Mathematical Geosciences

, Volume 43, Issue 6, pp 625–634 | Cite as

Abscissa-Transforming Second-Order Polynomial Functions to Approximate the Unknown Historic Production of Non-renewable Resources

Article

Abstract

For many non-renewable resources, reliable production data are only available from a certain point in time but not from the beginning of production periods. In order to constrain the unknown historic production of such resources for those ancient times for which no reliable annual production data are available we present a novel mathematical technique, based on Verhulst’s logistic function. The method is validated by the United States’ crude oil production for which the complete production cycle, starting in 1859, is well documented. Assuming that the oil production in the USA between 1859 and 1929 is unknown, our method yields values for this period of 16.0 gigabarrels (Gb) based on a second-order polynomial fit and 13.5 Gb based on a third-order polynomial fit of post-1929 production data, respectively. Especially the latter amount compares well with the actual value of 12.1 Gb, thus illustrating the strength of the method. For global gold (Au) production, our method yields an ancient production up to the year 1850, when official and reliable production statistics began, of approximately 10,000 metric tons (t) based on a second-order polynomial fit. For mercury (Hg) a production of 64,000 t was determined for the time up to the year 1900, when annual production figures started to become available, again using a second-order polynomial fit. While the results obtained by the application of second-order polynomial functions could be confirmed by higher-order polynomial functions in the cases of both USA oil as well as global Au production, this was not possible in the case of global Hg production because of a highly irregular production curve.

Keywords

Hubbert-linearization Ultimate recoverable amount Historic production figure Finite resources Mercury, gold 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bache JJ (1987) World gold deposits—a geological classification. Elsevier, New York Google Scholar
  2. Canogar R (2006) The Hubbert parabola. http://graphoilogy.blogspot.com/2006/09/hubbert-parabola.html. Accessed 09 Oct 2010
  3. Cargill SM, Root DH, Bailey EH (1980) Resource estimation from historical data: Mercury, a test case. Math Geol 12:489–522 CrossRefGoogle Scholar
  4. Emmons WH (1937) Gold deposits of the world. McGraw-Hill, New York Google Scholar
  5. Govett MH, Harrowell MR (1982) Gold: world supply and demand. Australian Mineral Economics Pty Ltd (AME), December 1982, Sydney, NSW Google Scholar
  6. Hubbert MK (1982) Techniques of prediction as applied to production of oil and gas. US Department of Commerce. NBS Special Publication 631:16–141 Google Scholar
  7. Kelly TD, Matos GR (2010) Historical statistics for mineral and material commodities in the united states: US Geological Survey Data Series 140, Version 2010 (online only). http://minerals.usgs.gov/ds/2005/140/mercury.pdf. http://minerals.usgs.gov/ds/2005/140/gold.pdf. Accessed 09 Oct 2010
  8. Meyers Konversationslexikon (1905) Edelmetalle Produktion seit 1493. http://www.retrobibliothek.de/retrobib/seite.html?id=104704 (in German). Accessed 09 Oct 2010
  9. Müller J, Frimmel HE (2010) Numerical analysis of historic gold production cycles and implications for future sub-cycles. Open Geol J 4:35–40 CrossRefGoogle Scholar
  10. US Energy Information Administration (2010) Petroleum navigator. http://www.eia.doe.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=MCRFPUS1&f=A. Accessed 25 Nov 2010
  11. USGS (2005) Mineral commodity summaries January 2005. http://minerals.usgs.gov/minerals/pubs/commodity/gold/gold_mcs05.pdf. Accessed 04 Dec 2010

Copyright information

© International Association for Mathematical Geosciences 2011

Authors and Affiliations

  1. 1.Geodynamics & Geomaterials Research Division, Institute of Geography & GeologyUniversity of WürzburgWürzburgGermany
  2. 2.Department of Geological SciencesUniversity of Cape TownRondeboschSouth Africa

Personalised recommendations