Estimating the number and locations of Euler poles

• Published in: GEM international journal on geomathematics 2014-11, Vol.5 (2), p.289-301
• Main Authors: Bachmann, F., Jupp, P. E., Schaeben, H.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Science and Engineering; Earth Sciences; Mathematics; Mathematics and Statistics; Original Paper
• ISSN: 1869-2672; 1869-2680
• DOI: 10.1007/s13137-014-0064-2

Plate tectonics is much concerned with Euler poles (axes of rotation) of plates. Each Euler pole has to be estimated from geological field data ( r 1 , ± n 1 ) , … , ( r n , ± n n ) , where (for i = 1 , … , n ) r i is a point on the unit sphere, S 2 , and ± n i is an axis in the tangent plane at r i . Such data are viewed here as regression data, in which the positions r i are values of a predictor on S 2 , while the corresponding tangential axes ± n i are responses in the tangent plane to S 2 at r i ( i = 1 , … , n ). A regression model is proposed, from which maximum likelihood estimates and confidence regions for the pole can be found. Since samples may come from unknown mixtures of populations, it is necessary to estimate the number of Euler poles and their locations. By extending the above regression model to a mixture model and using the EM algorithm, the number of Euler poles can be estimated and both point estimates and confidence regions for the poles can be obtained. The observations can then be allocated to the estimated Euler poles. The methods are illustrated by the analysis of some artificial data sets.