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2.
Earlier methods of fitting Pareto–lognormal distributions to large samples of worldwide metal deposit size data are improved by using a sliding window method for estimating upper-tail Pareto coefficients and constructing best-fitting lognormal QQ plots with their corresponding probability-density curves. Lower-tail Pareto distributions are fitted to some extent as well. Copper and Zn deposits of the world are taken as example in this paper. Three principal statistical laws resulting in the basic lognormal with two Pareto tails are thought to underlie the generation of Pareto–lognormals for amounts of metal in primarily hydrothermal ore deposits. Historical trends in mining and exploration are thought to create an excess of smaller deposits with respect to the basic lognormal that decreases steadily with increasing deposit size until it changes into a deficit slightly before median size is reached. This deficit decreases for the largest metal deposit sizes for which the upper-tail Pareto and extrapolated basic lognormal show similar size frequencies again. The Pareto–lognormal model can also be used to describe metal size-frequency distributions for smaller geographically coherent regions on the continents. A new version of the original model of de Wijs is considered to help explain why regional Pareto–lognormal distributions with lesser logarithmic variances and Pareto coefficients can be combined to form worldwide size-frequency distributions of the same type.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.

The Pareto-lognormal frequency distribution, which can result from multifractal cascade modeling, previously was shown to be useful to describe the worldwide size-frequency distributions of metals including copper, zinc, gold and silver in ore deposits. In this paper, it is shown that the model also can be used for the size-frequency distributions of these metals in Canada which covers 6.6% of the continental crust. Like their worldwide equivalents, these Canadian deposits show two significant departures from the Pareto-lognormal model: (1) there are too many small deposits, and (2) there are too few deposits in the transition zone between the central lognormal and the upper tail Pareto describing the size-frequency distribution of the largest deposits. Probable causes of these departures are: (1) historically, relatively many small ore deposits were mined before bulk mining methods became available in the twentieth century, and (2) economically, giant and supergiant deposits are preferred for mining and these have strongest geophysical and geochemical anomalies. It is shown that there probably exist many large deposits that have not been discovered or mined. Although overall the samples of the size-frequency distributions are very large, frequencies uncertainties associated with the largest deposits are relatively small and it remains difficult to estimate more precisely how many undiscovered mineral deposits there are in the upper tails of the size-frequency distributions of the metals considered.

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8.
In this article, we examine the use of an unconventional procedure, PETRIMES, to estimate mineral resources of mercury deposits in California. The study, which is based on the nonparametric discovery process model and Q-Q plots, suggests that a lognormal distribution is appropriate for the mercury deposits in California. The results of the assessment are summarized as follows: (1) the total number of mercury deposits in the population is approximately 165; (2) the median value of the largest undiscovered deposit size is 487 flasks; (3) the mean of the remaining mercury potential is 2,500 flasks; and (4) the population resource ranges from 1,040,000 to 4,300,000 flasks (at a 0.9 probability level).  相似文献   

9.
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.  相似文献   

10.
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.  相似文献   

11.
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.  相似文献   

12.
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.  相似文献   

13.
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.  相似文献   

14.
Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution   总被引:2,自引:0,他引:2  
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.  相似文献   

15.
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.  相似文献   

16.
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.  相似文献   

17.
This study is concerned with understanding of the formation of ore deposits (precious and base metals) and contributes to the exploration and discovery of new occurrences using artificial neural networks. From the different digital data sets available in BRGM's GIS Andes (a comprehensive metallogenic continental-scale Geographic Information System) 25 attributes are identified as known factors or potential factors controlling the formation of gold deposits in the Andes Cordillera. Various multilayer perceptrons were applied to discriminate possible ore deposits from barren sites. Subsequently, because artificial neural networks can be used to construct a revised model for knowledge extraction, the optimal brain damage algorithm by LeCun was applied to order the 25 attributes by their relevance to the classification. The approach demonstrates how neural networks can be used efficiently in a practical problem of mineral exploration, where general domain knowledge alone is insufficient to satisfactorily model the potential controls on deposit formation using the available information in continent-scale information systems.  相似文献   

18.
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.  相似文献   

19.
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.  相似文献   

20.
The rare earth elements (REE) have attracted much attention in recent years, being viewed as critical metals because of China’s domination of their supply chain. This is despite the fact that REE enrichments are known to exist in a wide range of settings, and have been the subject of much recent exploration. Although the REE are often referred to as a single group, in practice each individual element has a specific set of end-uses, and so demand varies between them. Future demand growth to 2026 is likely to be mainly linked to the use of NdFeB magnets, particularly in hybrid and electric vehicles and wind turbines, and in erbium-doped glass fiber for communications. Supply of lanthanum and cerium is forecast to exceed demand. There are several different types of natural (primary) REE resources, including those formed by high-temperature geological processes (carbonatites, alkaline rocks, vein and skarn deposits) and those formed by low-temperature processes (placers, laterites, bauxites and ion-adsorption clays). In this paper, we consider the balance of the individual REE in each deposit type and how that matches demand, and look at some of the issues associated with developing these deposits. This assessment and overview indicate that while each type of REE deposit has different advantages and disadvantages, light rare earth-enriched ion adsorption types appear to have the best match to future REE needs. Production of REE as by-products from, for example, bauxite or phosphate, is potentially the most rapid way to produce additional REE. There are still significant technical and economic challenges to be overcome to create substantial REE supply chains outside China.  相似文献   

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