Open AccessThe fit of polar wander curves by small circles using Marquardt's algorithm: statistical properties
Author(s) -
Schott J. J.,
Turlot J. C.,
Thomann J.
Publication year - 1991
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1991.tb00808.x
Subject(s) - ellipse , polar , consistency (knowledge bases) , mathematics , geometry , algorithm , curve fitting , geodesy , mathematical analysis , geology , statistics , physics , astronomy
SUMMARY 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.