Multifractal Properties of Time Series of Synthetic Earthquakes Obtained from a Spring-Block Model

Abstract

With the spring-block model proposed by Olami, Feder, and Christensen (OFC), we obtained a time series of synthetic earthquakes with different values of the conservation level (β), which measures the fraction of the energy that a relaxing block passes to its neighbors. The time series have multifractal characteristics, and we analyzed them with the Chhabra and Jensen method. We calculated the width, symmetry, and curvature parameters for each spectrum. As the value of conservation level increases, the spectra widen, the symmetric parameter increases, and the curvature around the maximum of the spectra decreases. In a long series of synthetic seismicity, we located earthquakes of the greatest magnitude and built overlapping windows before and after them. For the time series in each window, we performed multifractal analysis to obtain multifractal spectra. We also calculated the width, symmetry, and curvature around the maximum of the multifractal spectrum. We followed the evolution of these parameters before and after large earthquakes. We found that the multifractal spectra had greater widths, were less skewed to the left, and were very pointed around the maximum before rather than after large earthquakes. We studied and calculated the same parameters and found the same results in the analysis of the Southern California seismicity catalog. This suggests that there seems to be a process of preparation for a great earthquake and that its dynamics are different from the one that occurs after this mainshock based on the behavior of the parameters mentioned before.