressing permissive area, and mean (in logs) tons in deposits of the type, against number of deposits and total tonnage of deposits in the tract for the 50th percentile estimates. The regression equations (R ² = 0.91 and 0.95) can be used for all deposit types just by inserting logarithmic values of permissive area in square kilometers, and mean tons in deposits in millions of metric tons. The regression equations provide estimates at the 50th percentile, and other equations are provided for 90% confidence limits for lower estimates and 10% confidence limits for upper estimates of number of deposits and total tonnage. Equations for these percentile estimates along with expected value estimates are presented here along with comparisons with independent expert estimates. Also provided are the equations for correcting for the known well-explored deposits in a tract. These deposit-density models require internally consistent grade and tonnage models and delineations for arriving at unbiased estimates.     

A Comparison of the Weights-of-Evidence Method and Probabilistic Neural Networks

The need to integrate large quantities of digital geoscience information to classify locations as mineral deposits or nondeposits has been met by the weights-of-evidence method in many situations. Widespread selection of this method may be more the result of its ease of use and interpretation rather than comparisons with alternative methods. A comparison of the weights-of-evidence method to probabilistic neural networks is performed here with data from Chisel Lake-Andeson Lake, Manitoba, Canada. Each method is designed to estimate the probability of belonging to learned classes where the estimated probabilities are used to classify the unknowns. Using these data, significantly lower classification error rates were observed for the neural network, not only when test and training data were the same (0.02 versus 23%), but also when validation data, not used in any training, were used to test the efficiency of classification (0.7 versus 17%). Despite these data containing too few deposits, these tests of this set of data demonstrate the neural network's ability at making unbiased probability estimates and lower error rates when measured by number of polygons or by the area of land misclassified. For both methods, independent validation tests are required to ensure that estimates are representative of real-world results. Results from the weights-of-evidence method demonstrate a strong bias where most errors are barren areas misclassified as deposits. The weights-of-evidence method is based on Bayes rule, which requires independent variables in order to make unbiased estimates. The chi-square test for independence indicates no significant correlations among the variables in the Chisel Lake–Andeson Lake data. However, the expected number of deposits test clearly demonstrates that these data violate the independence assumption. Other, independent simulations with three variables show that using variables with correlations of 1.0 can double the expected number of deposits as can correlations of –1.0. Studies done in the 1970s on methods that use Bayes rule show that moderate correlations among attributes seriously affect estimates and even small correlations lead to increases in misclassifications. Adverse effects have been observed with small to moderate correlations when only six to eight variables were used. Consistent evidence of upward biased probability estimates from multivariate methods founded on Bayes rule must be of considerable concern to institutions and governmental agencies where unbiased estimates are required. In addition to increasing the misclassification rate, biased probability estimates make classification into deposit and nondeposit classes an arbitrary subjective decision. The probabilistic neural network has no problem dealing with correlated variables—its performance depends strongly on having a thoroughly representative training set. Probabilistic neural networks or logistic regression should receive serious consideration where unbiased estimates are required. The weights-of-evidence method would serve to estimate thresholds between anomalies and background and for exploratory data analysis.     

肯德可克金钴铋矿石选矿实验

采用预处理—浸出工艺技术,解决了该矿床半氧化矿石中Au、Ag、Co、Ni、Cu、Mo、Bi的选矿技术,使Au、Ag、Co、Ni、Cu、Mo的浸出率达90%以上,Bi的浸出率85%以上。     

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.     

An AHP–TOPSIS Predictive Model for District-Scale Mapping of Porphyry Cu–Au Potential: A Case Study from Salafchegan Area (Central Iran)

The Salafchegan area in central Iran is a greenfield region of high porphyry Cu–Au potential, for which a sound prospectivity model is required to guide mineral exploration. Satellite imagery, geological geochemical, geophysical, and mineral occurrence datasets of the area were used to run an innovative integration model for porphyry Cu–Au exploration. Five favorable multi-class evidence maps, representing diagnostic porphyry Cu–Au recognition criteria (intermediate igneous intrusive and sub-volcanic host rocks, structural controls, hydrothermal alterations, stream sediment Cu anomalies, magnetic signatures), were combined using analytic hierarchy process and technique for order preference by similarity to ideal solution to calculate a final map of porphyry Cu–Au potential in the Salafchegan area.     

Economic Filters Applied to Quantitative Mineral Resource Simulations

The U.S. Geological Survey has developed a technique that allows mineral resource experts to apply economic filters to estimates of undiscovered mineral resources. This technique builds on previous work that developed quantitative methods for mineral resource assessments. A Monte-Carlo calculation uses mineral deposit models to estimate commodity grades and tonnages of undiscovered deposits. The results then are analyzed using simple estimates of capital expenditures and daily operating costs for a mine and associated mill. The daily operating costs and the value of the ore are used to calculate the net present value of the deposit, which is compared to the capital expenditures to determine whether the deposit is economic. Repetition of these calculations for many deposits produces a table that can be interpreted in terms of the probability of there being deposits that have anet present value exceeding some specified amount. Sample calculations indicate that applying economic filters to simulated mineral resources might change the perception of the results compared to presenting the calculations in terms of the expected mean gross-in-place value of the minerals.     

Use of a Probabilistic Neural Network to Reduce Costs of Selecting Construction Rock

Rocks used as construction aggregate in temperate climates deteriorate to differing degrees because of repeated freezing and thawing. The magnitude of the deterioration depends on the rock's properties. Aggregate, including crushed carbonate rock, is required to have minimum geotechnical qualities before it can be used in asphalt and concrete. In order to reduce chances of premature and expensive repairs, extensive freeze-thaw tests are conducted on potential construction rocks. These tests typically involve 300 freeze-thaw cycles and can take four to five months to complete. Less time consuming tests that (1) predict durability as well as the extended freeze-thaw test or that (2) reduce the number of rocks subject to the extended test, could save considerable amounts of money. Here we use a probabilistic neural network to try and predict durability as determined by the freeze-thaw test using four rock properties measured on 843 limestone samples from the Kansas Department of Transportation. Modified freeze-thaw tests and less time consuming specific gravity (dry), specific gravity (saturated), and modified absorption tests were conducted on each sample. Durability factors of 95 or more as determined from the extensive freeze-thaw tests are viewed as acceptable—rocks with values below 95 are rejected. If only the modified freeze-thaw test is used to predict which rocks are acceptable, about 45% are misclassified. When 421 randomly selected samples and all four standardized and scaled variables were used to train aprobabilistic neural network, the rate of misclassification of 422 independent validation samples dropped to 28%. The network was trained so that each class (group) and each variable had its own coefficient (sigma). In an attempt to reduce errors further, an additional class was added to the training data to predict durability values greater than 84 and less than 98, resulting in only 11% of the samples misclassified. About 43% of the test data was classed by the neural net into the middle group—these rocks should be subject to full freeze-thaw tests. Thus, use of the probabilistic neural network would meanthat the extended test would only need be applied to 43% of the samples, and 11% of the rocks classed as acceptable would fail early.     

A Chart for Judging Optimal Sample Spacing for Ore Grade Estimation

Mineral deposit grades are usually estimated using data from samples of rock cores extracted from drill holes. Commonly, mineral deposit grade estimates are required for each block to be mined. Every estimated grade has always a corresponding error when compared against real grades of blocks. The error depends on various factors, among which the most important is the number of correlated samples used for estimation. Samples may be collected on a regular sampling grid and, as the spacing between samples decreases, the error of grade estimated from the data generally decreases. Sampling can be expensive. The maximum distance between samples that provides an acceptable error of grade estimate is useful for deciding how many samples are adequate. The error also depends on the geometry of a block, as lower errors would be expected when estimating the grade of large-volume blocks, and on the variability of the data within the region of the blocks. Local variability is measured in this study using the coefficient of variation (CV). We show charts analyzing error in block grade estimates as a function of sampling grid (obtained by geostatistical simulation), for various block dimensions (volumes) and for a given CV interval. These charts show results for two different attributes (Au and Ni) of two different deposits. The results show that similar errors were found for the two deposits, although they share similar features: sampling grid, block volume, CV, and continuity model. Consequently, the error for other attributes with similar features could be obtained from a single chart.     

Pareto–Lognormal Modeling of Known and Unknown Metal Resources

Recently, large worldwide databases with statistics on amounts of metal in mineral deposits have become available. Frequently, most metal is contained in the largest deposits for a metal. A major problem in meaningful modeling of the size–frequency distributions of the largest deposits is that they are very rare. Until now it was rather difficult to establish the exact form of their size–frequency distribution. However, because of the new very large databases it can now be concluded that two commonly used approaches (lognormal and Pareto) thought to be mutually incompatible in the past, are both correct with a high probability. One approach does not necessarily exclude validity of the other. Patiño-Douce (Nat Resour Res 25(1):97–124, 2016b) has shown that metal tonnage frequency distributions for worldwide metal deposits are approximately lognormal with similar standard deviations (σ) of log-transformed data. In this paper, it is assumed that worldwide metals satisfy both lognormal and Pareto models simultaneously. Copper and Au are taken for example for comparison with results previously obtained for these two metals in the Abitibi area of the Canadian Shield. Worldwide there are 2541 Cu deposits approximately satisfying a lognormal distribution. Total amount of Cu in these deposits is 2.319 × 10⁹ tons of Cu. However, the 45 largest deposits, which together contain 1.281 × 10⁹ tons of Cu, satisfy a Pareto distribution. If their lognormal model would apply in the upper tail as well, these 45 largest deposits should have contained only about 0.076 × 10⁹ tons of Cu. It is shown in detail for Cu that the best statistical model for Cu deposits is a worldwide Pareto–lognormal model in which the basic lognormal size–frequency distribution is flanked by two juxtaposed Pareto distributions for the largest and smallest Cu deposits, respectively. Both Pareto distributions smoothly change into the central lognormal by means of bridge functions that can be determined separately. The worldwide Pareto–lognormal model also was found to be applicable to several other metals, especially Ag, Ni, Pb, and U. For Au, the model does not work as well for the upper tail Pareto distribution as it does for the other metals taken for example.     

Are Fractal Dimensions of the Spatial Distribution of Mineral Deposits Meaningful?

It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically two fractal dimensions over separate non-overlapping spatial scales in the range of 5–1000 km. In particular, one typically observes a local dimension at spatial scales less than 30–60 km, and a regional dimension at larger spatial scales. The deposit type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This density function is only dependent on the distribution of deposits and is independent of the definition of the permissive area. Density functions for porphyry copper deposits appear to be significantly different for regions in the Andes, Mexico, United States, and western Canada. Consequently, depending on which regional density function is used, quite different estimates of numbers of undiscovered deposits can be obtained. These fractal properties suggest that geologic studies based on mapping at scales of 1:24,000 to 1:100,000 may not recognize processes that are important in the formation of mineral deposits at scales larger than the crossover points at 30–60 km.     

Basic concepts in three-part quantitative assessments of undiscovered mineral resources

Since 1975, mineral resource assessments have been made for over 27 areas covering 5×10⁶ km² at various scales using what is now called the three-part form of quantitative assessment. In these assessments, (1) areas are delineated according to the types of deposits permitted by the geology,(2) the amount of metal and some ore characteristics are estimated using grade and tonnage models, and (3) the number of undiscovered deposits of each type is estimated.Permissive boundaries are drawn for one or more deposit types such that the probability of a deposit lying outside the boundary is negligible, that is, less than 1 in 100,000 to 1,000,000.