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Department of Mathematical Sciences

Academic Staff

Publication details for Jochen Einbeck

Julian, B.R., Foulger, G.R., Hatfield, O., Jackson, S.E., Simpson, E., Einbeck, J. & Moore, A. (2015). Hotspots in Hindsight. In The Interdisciplinary Earth: A Volume in Honor of Don L. Anderson. Foulger, G.R., Lustrino, M. & King, S.D. Boulder, Colorado Washington, DC: The Geological Society of America / AGU. 105-121.

Author(s) from Durham


Several workers have suggested that the locations of melting anomalies (hotspots) and the original locations of large igneous provinces (LIPs) and kimberlite pipes lie preferentially above the margins of two large low-shear-velocity provinces, or LLSVPs, near the bottom of the mantle, and that the geographical correlations have high confidence levels (>99.9999%). They conclude that the LLSVP margins are “plume-generation zones”, and that deep-mantle plumes cause hotspots, LIPs, and kimberlites. This conclusion raises questions about what physical processes could be responsible, because, for example, the LLSVPs are apparently dense and not abnormally hot.

The supposed LIP-hotspot-LLSVP correlations probably are examples of the “hindsight heresy”, of performing a statistical test using the same data sample that led to the initial formulation of a hypothesis. In this process, an analyst will consider and reject many competing hypotheses, but will not adjust statistical assessments correspondingly. Furthermore, an analyst will test extreme deviations of the data, but not take this fact into account. “Hindsight heresy” errors are particularly problematical in Earth science, where it commonly is impossible to conduct controlled experiments.

For random locations on the globe, the number of points within a specified distance of a given curve follows a cumulative binomial distribution. We use this fact to test the statistical significance of the observed hotspot-LLSVP correlation using several hotspot catalogs and mantle models. The results indicate that the actual confidence levels of the correlations are two or three orders of magnitude smaller than claimed. The tests also show that hotspots correlate well with presumably shallowly rooted features such as spreading plate boundaries.

Nevertheless, the correlations are significant at confidence levels in excess of 99%. But this is confidence that the null hypothesis of random coincidence is wrong. It is not confidence about what hypothesis is correct. The correlations probably are symptoms of as-yet-unidentified processes.

These observations emphasize the importance of the distinction between correlation and causation, and underline the necessity of taking geological factors into account. Consideration of the kimberlite data set in the context of geological setting, for example, suggests that the apparent association with the LLSVP margins results from the fact that the Kaapvaal craton, the site of most of the kimberlites considered, lies in southern Africa, and that kimberlite eruptions are sensitive primarily to stress in the lithosphere.