Spherical Regression and the Statistics of Tectonic Plate Reconstructions

Summary This paper discusses some of the statistics of estimated rotations with special attention to the statistics that applies in the reconstruction of tectonic plate motions. Two models are presented: the spherical regression model, that deals with a highly idealized form of the data, and a more realistic analysis for the types of data used in plate reconstructions. The discussion of the spherical regression model focuses on the interplay of the geometry of the plate boundaries and the statistical properties of a least square estimator. Because the errors in tectonic data are extremely concentrated, the more realistic analysis reduces to a linear regression. Once this is realized, many problems of geophysical interest, such as triple junctions can be handled. The paper closes with a selection of possible problems for further consideration.