Time-Dependent Scaling Patterns in Sarpol-e Zahab Earthquakes

In this paper, the dynamics of the seismic activity and fractal structures in magnitude time series of Sarpol-e Zahab earthquakes are investigated. In this case, the dynamics of the seismic activity is analyzed through the evolution of the scaling parameter so-called Hurst exponent. By estimating the Hurst parameter, we can investigate how the consecutive earthquakes are related. It has been observed that more than one scaling exponent is needed to account for the scaling properties of earthquake time series. Therefore, the influence of different time-scales on the dynamics of earthquakes is measured by decomposing the seismic time series into simple oscillations associated with distinct time-scales. To this end, the Empirical Mode Decomposition (EMD) method was used to estimate the locally long-term persistence signature derived from the Hurst exponent. As a result, the time dependent Hurst exponent, H(t), was estimated and all values of H>0.5 was obtained, indicating that a long-term memory exists in earthquake time series. The main contribution of this paper is estimating H(t) locally for different time-scales and investigating the long-memory behavior that exists in the non-stationary multifractal time-series. The time-dependent scaling properties of earthquake time series are associated with the relative weights of the amplitudes at characteristic frequencies.
The superiority of the method is the simplicity and the accuracy in estimating the Hurst exponent of earthquakes in each time, without any assumption on the probability distribution of the time series. We investigated the negative and positive autocorrelations that exist between consecutive seismic activities by estimating the time-dependent Hurst parameter, H * (t). To this end, the empirical mode decomposition and the Hilbert-Huang transform are applied. Using this method, the seismic activities are studied locally, and the autocorrelation between consecutive earthquakes are estimated in each time. We have investigated the superiority of the estimator by simulation. Furthermore, the method is applied in estimating H * (t) of earthquakes occurred in Sarpol-e Zahab during November 12, 2017 to January 20, 2018. By estimating the Hurst parameter locally, and considering the values of H * (t) that are greater than 0.5, we identify that the long memory behavior exist in consecutive earthquakes during 25/11/2017 and 13/1/2018. It is also seen that, in spite of small values of H * (t) for some times, which shows the stochastic behavior in earthquakes, the local Hurst parameters are tending to be greater than 0.5, and after this patterns, a peak in magnitude is seen. This paper shows that the combination of the EMD and its associated Hilbert spectral analysis offers a powerful tool to uncover the time-dependent scaling patterns of consecutive seismic activities data. 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 that 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 that 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 mainshocks.