The fit of polar wander curves by small circles using Marquardt's algorithm: statistical properties

Abstract

The method of constructing smooth apparent polar wander paths by fitting to small circle arcs is re‐examined. The calculation of the best fitting small circle axis and angle is carried out by means of an iterative, rapidly convergent method. In addition, statistical properties are derived for the various estimated parameters in the linear asymptotic approximation, which allows, in particular, the determination of ellipses of confidence around the calculated poles of the model. Applications to the North American apparent polar wander path using previously published data sets are given as illustrations. In each case, the consistency of the inferred statistics has been checked by simulations. Copyright © 1991, Wiley Blackwell. All rights reserved