Detection of Long-Range Correlations and Trends Between Earthquakes in California

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 Earthquakes. The long-range correlations are usaully 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 California during 12 years, from2/24/2007 to 9/29/2017. 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). Estimationg 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 future main shocks.