Fitting polar wander paths

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Abstract

A formalized method of constructing a best-fitting smooth curve, with confidence limits, to sequential data on a sphere is proposed and a method of least-squares alignment of two time series on a sphere is discussed. The procedure, developed from Gould's regression technique for angular variates (corresponding to multiple regression analysis for normally distributed variates), involves fitting cubic splines using a weighted (robust) least-squares approximation. Paths of apparent polar wander (APW) are defined continuously, have continuous first and second derivatives and always lie on the sphere. The cross-validation mean square deviation is used to determine the degree of smoothing. North American and European APW paths, their 95% confidence bands and apparent polar accelerations for the last 500 Ma have been calculated.

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