Metallic Mineral Resources in the Twenty-First Century: II. Constraints on Future Supply

Supplying worldwide demand of metallic raw materials throughout the rest of this century may require 5–10 times the amount of metals contained in known ore deposits. This demand can be met only if mineral deposits containing the required masses of metals, in excess of present day ore reserves, exist in the Earth’s crust. It is, by definition, not known whether or not such mineral deposits exist. On the basis of the statistical distribution of metal tonnages contained in known ore deposits, however, it is possible to place constraints on the size distribution of the deposits that must be discovered in order to meet the expected demand. A nondimensional analysis of the distribution of metal tonnages in deposits of 20 metals shows that most of them follow distributions that, although not strictly lognormal, share important characteristics with a lognormal distribution. Chief among these is the observation that frequency falls off symmetrically and geometrically with deposit size, relative to a median deposit size that is approximately equal to the geometric mean deposit size. An immediate consequence of this behavior is that most of the metal endowment is concentrated in deposits that are several orders of magnitude larger than the median deposit size, and that are much rarer than the most common deposits that cluster around the median deposit size. The analysis reveals remarkable similarities among the statistical distributions of most of the metals included in this study, in particular, the fact that distribution of most metals can be fully described with essentially the same value (about 2–3) of the scale parameter, σ, which is the only parameter needed to describe the behavior of a normalized lognormal variable. This observation makes it possible to derive the following general conclusions, which are applicable to most metals—both scarce and abundant. First, it is unlikely that undiscovered mineral deposits of sizes comparable to those that contain most of the known metal endowment exist in sufficient quantities to supply the expected worldwide demand throughout the rest of this century. Second, if the expected demand is to be met, one must hope that very large deposits, perhaps up to one order of magnitude larger than the largest known deposits, exist in accessible portions of the Earth’s crust, and that these deposits are discovered.     

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.     

Estimates of Number of Undiscovered Deposits of Gold,Silver, Copper,Lead, and Zinc in the United States

Estimates of the number of undiscovered deposits offer a unique perspective on the nation's undiscovered mineral resources. As part of the 1998 assessment of undiscovered deposits of gold, silver, copper, lead, and zinc, estimates of the number of deposits were made for 305 of the 447 permissive tracts delineated in 19 assessment regions of the country. By aggregating number of undiscovered deposits by deposit type and by assessment region, a picture of the nation's undiscovered resources has emerged. For the nation as a whole, the mean estimate for the number of undiscovered deposits is 950. There is a 90% chance there are at least 747 undiscovered deposits and a 10% chance there are as many as 1,160 undiscovered deposits. For Alaska, the mean estimate for the number of undiscovered deposits is 281. There is a 90% chance there are at least 168 undiscovered deposits and a 10% chance there are as many as 402 undiscovered deposits. Assuming that the majority of deposits used to create the grade and tonnage models that formed the basis for estimating the number of undiscovered deposits are significant deposits, there remain about as many undiscovered deposits as have already been discovered. Consideration of the number of undiscovered deposits as part of national assessments carried out on a recurring basis serves as a leading indicator of the nation's total mineral resources.     

The study of the undiscovered mineral resources of the Tongass National Forest and adjacent lands,Southeastern Alaska

The quantitative probabilistic assessment of the undiscovered mineral resources of the 17.1-million-acre Tongass National Forest (the largest in the United States) and its adjacent lands is a nonaggregated, mineral-resource-tract-oriented assessment designed for land-planning purposes. As such, it includes the renewed use of gross-in-place values (GIPV's) in dollars of the estimated amounts of metal contained in the undiscovered resources as a measure for land-use planning.Southeastern Alaska is geologically complex and contains a wide variety of known mineral deposits, some of which have produced important amounts of metals during the past 100 years. Regional geological, economic geological, geochemical, geophysical, and mineral exploration history information for the region was integrated to define 124 tracts likely to contain undiscovered mineral resources. Some tracts were judged to contain more than one type of mineral deposit. Each type of deposit may contain one or more metallic elements of economic interest. For tracts where information was sufficient, the minimum number of as-yet-undiscovered deposits of each type was estimated at probability levels of 0.95, 0.90, 0.50, 0.10, and 0.05.The undiscovered mineral resources of the individual tracts were estimated using the U.S. Geological Survey's MARK3 mineral-resource endowment simulator; those estimates were used to calculate GIPV's for the individual tracts. Those GIPV's were aggregated to estimate the value of the undiscovered mineral resources of southeastern Alaska. The aggregated GIPV of the estimates is $40.9 billion.Analysis of this study indicates that (1) there is only a crude positive correlation between the size of individual tracts and their mean GIPV's: and (2) the number of mineral-deposit types in a tract does not dominate the GIPV's of the tracts, but the inferred presence of synorogenic-synvolcanic nickel-copper, porphyry copper skarn-related, iron skarn, and porphyry copper-molybdenum deposits does. The influence of this study on the U.S. Forest Service planning process is yet to be determined.     

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.     

Statewide Estimates of Undiscovered Deposits of Gold,Silver, Copper,Lead, and Zinc

Estimates of the number of undiscovered deposits on a statewide basis offer a different perspective on the nation's undiscovered resources of gold, silver, copper, lead, and zinc. Mean estimates of the number of undiscovered deposits statewide were extracted from the estimates of undiscovered deposits nationwide. More than 50 undiscovered deposits are estimated to occur in Alaska, Arizona, Nevada, and Wisconsin. Estimating the number of undiscovered deposits statewide serves as a measure of a state's total remaining mineral resources in known conventional deposit types.     

Rank-Size Statistical Assessments of Undiscovered Gold Endowment in the Bendigo and Stawell Zones (Victoria) and the Mossman Orogen (Queensland), Australia: Comparison with Three-Part Assessment Results

The Bendigo and Stawell zones in Victoria and the Mossman Orogen in north Queensland host numerous orogenic gold deposits and are likely to contain significant undiscovered gold resources. This paper discusses applications of Zipf’s law to estimate the scale of residual gold endowment in each of the regions. Testing various plausible scenarios on whether or not the largest deposit in each region has been discovered and its endowment adequately evaluated provided some measure of uncertainty of assessment results. The Bendigo and Stawell zones are estimated to host 12 undiscovered ore fields with >31 t (1 Moz) of contained gold and another 35 undiscovered ore fields with >10 t (0.32 Moz) of gold, containing in total 1600 t (51 Moz) of gold. The total residual orogenic gold endowment of the Mossman Orogen is estimated to be between 3 and 30 t of gold, contained in extensions of known deposits and up to six significant undiscovered gold ore fields each containing >1 t of gold. These estimates are comparable to results of recent three-part quantitative mineral resource assessments for those areas.     

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.     

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.     

Typing Mineral Deposits Using Their Grades and Tonnages in an Artificial Neural Network

A test of the ability of a probabilistic neural network to classify deposits into types on the basis of deposit tonnage and average Cu, Mo, Ag, Au, Zn, and Pb grades is conducted. The purpose is to examine whether this type of system might serve as a basis for integrating geoscience information available in large mineral databases to classify sites by deposit type. Benefits of proper classification of many sites in large regions are relatively rapid identification of terranes permissive for deposit types and recognition of specific sites perhaps worthy of exploring further.Total tonnages and average grades of 1,137 well-explored deposits identified in published grade and tonnage models representing 13 deposit types were used to train and test the network. Tonnages were transformed by logarithms and grades by square roots to reduce effects of skewness. All values were scaled by subtracting the variable's mean and dividing by its standard deviation. Half of the deposits were selected randomly to be used in training the probabilistic neural network and the other half were used for independent testing. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class (type) and each variable (grade or tonnage).Deposit types were selected to challenge the neural network. For many types, tonnages or average grades are significantly different from other types, but individual deposits may plot in the grade and tonnage space of more than one type. Porphyry Cu, porphyry Cu-Au, and porphyry Cu-Mo types have similar tonnages and relatively small differences in grades. Redbed Cu deposits typically have tonnages that could be confused with porphyry Cu deposits, also contain Cu and, in some situations, Ag. Cyprus and kuroko massive sulfide types have about the same tonnages. Cu, Zn, Ag, and Au grades. Polymetallic vein, sedimentary exhalative Zn-Pb, and Zn-Pb skarn types contain many of the same metals. Sediment-hosted Au, Comstock Au-Ag, and low-sulfide Au-quartz vein types are principally Au deposits with differing amounts of Ag.Given the intent to test the neural network under the most difficult conditions, an overall 75% agreement between the experts and the neural network is considered excellent. Among the largestclassification errors are skarn Zn-Pb and Cyprus massive sulfide deposits classed by the neuralnetwork as kuroko massive sulfides—24 and 63% error respectively. Other large errors are the classification of 92% of porphyry Cu-Mo as porphyry Cu deposits. Most of the larger classification errors involve 25 or fewer training deposits, suggesting that some errors might be the result of small sample size. About 91% of the gold deposit types were classed properly and 98% of porphyry Cu deposits were classes as some type of porphyry Cu deposit. An experienced economic geologist would not make many of the classification errors that were made by the neural network because the geologic settings of deposits would be used to reduce errors. In a separate test, the probabilistic neural network correctly classed 93% of 336 deposits in eight deposit types when trained with presence or absence of 58 minerals and six generalized rock types. The overall success rate of the probabilistic neural network when trained on tonnage and average grades would probably be more than 90% with additional information on the presence of a few rock types.     

Map Scale Effects on Estimating the Number of Undiscovered Mineral Deposits

Estimates of numbers of undiscovered mineral deposits, fundamental to assessing mineral resources, are affected by map scale. Where consistently defined deposits of a particular type are estimated, spatial and frequency distributions of deposits are linked in that some frequency distributions can be generated by processes randomly in space whereas others are generated by processes suggesting clustering in space. Possible spatial distributions of mineral deposits and their related frequency distributions are affected by map scale and associated inclusions of non-permissive or covered geological settings. More generalized map scales are more likely to cause inclusion of geologic settings that are not really permissive for the deposit type, or that include unreported cover over permissive areas, resulting in the appearance of deposit clustering. Thus, overly generalized map scales can cause deposits to appear clustered. We propose a model that captures the effects of map scale and the related inclusion of non-permissive geologic settings on numbers of deposits estimates, the zero-inflated Poisson distribution. Effects of map scale as represented by the zero-inflated Poisson distribution suggest that the appearance of deposit clustering should diminish as mapping becomes more detailed because the number of inflated zeros would decrease with more detailed maps. Based on observed worldwide relationships between map scale and areas permissive for deposit types, mapping at a scale with twice the detail should cut permissive area size of a porphyry copper tract to 29% and a volcanic-hosted massive sulfide tract to 50% of their original sizes. Thus some direct benefits of mapping an area at a more detailed scale are indicated by significant reductions in areas permissive for deposit types, increased deposit density and, as a consequence, reduced uncertainty in the estimate of number of undiscovered deposits. Exploration enterprises benefit from reduced areas requiring detailed and expensive exploration, and land-use planners benefit from reduced areas of concern.     

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.     

Estimation of undiscovered deposits in quantitative mineral resource assessments—examples from Venezuela and Puerto Rico

Quantitative mineral resource assessments used by the United States Geological Survey are based on deposit models. These assessments consist of three parts: (1) selecting appropriate deposit models and delineating on maps areas permissive for each type of deposit; (2) constructing a grade-tonnage model for each deposit model; and (3) estimating the number of undiscovered deposits of each type. In this article, I focus on the estimation of undiscovered deposits using two methods: the deposit density method and the target counting method.In the deposit density method, estimates are made by analogy with well-explored areas that are geologically similar to the study area and that contain a known density of deposits per unit area. The deposit density method is useful for regions where there is little or no data. This method was used to estimate undiscovered low-sulfide gold-quartz vein deposits in Venezuela.Estimates can also be made by counting targets such as mineral occurrences, geophysical or geochemical anomalies, or exploration plays and by assigning to each target a probability that it represents an undiscovered deposit that is a member of the grade-tonnage distribution. This method is useful in areas where detailed geological, geophysical, geochemical, and mineral occurrence data exist. Using this method, porphyry copper-gold deposits were estimated in Puerto Rico.     

Sequential Simulation Approach to Modeling of Multi-seam Coal Deposits with an Application to the Assessment of a Louisiana Lignite

There are multiple ways to characterize uncertainty in the assessment of coal resources, but not all of them are equally satisfactory. Increasingly, the tendency is toward borrowing from the statistical tools developed in the last 50 years for the quantitative assessment of other mineral commodities. Here, we briefly review the most recent of such methods and formulate a procedure for the systematic assessment of multi-seam coal deposits taking into account several geological factors, such as fluctuations in thickness, erosion, oxidation, and bed boundaries. A lignite deposit explored in three stages is used for validating models based on comparing a first set of drill holes against data from infill and development drilling. Results were fully consistent with reality, providing a variety of maps, histograms, and scatterplots characterizing the deposit and associated uncertainty in the assessments. The geostatistical approach was particularly informative in providing a probability distribution modeling deposit wide uncertainty about total resources and a cumulative distribution of coal tonnage as a function of local uncertainty.     

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.     

Resource depletion calculated by the ratio of the reserve plus cumulative consumption to the crustal abundance for gold

The magnitude of the world's mineral consumption has increased sharply, and there is no sign that growth is likely to stop in the near future. Currently, new discoveries and technology add to the reserves of varous mineral commodities at a rate that has exceeded depletion. As a result, life expectancies have remained nearly constant. However, it is questionable whether this condition is sustainable in the future. Therefore, most of our attention to the future has been focused on potentially recoverable resources. The potentially recoverable resources for 35 minerals in the Earth's crust were estimated based on the relationship between crustal abundance and the reserve of currently recoverable gold. The ratio of the reserve plus cumulative consumption to the abundance of gold is appropriate for calculating reserves of other mineral resources because gold has the highest profit margin for exploration of reserves. From an economic perspective, the price of gold is 350 times the mean value of 33 other resources for calculating production versus price. New mining technologies and new processing methods have been developed during the last 20 years as a response to high prices. As a result, five times the reserves available in 1970 have now been discovered, and two times the reserves available in 1970 were consumed during the past two decades. It is questionable whether other mineral commodities can reach the ratio of reserve plus cumulative consumption to abundance that gold does. Using this concept, the limit of the Earth's resources under present technology was calculated for 35 mineral resources, based on the ratio of the reserve plus cumulative consumption to abundance for gold. Even though recoverable tonnage of lead, silver, tin, boron, copper, and mercury from ore deposits in the Earth's crust is relatively low, the abundance of these metals is apparently sufficient for future supplies. However, considering the special situation of gold created by its very high price compared to world production, there is anxiety concerning steep increases in the price or depletion of these metals, which have a shorter lifetime from a geochemical point of view.     

Global Resource Assessments of Primary Metals: An Optimistic Reality Check

The mining of primary metals is critical for a range of modern infrastructure and goods and the continuing growth in global population and consumption means that these primary metals are expected to remain in high demand. However, metallic deposits are, in essence, finite and non-renewable—leading to some concern that we may run out of a given metal in the future. Here, we address this concern by presenting a brief review of the reporting of mineral resource estimates, compiling detailed datasets for national and global trends in mineral resources for numerous metals, and present detailed case studies of major mining projects or fields. The evidence clearly shows strong growth in known mineral resources and cumulative production over time rather than any evidence of gradual resource depletion. In addition, the key factors that already govern existing mining projects and mineral resources are certainly social, environmental and economic in nature rather than geological or related to physical resource depletion. Overall, there is great room for optimism in terms of humankind’s ability to supply future generations with the metals they will require.     

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.     

Metallic Mineral Resources in the Twenty-First Century. I. Historical Extraction Trends and Expected Demand

Industrial, technological, and economic developments depend on the availability of metallic raw materials. As a greater fraction of the Earth’s population has become part of developed economies and as developed societies have become more affluent, the demand on metallic mineral resources has increased. Yet metallic minerals are non-renewable natural resources, the supply of which, even if unknown and potentially large, is finite. An analysis of historical extraction trends for eighteen metals, going back to the year 1900, demonstrates that demand of metallic raw materials has increased as a result of both increase in world population and increase in per-capita consumption. These eighteen metals can be arranged into four distinct groups, for each of which it is possible to identify a consistent pattern of per-capita demand as a function of time. These patterns can, in turn, be explained in terms of the industrial and technological applications, and in some cases conventional uses as well, of the metals in each group. Under the assumption that these patterns will continue into the future, and that world population will grow by no more than about 50% by the year 2100, one can estimate the amount of metallic raw materials that will be required to sustain the world’s economy throughout the twenty-first century. From the present until the year 2100, the world can be expected to require about one order of magnitude more metal than the total amount of metal that fueled technological and economic growth between the age of steam and the present day. For most of the metals considered here, this corresponds to 5–10 times the amount of metal contained in proven ore reserves. The two chief driving factors of this expected demand are growth in per-capita consumption and present-day absolute population numbers. World population is already so large that additional population growth makes only a small contribution to the expected future demand of metallic raw materials. It is not known whether or not the amount of metal required to sustain the world’s economy throughout this century exists in exploitable mineral resources. In the accompanying paper, I show that it is nevertheless possible to make statistical inferences about the size distribution of the mineral deposits that will need to be discovered and developed in order to satisfy the expected demand. Those results neither prove nor disprove that the needed resources exist but can be used to improve our understanding of the challenges facing future supply of metallic raw materials.     

Categorization of Mineral Resources Based on Different Geostatistical Simulation Algorithms: A Case Study from an Iron Ore Deposit

Mineral resource classification plays an important role in the downstream activities of a mining project. Spatial modeling of the grade variability in a deposit directly impacts the evaluation of recovery functions, such as the tonnage, metal quantity and mean grade above cutoffs. The use of geostatistical simulations for this purpose is becoming popular among practitioners because they produce statistical parameters of the sample dataset in cases of global distribution (e.g., histograms) and local distribution (e.g., variograms). Conditional simulations can also be assessed to quantify the uncertainty within the blocks. In this sense, mineral resource classification based on obtained realizations leads to the likely computation of reliable recovery functions, showing the worst and best scenarios. However, applying the proper geostatistical (co)-simulation algorithms is critical in the case of modeling variables with strong cross-correlation structures. In this context, enhanced approaches such as projection pursuit multivariate transforms (PPMTs) are highly desirable. In this paper, the mineral resources in an iron ore deposit are computed and categorized employing the PPMT method, and then, the outputs are compared with conventional (co)-simulation methods for the reproduction of statistical parameters and for the calculation of tonnage at different levels of cutoff grades. The results show that the PPMT outperforms conventional (co)-simulation approaches not only in terms of local and global cross-correlation reproductions between two underlying grades (Fe and Al₂O₃) in this iron deposit but also in terms of mineral resource categories according to the Joint Ore Reserves Committee standard.