Fractal analysis for geomagnetic secular variations

Abstract

Fractal Analysis deals with the science of complexity. Fractal analysis is more economical and most powerful method for analyzing the time series data. Fractal geometry allows the description of natural patterns by simple numbers, to facilitate their comparison and to establish and test models of pattern formation (Kruhl, 1994) The purpose of this paper is to study the geometrical complexity of geomagnetic secular variations estimated by fractal dimension, the disorder of the unpredictable secular variations estimated by Lyapunov exponent and the non linear system represented at each instant of time by a point which traces out a trajectory during this time defined by the state of variables- phase space analysis, for the available data of geomagnetic secular variations at Indian observatories. The result of the analysis confirms the previous results of secular variation anomalies at the Indian observatories. Regional inconsistencies for the declination (D) and vertical (Z) components for the Hyderabad and Sabhawala observatories are brought out in this paper. Analytical technique and the results of the analysis are discussed