Higuchis Method applied to the detection of periodic components in time series and its application to seismograms

Abstract

At the moment, the analysis of the named complex systems is based mainly on the study of the properties of the signals that is possible to measure. In general, these signals are obtained in a discreet way; therefore they constitute the so called time series in a natural way. Time series of complex systems present fractal and multifractal properties. The Higuchis method is a method that if applied appropriately it can determine in a reliable way the fractal dimension D of the analyzed time series, this fractal dimension allows us to characterize the degree of correlation of the series. However, when analyzing some time series as heart interbeat, atmospheric pollutants (ozone), seismograms, etc., with the Higuchis method, there are oscillations that have been observed at the right of the graph, that correspond to the considered big scales, which can cause a mistaken determination of the fractal dimension. In this work, an appropriate explanation is given to this type of behaviour, this fact enhances the understanding of the Higuchis method, and we propose also its application as detector and alarm of possible earthquakes.