Abstract

Benford's law predicts that the distribution of first digits of real-world observations is not uniform, but instead the lower digits (1, 2, and 3) occur more frequently than the higher ones (… , 8, 9). It has been shown that the use of Benford's law may help as a validity check on databases, and that the first-digit rule may provide new ways to detect anomalous signals in data sets. In fact, nonconformity to Benford's law could be an indicator of (1) incompleteness, (2) excessive data round-off, or (3) data errors, inconsistencies, or anomalies. This law has long been known, but has received little attention, in earth sciences. In this work, we first test the conformity of three volcanology-related data sets, and then we consider the relevance and potential utility of using Benford's law to assess the integrity and authenticity of the presented volcanological data. The first two data sets are the area in square kilometers and age in years of collapse calderas extracted from the Collapse Caldera Database (CCDB), covering areas from 0.03 to 4700 km2 and ages from a few years to 2000 Ma. The third data set is the duration in days of the volcanic eruptions that occurred between A.D. 1900 and 2009 according to the Smithsonian's Global Volcanism Program catalogue (http://www.volcano.si.edu). Results obtained indicate that the volcanological data sets of this study follow Benford's law. The present analysis shows that excessive data round-off, data errors, or anomalies may be detected when comparing the data with Benford's law expected frequencies.

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