Analysis of seismic dynamical systems

Abstract

A procedure is presented for the analysis of complex stationary time series for which the Fourier power spectra reveals broadband noise or broadened pulses. We first determine the Hurst exponent from which we may know whether the time series under study is mainly random or if the data points present correlations. If the data are correlated, a chaotic analysis will reveal whether they may be interpreted as a low dimensional nonlinear system (defined by a low correlation dimension and a finite and positive Kolmogorov entropy and largest positive Lyapunov exponent) or as a stochastic process. We have studied three kind of temporal series: inter-event time series of infrasonic pulses recorded at Stromboli volcano, and, S-coda waves and microseisms, that have been recorded at the eastern Pyrenees. Results show that microseisms and Coda waves can be modeled as a low dimensional deterministic system, Correlation dimensions 2.3, 3.2, respectively. At the contrary infrasonic has resulted stochastic. This chaotic character can be attributed to the medium properties. Coda waves with scattering through a fractal distribution of scatters or to multiple reflection inside resonators (for example sedimentary basins) and microseisms as a propagation of wave guide of variable cross section which have the same temporal characteristics as a nonlinear forced oscillator.