DescriptionIn geology, a hotspot is a location on the Earth's surface demonstrating active volcanism for an extended period of time. There is a controversy in Earth Science regarding whether volcanic regions like Hawaii and Iceland are fed from the core-mantle boundary at 3000 km depth in the Earth, or whether they are shallow-sourced (Foulger, 2010). Some references supporting the deep model claim that volcanic regions at the surface correlate spatially with the velocity of seismic waves (or the velocity gradient) in the Earth's interior (Torsvik et. al, 2006). Seismic waves comprise energy that travels through the Earth as compressional or shear waves, and are a result of earthquakes and explosions.Statistically, it has not been convincingly demonstrated yet whether the claimed correlations are robust to subjective selection and classification of the items being correlated, e.g. the "hotspots", and whether these correlations are even well defined in a mathematically sound sense. The project will begin with some exploratory data analysis, using data featuring hotspots and seismic velocities provided by Professor Gillian Foulger from the Earth Science Department. This first analysis will involve unsupervised statistical learning techniques such as cluster analysis or principal curves (see, for instance, Hastie, Tibshirani & Friedman, 2001). The project will then proceed with formulating the involved items (hotspot locations, etc.) in such a way that the correlations can be tested in some meaningful way. The significance of the correlations is to be tested using appropriate multivariate simulation techniques, possibly involving fuzzy methods (where objects are not characterized by their existence or non-existence, but by the probability of their existence). PrerequisitesStatistical Methods III
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email: jochen.einbeck "at" durham.ac.uk