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The AAPG/Datapages Combined Publications Database

CSPG Special Publications


Facts and Principles of World Petroleum Occurrence — Memoir 6, 1980
Pages 987-987
Symposium Abstracts

Pros and Cons of Zipf’s Law as a Resource Appraisal Tool: Abstract

E. C. Dahlberg1

A hopefully accurate prediction of the total amount of a resource material, of which only a part has been discovered and produced, is the major objective of a resource assessment. Such points as how many deposits remain to be discovered; how rich will they be as individuals and what will be their total volume must be addressed. Inferences from empirical or mathematical models generally based on analogs are generally utilized.

Zipf’s Law (Zipf, 1949), when applied to mineral resource populations, postulates most simply that the largest will be twice the size of the second, three times as great as the third, and one hundred times bigger than the hundredth, etc. This implies that deposits become infinitesimally small as their number goes to infinity. When deposit or pool size versus rank is plotted on double logarithmic paper, the law graphs as a straight line with a slope of minus one. The Y intercept, with size as the ordinate, equals that of the item designated as first rank. The correspondence of actual sets of hydrocarbon, uranium and metallic resource data to the Zipf line is tantalizingly tight in many instances, though heroic assumptions must often be made.

With Zipf’s Law, Follinsbee (1977), from 300 giant fields, predicted a worldwide initial reserve of 149 × 109m3 (942 billion barrels) to be yielded by 300 fields and 288 × 109m3 (1814 billion barrels) accounted for by 100 000 pools of greater than 238 × 103m3 (1.5 million barrels) (if they can be found).

Rowlands and Sampey (1977) concluded from Zipf that 65% of the Zambian stratiform copper deposits still remain to be discovered.

Zipf’s Law suggests also (assuming Provost to be the largest) that 660 Viking oil pools, with initial inplace reserves of at least 159 × 103m3 (a million barrels), exist in Western Canada. If Provost is really the second largest Viking pool, the Law proclaims the existence of a yet-to-be discovered pool of greater than 159 × 106m3 (a billion barrels), a real exploration plum!

Acknowledgments and Associated Footnotes

1 Geological Survey of Canada, 3303 - 33rd Street N.W., Calgary, Alberta T2L 2A7

Copyright © 2009 by the Canadian Society of Petroleum Geologists