Zipf?s Law: A Viable Geological Paradigm?

Abstract

Zipf’s Law originally was proposed as a guide to a statistical distribution in social studies. The law describes a relationship between size and rank of discrete phenomena. It is a variant of Pareto’s 1927 Law known as the 80/20 rule and is similar to Bode’s Law in concept. The relationship described by Zipf’s Law is a succession of order data with the largest followed by half the size for the next largest, which in turn, the next is half that size, and so on. In geology, it has been used with moderate success in resource assessment of mining and petroleum. In essence, it predicts how many entities of a certain size may be left in a sequence of decreasing size assuming the largest has been ascertained. Examples of applications would be plotting the rank and size of ore deposits or oil fields to determine how many deposits remained undiscovered and their size. After a flurry of papers in the 1970s and 1980s, application of the law apparently either was successful and thus not reported in way the literature or was determined to be ineffectual and its use discontinued, but either way the law lapsed into obscurity. Examples of oil- and gas-field size in Kansas, the occurrence of historic earthquakes that affected the state, and size of anticlines (plains-type folds) are presented to illustrate application and limits of Zipf’s Law.