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Earth's copper resources estimated from tectonic diffusion of porphyry copper deposits

¹ Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA
² Department of Earth Sciences, Syracuse University, Syracuse, New York 13244-1070, USA

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS USED FOR ESTIMATING... METHOD USED IN THIS... APPLICATION OF THE MODEL... SIGNIFICANCE AND RAMIFICATIONS... REFERENCES CITED

 
Improved estimates of global mineral endowments are relevant to issues ranging from strategic planning to global geochemical cycling. We have used a time-space model for the tectonic migration of porphyry copper deposits vertically through the crust to calculate Earth's endowment of copper in mineral deposits. The model relies only on knowledge of numbers and ages of porphyry copper deposits, Earth's most widespread and important source of copper, in order to estimate numbers of eroded and preserved deposits in the crust. Model results indicate that 125,895 porphyry copper deposits were formed during Phanerozoic time, that only 47,789 of these remain at various crustal depths, and that these contain 1.7 x 10¹¹ tonnes (t) of copper. Assuming that other types of copper deposits behave similarly in the crust and have abundances proportional to their current global production yields an estimate of 3 x 10¹¹ t for total global copper resources at all levels in Earth's crust. Thus, 0.25% of the copper in the crust has been concentrated into deposits through Phanerozoic time, and about two-thirds of this has been recycled by uplift and erosion. The amount of copper in deposits above 3.3 km, a likely limit of future mining, could supply current world mine production for 5500 yr, thus quantifying the highly unusual and nonrenewable nature of mineral deposits.

Key Words: copper • resources • ore deposit • mineral deposit • tectonic • computational model

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS USED FOR ESTIMATING... METHOD USED IN THIS... APPLICATION OF THE MODEL... SIGNIFICANCE AND RAMIFICATIONS... REFERENCES CITED

 
We report here a new approach for quantifying the mineral endowment of Earth's crust, information that is relevant to issues ranging from economic development and strategic planning to chemical differentiation of Earth (Gordon et al., 1984; Mikesell, 1986; Menzie, 1997; Farina, 2006; Tilton, 2003, 2006). Here we estimate remaining crustal resources of copper, which has increased in price by 460% between 2003 and 2007. Similar price changes for many mineral commodities, due partly to increased demand from newly expanding economies, have raised awareness of the limits to our mineral supplies and the need for improved estimates of global mineral endowments.

	METHODS USED FOR ESTIMATING GLOBAL MINERAL RESOURCES

TOP ABSTRACT INTRODUCTION METHODS USED FOR ESTIMATING... METHOD USED IN THIS... APPLICATION OF THE MODEL... SIGNIFICANCE AND RAMIFICATIONS... REFERENCES CITED

 
Efforts to estimate Earth's mineral endowment must extrapolate information on known deposits at and near the surface into less explored and deeper parts of the subsurface. These extrapolations are commonly based on two types of information, geologic and economic (Singer and Mosier, 1981; Harris, 1984; McLaren and Skinner, 1987). Geologic estimates compile information from well-explored areas on specific types of mineral deposits and their geologic environment, and extrapolate this information into less explored regions (Singer, 1993; Singer et al., 2005b). Economic estimates compile production or reserve data from known deposits, which are assumed to be sufficiently numerous and widespread to provide a representative sample of the entire planet (Lasky, 1950; Folinsbee, 1977; Howarth et al., 1980; Cargill et al., 1981; DeYoung, 1981). One widely used method of this type assumes that mineral consumption is relatively inelastic and changes symmetrically through time (Hewett, 1929; Hubbert, 1962; Roper, 1978; Bartlett, 2000; Deffeyes, 2005).

Although both methods have advantages, the best results should be obtained from a theoretical framework that extrapolates geologic and economic information from Earth's surface to depth. Development of such a framework requires an understanding of the factors that control the number and spatial distribution of ore deposits in the crust. Several studies have shown that preservation of deposits, not just their formation, plays a key role in this regard. For example, porphyry copper and skarn deposits in the western U.S. occupy regions of shallow and intermediate erosion, respectively (Barton et al., 1988). These relations were treated theoretically by Veizer et al. (1989), who showed that global cycling rates (expressed as deposit half-lives) for different types of ore deposits range from 1.7 b.y. to 3 m.y., depending on depths of crustal emplacement, and by Barton (1996), who used a model based on work of Koons (1989) for reduction of topographic relief in convergent margin settings to determine proportions of eroded, exposed, and hidden intrusion-related deposits.

	METHOD USED IN THIS STUDY

TOP ABSTRACT INTRODUCTION METHODS USED FOR ESTIMATING... METHOD USED IN THIS... APPLICATION OF THE MODEL... SIGNIFICANCE AND RAMIFICATIONS... REFERENCES CITED

 
The methodology applied in this study uses the age-frequency distribution of known deposits of a specific type to constrain a steady-state model of vertical tectonic movement of deposits through Earth's crust with time, including burial and subsidence as well as uplift and erosion (Wilkinson and Kesler, 2007). Age-frequency data for porphyry copper deposits (as well as many other ore deposit types) define log normal distributions in which deposit frequency increases abruptly with increasing age to a modal maximum, and then decreases gradually with greater age. This distribution reflects the fact that ore bodies are emplaced over some restricted range of crustal depths and then dispersed vertically through the crust as time passes.

Computationally, the model forms a series of deposits of a specific type and allows them to be displaced upward (uplift) or downward (burial), or to remain at the same level (stasis), with the passage of each time interval such that individual deposits in the series follow one of many different possible depth-time paths (Fig. 1). The model evaluates numerous possible up-stasis-down combinations for a group of deposits until it yields a best model fit to their age-frequency distribution (Fig. 2). Because the model simulates the migration of deposits through Earth's crust with time, it also provides information on the number and distribution of deposits in the subsurface, the most important requirement for estimating global resources. Confirmation of the model is provided by the fact that it closely reproduces known age-frequency patterns for the deposits, and yields erosion (denudation) rates identical to those estimated for continent-scale terrains by numerous other methods (Kesler and Wilkinson, 2006; Wilkinson and Kesler, 2007).

View larger version (45K): [in this window] [in a new window]   Figure 1. Time-space trajectories of 231 theoretical Phanerozoic porphyry copper deposits (light gray lines) emplaced at crustal depth of 2 km (arrow) relative to Earth's surface (straight heavy line), and tectonically moved (with the same probability) up, horizontally, or down by 468 m in age-depth space with each age step of 106 yr. Four paths (with ages and maximum burial depths) illustrate the range of burial histories. Numbered lines represent possible paths taken by: (1) Miami-Inspiration in Arizona (Livingston et al., 1968), (2) Gibraltar in British Columbia, (Bysouth et al., 1995), and (3) Chapada in Brazil (Richardson et al., 1986). Others remain in subsurface (e.g., 4) at various depths, including deposits that might enter mantle through crustal delamination. Inset to lower right shows age frequency distribution of 5000 such deposits (binned over 5 m.y.) that are now exposed at the theoretical Earth surface (straight heavy line). Note that numbers of deposits increase rapidly to modal age of 10 m.y., and then decrease gradually with increasing age.

View larger version (67K): [in this window] [in a new window]   Figure 2. Distribution of porphyry copper deposits in age (X axis)-depth (Y axis) space (upper panel) resulting from burial histories such as those taken by deposits in Figure 1. Colors are log scaled as number of deposits in a 1 m.y. x 1 km area. Lower panel compares age-frequency distributions for real deposits (light blue bars) and deposits at model surface (dark blue line). Good agreement between model and observed age frequencies indicates that, over the past 545 m.y., porphyry copper deposits emplaced at crustal depth of 1.9 ± 1 km formed at rate of 231 deposits/m.y. (Table 1). Histogram to left (yellow) shows vertical distribution of total copper endowments in porphyry copper deposits over 1 km crustal depth intervals; modal depth is 2.8 km (Table 1).

	APPLICATION OF THE MODEL TO GLOBAL COPPER RESOURCES

TOP ABSTRACT INTRODUCTION METHODS USED FOR ESTIMATING... METHOD USED IN THIS... APPLICATION OF THE MODEL... SIGNIFICANCE AND RAMIFICATIONS... REFERENCES CITED

Roth et al., 1991) are not sufficiently numerous to change these totals significantly, making this result a good estimate of the number of porphyry copper deposits in Earth's crust.

Because the calculation is based on random tectonic dispersion of deposits in the crust, the copper content of deposits at the surface (with the possible exception of supergene deposits) will be representative of deposits in the subsurface. Metal endowments of all mineral deposits are highly skewed, with a few large deposits and many small ones, and this is true for porphyry copper deposits. In the absence of geological knowledge to the contrary, we have made the assumption that the distribution of metal endowments is similar in the known and unknown deposit populations. In the known population, grade-tonnage data are available for 373 deposits of Phanerozoic and probable Phanerozoic age, which contain a total of 1.3 x 10⁹ tonnes (t) of copper (Singer et al., 2005a). Grade-tonnage data are not available for another 258 deposits of known and suspected Phanerozoic age, but if they have the same grade-tonnage distribution, near-surface Phanerozoic-age porphyry copper deposits contain 1.9 x 10⁹ t of copper. Thus, if currently known deposits represent 1.2% of the Phanerozoic total, Earth's porphyry copper deposits contain 1.7 x 10¹¹ t of copper (Table 1).

Global Copper Resources and Comparison to Other Estimates
Singer (1995) estimated that porphyry copper deposits account for 57% of world discovered copper. If this proportion also reflects the abundance of porphyry copper deposits relative to other copper deposits in the subsurface, Earth's total copper endowment in ore deposits is 3 x 10¹¹ t (Table 1). This estimate is probably low for several reasons. First, volcanogenic massive sulfide and sediment-hosted deposits, which form in basinal settings where preservation is greater, are more abundant in Precambrian terrains than porphyry copper deposits (Goodfellow et al., 1993; Franklin et al., 2005). Second, increasing copper prices and improved technology will convert lower grade deposits to ore. The degree to which these factors will increase global resources involves the complex and still unresolved interplay between extrapolation of the Lasky relation (Lasky, 1950; DeYoung, 1981) and mineral content of ore deposits compared to average rocks (Skinner, 1976; Singer, 1977). This uncertainty will be compensated for, however, by a third factor; i.e., as more porphyry copper deposits are found at the surface, the model will predict proportionally more in the subsurface. It is unlikely, however, that these factors will increase our estimate of total copper resources by more than 100%.

The only large-scale estimate to which we can compare our result is the assessment by the U.S. Geological Survey of copper resources in the U.S. (U.S. Geological Survey National Mineral Resource Assessment Team, 2000), which was based on years of geological mapping. This study concluded that the total (produced, discovered, and undiscovered) copper endowment for the U.S. is 6.4 x 10⁸ t to a 1 km depth, a reasonable depth to which geological estimates can be extrapolated. Using the distribution of deposits with depth indicated by our calculation (Fig. 2) and assuming that Earth's copper deposits are evenly distributed, our model indicates that deposits in the upper kilometer of the U.S. contain 7 x 10⁸ t of copper. These estimates are very similar even if our estimate is doubled.

	SIGNIFICANCE AND RAMIFICATIONS OF THIS ESTIMATE

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Our estimate of 3 x 10¹¹ t for Earth's minimum copper endowment can be considered in terms of two very different questions. First, from a societal perspective, we can ask what our results say about future mineral supplies and estimation methods. The close correspondence between our estimate and that of the U.S. Geological Survey indicates that geological methods yield good estimates of shallow (<1 km) mineral resources. Geological estimates therefore provide guidance to the location of shallow resources that must be discovered by exploration, and can guide land-use decisions by forward-looking citizens and governments. By extending these estimates to greater depth, our results provide quantitative confirmation that society's long-term copper supplies must come from deeper levels of the crust. This will require extensive underground mining, which involves less disturbance of the surface, but work in hostile environments with high temperatures, weak rock, and difficult access. Current underground mining reaches depths of 1.5 km in many areas and 3 km locally. Assuming 3.3 km as the likely limit of mining in the foreseeable future, our results indicate a recoverable resource of 8.9 x 10¹⁰ t of copper. At current mining rates, this can supply world copper mine production for 5500 yr. Any significant increase in this number will require advances in deep exploration and mining methods.

From a geochemical perspective, we can ask just how efficient Earth is in forming copper deposits. Magmas that form porphyry copper deposits are largely partial melts of lower crustal rocks (Richards, 2003), and other types of copper deposits are derived more directly from crustal rocks. For a mass of 1.52 x 10¹⁹ t (Lodders and Fegley, 1998) and an average copper content of 26 ppm (Shaw et al., 1986; Wedepohl, 1995; Rudnick and Fountain, 1995; McLennan and Taylor, 1996), the continental crust contains 3.9 x 10¹⁴ t of copper. Our estimate of 3 x 10¹¹ t of copper in deposits in the crust is 0.08% of this amount. If porphyry copper deposits remaining in the crust constitute 38% of all that formed during Phanerozoic time, and if this proportion applies to other types of copper deposits, then 0.24% of the copper in the crust has been concentrated into copper deposits during the Phanerozoic, and most of that has been redispersed by uplift and erosion. Even with the uncertainties indicated above, this quantifies the highly anomalous and nonrenewable nature of mineral deposits.

	ACKNOWLEDGMENTS

 
We are grateful to D.A. Singer for insightful discussion of our effort and to Philip Candela, Eric Seedorff, and three additional reviewers for helpful comments.

	REFERENCES CITED

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Received for publication 27 July 2007

Revised manuscript received 27 November 2007

Manuscript accepted 4 December 2007

This Article Abstract Figures Only Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Google Scholar Articles by Kesler, S. E. Articles by Wilkinson, B. H. GeoRef GeoRef Citation