Multifractal Analysis for the Overlapping Windows Method of a Time Series of Synthetic Earthquakes obtained with a Spring-Block Model

We work with the model proposed by Olami, Feder and Christensen (OFC) to build time series with 10 000 000 data of synthetic earthquakes magnitudes, and conservation value β = 0.2. In this time series, we located the earthquakes with greater magnitude. We built 160 windows before and after these great earthquakes. The windows have 1024 data with an overlap of 896 points. For each windows, the values of the multifractality degree Δλ and the parameter of symmetry were calculated. We follow the evolution of these parameters before and after the big earthquakes. The multifractal spectra have larger widths before than after the earthquake. The multifractal spectra of the 320 windows are left skewed, but the multifractal spectra of the time series before the earthquake are more biased towards the left than the multifractal spectra after the earthquake. Finally, we measured the curvature K around the maximum of the multifractal spectra, the K value is bigger before than after the earthquake. This suggests that there is apparently a process of preparation for the earthquake and that the dynamics after the earthquake is very different.