Study of Geomagnetic Field Reversals using the Mellin Transform

Abstract

An analysis has been made from the geomagnetic field reversals of both normalised and reversed polarity bias (NPB and RPB) of Phanerozoic period i.e., 0-570 m.y. using the Mellin Transform which is conceptually a different mathematical approach compared to the Fourier, Walsh and Circular transform methods. The Mellin transformed geomagnetic reversals have revealed some significant discontinuities at different periods of 30, 84, 97, 120, 145, 200, 285, 354 (?), 394 (?), 437 and 542 m.y. and field reverslas obey gamma distribution that confirms Naidu’s (1971) empirical formulation. The Mellin transform of two equal subgroups namely 0-285 m.y. and 286-570 m.y. of the geomagnetic reversals of both normalised and reversed polarity bias have revealed two distinct breaks at 30 m.y. and 97 m.y., but the other breaks which appeared on 0-570 m.y. data are not distinctly repeated. Subsequently, the correlation coefficient of the original and transformed data for entire data length and its two equal subgroups found to be positive implying that the two equal subgroups may relate linearly, whereas the F-Statistic value substantially differs from the tabulated value and this suggests that the long-term periodicity does not exist at all.