Grade-and-Tonnage Models

Mineral deposit models are important in quantitative resource assessments for two reasons: (1) grades and tonnages of most deposit types are significantly different (Singer, Cox, and Drew, 1975; Singer and Kouda, 2003), and (2) deposit types occur in different geologic settings that can be identified from geologic maps. If assessments were only conducted to estimate amounts of undiscovered metals, we would need contained metal models, but determining whether the metals might be economic to recover is an important quality of most assessments, and grades and tonnages are necessary to estimate economic viability of mineral deposits (see chapter 5). In this chapter, we focus on the first part of three-part assessments: grade-and-tonnage models. Too few thoroughly explored mineral deposits are available in most areas being assessed for reliable identification of the important geoscience variables or for robust estimation of undiscovered deposits, so we need mineral-deposit models that are generalized. Well-designed and well-constructed grade-and-tonnage models allow mineral economists to determine the possible economic viability of the resources in the region and provide the foundation for planning. Thus, mineral deposit models play the central role in transforming geoscience information to a form useful to policy-makers. Grade-and-tonnage models are fundamental in the development of other kinds of models such as deposit-density and economic filters. Frequency distributions of tonnages and average grades of well-explored deposits of each type are employed as models for grades and tonnages of undiscovered deposits of the same type in geologically similar settings. Grade-and-tonnage models (Cox and Singer, 1986; Mosier and Page, 1988; Bliss, 1992a, 1992b; Cox et al., 2003; Singer, Berger, and Moring, 2008) combined with estimates of number of undiscovered deposits are the fundamental means of translating geologists’ resource assessments into a language that decision-makers can use. For example, creation of a grade-and-tonnage model for rhyolite-hosted Sn deposits in 1986 demonstrated for the first time that 90 percent of such deposits contain less than 4,200 tons of ore. This made it clear that an ongoing research project by the U.S. Geological Survey on this deposit type could have no effect on domestic supplies of tin, and the project was cancelled.

Integration of Grades, Tonnages, Number of Deposits, and Economic Effects

Now that all of the fundamental parts of a quantitative mineral resource assessment have been discussed, it is useful to reflect on why all of the work has been done. As mentioned in chapter 1, it is quite easy to generate an assessment of the “potential” for undiscovered mineral resources. Aside from the question of what, if anything, “potential” means, there is the more serious question of whether a decision-maker has any use for it. The three-part form of assessment is part of a system designed to respond to the needs of decision-makers. Although many challenging ideas are presented in this book, it has a different purpose than most academic reports. This book has the same goal as Allais (1957)—to provide information useful to decision makers. Unfortunately, handing a decision-maker a map with some tracts outlined and frequency distributions of some tonnages and grades along with estimates of the number of deposits that might exist along with their associated probabilities is not really being helpful—these need to be converted to a language understandable to others. This chapter summarizes how these various estimates can be combined and put in more useful forms. If assessments were conducted only to estimate amounts of undiscovered metals, we would need contained metal models and estimates of the number of undiscovered deposits. Grades are simply the ratio of contained metal to tons of ore (chapter 6), so contained metal estimates are available for each deposit. In the simplest of all cases, one could estimate the expected number of deposits with equation 8.1 (see chapter 8) and multiply it by the expected amount of metal per deposit, such as the 27,770 tons of copper in table 9.1, to make an estimate of the expected amount of undiscovered metal. As pointed out in chapter 1, expected amounts of resources or their values can be very misleading because they provide no information about how uncommon the expected value can be with skewed frequency distributions that are common in mineral resources; that is, uncertainty is ignored.

Mineral Resources and Society

Modern society cannot live without electric and electronic products, concrete, glass, fertilizers, ceramics, motor vehicles, airplanes, refrigerators, stoves, and medical equipment, all of which are made with products of mining. In the 1950s and again in the 1970s there was serious concern about whether we would run out of mineral resources. This recurring theme is driven largely by the increasing amounts of mineral material produced from mines and used by society over time. One of the most striking aspects of the increasing quantities of mineral materials produced has been that prices of many minerals have been declining for more than 100 years. Historically, prices of nonfuel mineral materials have declined relative to consumer goods and wages (Barnett and Morse, 1963). The declining prices have had a positive influence on general economies of mineral users by reducing prices of the factors of production of finished goods. Because mineral commodities are the building blocks of so many industries and products, the declining prices reverberate throughout the economy. Declining mineral commodity prices have largely been due to the successes of mining engineers in repeatedly lowering mining and processing costs and of geologists in lowering discovery costs of mineral deposits. Demonstrating the variability of commodity prices, between 2003 and 2008 prices have dramatically increased, and in 2008 they declined again. Understanding how it is possible to have both increasing production and decreasing and more recently increasing and then decreasing prices of minerals is important to assessors and to decision-makers. Decision-makers, whether concerned about regional development, exploration, or land management, are faced with the dilemma of obtaining new information, or allowing or encouraging others to obtain it, and the possible benefits and costs of development if mineral deposits of value are discovered. The intent in this chapter is to provide decision-makers and assessors a modern perspective on the geologic controls of mineral supply and demand and on the importance to supply of different kinds of mineral deposits and occurrences.

Estimating the Number of Undiscovered Deposits

The third part of three-part assessments is the estimate of some fixed but unknown number of deposits of each type that exist in the delineated tracts. Until the area being considered is thoroughly and extensively drilled, this fixed number of undiscovered deposits, which could be any number including 0, will not be known with certainty. This number of deposits has meaning only in terms of a grade-and-tonnage model. If this requirement did not exist, any wisp of minerals could be considered worthy of estimation, and even in small regions, we would need to estimate millions of “deposits.” For example, it is not difficult to imagine tens of thousands of fist-sized skarn copper “deposits” in parts of western United States—even in this example, we have used “deposit” size to provide important information. In another example, Wilson et al. (1996) estimated five or more epithermal gold vein deposits at the 90 percent level but provided no grade-and-tonnage model, so these estimated deposits could be any size. To provide critical information to decision-makers, the grade-and-tonnage model is key, and the estimated number of deposits that might exist must be from the grade-and-tonnage frequency distributions. In three-part assessments, the parts and estimates are internally consistent in that delineated tracts are consistent with descriptive models, grade-and-tonnage models are consistent with descriptive models and with known deposits in the area, and estimates of number of deposits are consistent with grade-and-tonnage models. Considerable care must be exercised in quantitative resource assessments to prevent the introduction of biased estimates of undiscovered resources. Biases can be introduced into these estimates either by a flawed grade-and-tonnage model or by the lack of consistency of the grade-and-tonnage model with the number-of-deposit estimates. For this reason, consistency of estimates of number of deposits with the grade-and-tonnage models is the most important guideline. Issues about consistency of mineral deposit models are discussed in chapters 3 through 6. Grade-and-tonnage models (chapter 6), which are the first part of three-part assessments, are of particular concern. In this chapter, the focus is on making unbiased estimates of the number of undiscovered deposits.

Delineation of Permissive Tracts

The nonuniform global distributions of metals discussed in chapter 2 are also evident within most countries. Knowledge of the spatial distributions of mineral resources is invaluable in planning. In order to be able to consistently assess the undiscovered mineral resources of regions, as the second part of three-part assessments, areas should be delineated where geology permits the existence of deposits of one or more specified types. These areas, called permissive tracts, are based on geologic criteria derived from deposit models that are themselves based on studies of known deposits outside and perhaps within the study area. Thus, deposit models play the central role in identifying relevant information and in integrating the various kinds of information to delineate permissive tracts. Permissive boundaries are defined such that the probability of deposits of the type delineated occurring outside the boundary are negligible, that is, less than 1 in 100,000. Areas are excluded from these tracts only on the basis of geology, knowledge about unsuccessful exploration, or the presence of barren overburden exceeding some predetermined thickness. A geologic map is the primary local source of information for delineating tracts and identifying which are permissive for different deposit types. Map scales affect the quality and nature of information available for delineations and determine the extent to which geologic units are combined and how cover is represented. Probably the second most important kind of information is an inventory of known deposits and prospects in and near the region being assessed. Tracts may or may not contain known deposits. Because of incomplete deposit descriptions, it often is difficult to identify deposit types for many prospects, occurrences, and some deposits, but those that can be identified increase confidence in domains delineated for the deposit type. Typed prospects may indicate the possibility of some deposit types where the type had not been expected or place limits on the kinds and sizes of deposits that could occur elsewhere. The map of deposits and occurrences classified into deposit types then serves as a check on the accuracy of the delineation of tracts permissive for types rather than a determinant of the delineation.

Descriptive Models

Mineral deposit models play a central role in an information system that will help the policy makers to make their decisions. Ideally, the different kinds of deposit models would provide the necessary and sufficient information to discriminate (1) possible mineralized environments from barren environments, (2) types of known deposits from each other, and (3) mineral deposits from mineral occurrences. Probably the most important part of creating mineral deposit models is the planning stage in which consideration of the purpose and possible uses of the models should determine the character of the models. The way to describe a model is first by thinking about what it is for, about its function, not the list of items that make up its structure (Churchman, 1968). Although there are many fine compendiums of mineral deposit models (Australian Geological Survey Organisation, 1998; Eckstrand, Sinclair, and Thorpe, 1995; Kirkham et al., 1993; Lefebure and Hoy, 1996; Lefebure and Ray, 1995; Roberts and Sheahan, 1988; Rongfu, 1995; Sheahan and Cherry, 1993), the focus in this book is on deposit models applied to quantitative resource assessment. The focus of this chapter is the descriptive aspects of the deposits because the goal is to provide a basis for interpreting geologic observations rather than to provide interpretations in search of examples (Cox, Barton, and Singer, 1986). Thus, the discussion herein is limited to mineral deposit models specifically designed for quantitative assessments such as those in Cox and Singer (1986), Bliss (1992a), Orris and Bliss (1991, 1992), and Rogers et al. (1995). Mineral deposits modeled for three-part assessments are defined as mineral occurrences of sufficient size and grade that they might, under favorable circumstances, be economic. Although history suggests that we can expect discoveries of as-yet-unrecognized deposit types, the three-part assessments discussed here do not include resources from these deposits simply because they cannot be modeled. Most published quantitative mineral resource assessments that have used models have relied upon descriptive and grade-and-tonnage models (chapter 6), which are also the foundations of other kinds of models such as deposit-density models (chapter 4) and economic cost models (chapter 5).

Introduction

Every day, somewhere in the world, decisions are made about how public lands that might contain undiscovered resources should be used or whether to invest in exploration for minerals. Less frequently, decisions are made concerning mineral resource adequacy, national policy, and regional development. Naturally, the people making the decisions would like to know the exact consequences of the decisions before the decisions are made. Unfortunately, it is not possible to inform these decision-makers, with any certainty, about amounts, discoverability, or economics of undiscovered mineral resources. The kind of assessment recommended in this book is founded in decision analysis in order to provide a normative framework for making decisions concerning mineral resources under conditions of uncertainty. Our goal is to make explicit the factors that can affect a mineral-related decision so that the decision-maker can clearly see the possible consequences of the decision. This means that we start with the question of what kinds of issues decision-makers are trying to resolve and what types and forms of information would aid in resolving these issues. This book has a different purpose than academic reports common to many assessments, and it is not designed to help select sites for exploration. The audience for products of assessments discussed here comprises governmental and industrial policy-makers, managers of exploration, planners of regional development, and similar decision-makers. Some of the tools and models presented here are useful for selection of exploration sites, but that is a side benefit. The focus of this book is on the practical integration of the fundamental kinds of information needed by the decision-maker. The integrated approach to assessment presented in this book focuses on three assessment parts and the models that support them. The first part uses models of tonnages and grades to estimate possible tonnages and grades of undiscovered deposits. The second part develops mineral resource maps that explore whether an area’s geology permits the existence of one or more types of mineral deposits. The product of this part of the assessment is identification of so-called permissive tracts of land.

The Future of Quantitative Resource Assessments

The difference between the ideas presented by Allais (1957) fifty years ago and those presented in this book reflect a significant growth in knowledge since his work, and the recognition of the value of, and ways to capture, geologic information. We now can use geologic maps to divide large regions into parts that could contain different kinds of mineral deposits, and we know that these different kinds of mineral deposits are significantly different in the amounts and qualities of minerals of interest to society, which affect chances that the deposits will be sought, found, and exploited by society. It is important to remember that our goal is to provide unbiased estimates of undiscovered mineral resources and then to minimize the uncertainty associated with the estimates. Here we point out where there are opportunities to improve the three-part form of quantitative mineral resource assessment. Many of these opportunities come from identified sources on uncertainties in present assessments of all kinds, such as assessing resources under cover. Some of the improvements can be made in parts of the present assessments that are not completed such as economic filters. Additional opportunities come from the possibilities of harnessing the power of new technologies such as probabilistic neural networks to well-designed applications in these kinds of assessments. Future quantitative assessments will be expected to estimate quantities, values, and locations of undiscovered mineral resources in a form that conveys both economic viability and uncertainty associated with the resources. Uncertainties about undiscovered resources can be addressed and reduced through improved mineral deposit models, better economic filters and simulators, and application of new technologies to integrate information and by better dealing with geographic uncertainty due to covered terrains (Singer, 2001). Finally, all of these possible ways to improve assessments rely on careful applications of the tools. Research opportunities in quantitative resource assessment could be identified in at least three ways: (1) by listing unfinished or flawed parts of assessment tools, (2) by pointing to new technologies that could improve assessments, and (3) by focusing on tasks that could most significantly reduce uncertainties in assessments, and here we consider each.

Exploration Risk

It is commonly said that mineral exploration is a risky business, but what does that really mean? Although exploration can be financially rewarding, there is a high probability that a single venture will be a failure. Risk is defined as chance of failure or loss and its adverse consequence (i.e., failure or loss). Risk differs from uncertainty in that uncertainty simply means lack of knowledge of the outcome or result, whereas risk involves a loss. Thus, one could be uncertain of an outcome, but not necessarily be at risk of losing something. In risk analysis, two quantities are estimated: the magnitude (severity) of the possible adverse consequence(s), and the likelihood (probability) of occurrence of each consequence. Procedures of risk analysis are well established, if not simple, and are applied in both business and engineering (Aven, 2003; Bárdossy and Fodor, 2004; Davis and Samis, 2006). Mineral exploration is an economic activity involving risk and uncertainty, so risk also must be defined in an economic context in which the extent of the loss is defined. Successful mineral exploration strategy requires identification of some of the risk sources and consideration of them in the decision-making process so that controllable risk can be reduced. It is not uncommon to see recommendations that exploration firms should accept all projects with positive expected monetary values—that is, projects that have a positive economic value after being multiplied by the probability of deposit discovery and subtraction of exploration costs. Clearly, this strategy would be unwise for a firm with limited resources if the chance of failure were significant. Both expected monetary values and the probabilities of various outcomes such as economic failure should be considered in the decision-making process. Because economic return, when measured by net present value, is closely related to the size of mineral deposits, and because deposit sizes can be represented by highly skewed frequency distributions, achieving expected monetary or higher values tends to be a low-probability outcome. This and the typical rareness of mineral deposits are the fundamental reasons for the high risk in mineral exploration.

Economic Analysis

Estimated undiscovered mineral resources are based on grade-and-tonnage models made up of deposits of varying economic viability (chapter 6). Many deposits used in grade-and-tonnage models have not been developed because they cannot yet be mined economically. Although technological advances act over time to lower mining costs and environmental impacts, thereby allowing formerly uneconomic deposits to become operating mines, some deposits in these models might “never” be mined for one or more of a variety of reasons, including relatively low tonnages and grades, deep burial, or occurrence in or near environmentally sensitive areas. Few nonacademic problems related to mineral resources are resolved by knowing the amount of metal that exists in some piece of land. Mineral policy issues and problems typically revolve around the effects of minerals that might be economically extracted. This is true if the problem concerns exploring or developing minerals, values of alternative uses of the land, or environmental consequences of minerals development. In resource assessments of undiscovered mineral deposits and in the early stages of exploration, including planning, a need for prefeasibility cost models exists. In exploration, these models separate economic from uneconomic deposits to help focus on targets that can benefit the exploration enterprise. In resource assessment, these cost models can be used to eliminate deposits that would probably be uneconomic even if discovered and allow estimation of the social value of the resources. Data used in grade-and-tonnage models do not necessarily represent economic deposits. Many of the deposits used in the models were found not to be economic and were not mined, whereas other deposits were mined long ago under economic conditions that no longer exist. In this chapter we briefly explore some alternative measures of value used in assessments and then develop the basis for simplified economic filters to separate the clearly economic from the clearly uneconomic deposits. The equations used are not difficult, but they require care in their application because many of the apparently small cost factors can have large effects on the final economic discrimination.