LONG-RANGE CORRELATIONS AND TRENDS BETWEEN CONSECUTIVE EARTHQUAKES

One of the most interesting properties that time series of different kind of phenomena exhibit, is the long-range correlation, also known as long memory or long-range persistence, means that the auto-covariance function decays exponentially, by a spectral density that tends to infinity (Bardet et al., 2003; Cajueiro & Tabak, 2004). Self-similarprocesses have been used successfully to model data exhibiting long memory and arising in a wide variety of fields, ranging from physics (geophysics, turbulence, hydrology, solid-state physics, …) or biology (DNA sequences, heat rate variability, auditory nerves spike trains, …), to human operated systems (telecommunications network traffic, image processing, pattern recognition, finance, …). For self-similar (or scale invariant) processes, the probabilistic properties of the process remain invariant when it isviewed at different time-scales. In mathematical expression, a stochastic process {X (t ), t ÎR +}is scale invariant or selfsimilar with Hurst parameter H, if for all l > 0 it follows the scaling law: X (lt ) º lHX (t ), t ÎR + , where º means equality in all finite dimensional distributions (Borgnat, 2005). The index H characterizes the self-similar behavior of the process, and a very large variety of methods has been proposed in the literature for estimating it (Bardet et al., 2003; Beran, 1994). In this paper, we investigate the long-range correlations and trends between consecutive earthquakes by means of the scaling parameter so-called locally Hurst parameter, H(t), and examine its variations in time, to find a specific pattern exists between foreshocks, main shock and the aftershocks. The long-range correlations are usually detected by calculating a constant Hurst parameter. However, the multi-fractal structure of earthquakes caused that more than one scaling exponent is needed to account for the scaling properties of such processes. Thus, in this paper, we consider the time-dependent Hurst exponent, to realize scale variations in trend and correlations between consecutive seismic activities, for all times. We apply the Hilbert-Huang transform to estimate H(t) for the time series extracted from seismic activities occurred in Iran. The superiority of the method is discovering some specific hidden patterns exist between consecutive earthquakes, by studying the trend and variations of H(t). Estimating H(t) only as a measure of dependency, may lead to misleading results, but using this method, the trend and variations of the parameter is studying to discover hidden dependencies between consecutive earthquakes. Recognizing such dependency patterns can help us in prediction of main shocks (Figures 1 and 2).

کلیدواژه ها:

Long-range dependence ، Time-dependent Hurst exponent ، Hilbert-Huang transform ، Empirical mode decomposition ، Seismic activities