『Abstract
　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 〜1.7×10¹¹tonnes (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 3×10¹¹ 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.

Keywords: copper; resources; ore deposit; mineral deposit; tectonic; computational model.』

『要旨
　世界の鉱物の資源の良い見積りは、戦略的な計画から世界での地球化学的循環までにわたる諸問題に関連している。我々は、鉱床として存在する地球の銅の量を計算するために、地殻を垂直方向に貫く斑岩銅鉱床の構造的移動についての時間−空間モデルを用いた。地殻の浸食された鉱床と保存された鉱床の数を見積るために、モデルは地球でもっとも広範かつ重要な銅資源である斑岩銅鉱床の数と時代の知識のみによっている。モデルの結果は、125,895に達する斑岩銅鉱床が顕生代の間に形成され、このうちのたったの47,789が様々な深さの地殻に残されており、それは1700億トンの銅を含むことを示している。他のタイプの銅鉱床も地殻で同様にふるまい、現在の世界生産に比例する量があると仮定すると、地殻でのすべての世界銅資源の合計は3000億トンの見積りとなる。このように、地殻における銅の0.25％ほどが顕生代を通じて鉱床として濃集され、この約2/3が隆起と浸食によって再循環された。将来における採掘の限界と思える地下3.3キロメートル以内にある鉱床の銅の量は、現在の世界の鉱山生産量の5500年分を供給できるもので、これは鉱床の非常に異常で再生できない性質を量で表している。』

Introduction
Methods used for estimating global mineral resources
Method used in this study
Application of the model to global copper resources
　Porphyry copper resources
　Global copper resources and comparison to other estimates
Significance and ramifications of this estimate
Acknowledgments
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