Multifractal detrended cross-correlation analysis of temporal and spatial seismic data

We use Multi-Fractal Detrended Cross-Correlation Analysis (MF-DXA) method to investigate the cross-correlation of temporal and spatial inter-events seismic data, which expected to be correlated. The mentioned data are the California earthquakes' data which are simultaneously recorded, over an extended period of time. We get the cross-correlation exponent 0.76 +/- 0.01. We determine generalized Hurst exponent and singularity spectrum and find that these sequences are joined in various scales and have a multifractality behavior. It means that the correlation in small scales of the sequences (the earthquakes which are close together in space and time) are different from in the large ones. We also find that in spite of the multifractal behavior of temporal and spatial time series, their cross series shows fractal behavior, meaning that the statistical properties of the cross series are invariant under the change of scale.