Statistics for Modeling Heavy Tailed Distributions in Geology: Part II. Applications

In this paper, we present three diverse types of applications of extreme value statistics in geology, namely: earthquakes magnitudes, diamond values, and impact crater size distribution on terrestrial planets. Each of these applications has a different perspective toward tail modeling, yet many of these phenomena exhibit heavy or long tails which can be modeled by power laws. It is shown that the estimation of important tail characteristics, such as the extreme value index, is directly linked to the interpretation of the underlying geological process. Only the most extreme data are useful for studying such phenomena, so thresholds must be selected above which the data become power laws. In the case of earthquake magnitudes, we investigate the use of extreme value statistics in predicting large events on the global scale and for shallow intracontinental earthquakes in Asia. Large differences are found between estimates obtained from extreme value statistics and the usually applied standard statistical techniques. In the case of diamond deposits, we investigate the impact of the most precious stones in the global valuation of primary deposits. It is shown that in the case of Pareto-type behavior, the expected value of few extreme stones in the entire deposit has considerable influence on the global valuation. In the case of impact crater distributions, we study the difference between craters distributions on Earth and Mars and distributions occurring on other planets or satellites within the solar system. A striking result is that all planets display the same distributional tail except for Earth and Mars. In a concluding account, we demonstrate the apparent loghyperbolic variation in all of the above-mentioned examples.