Wavelet-based multiscale resolution analysis of real and simulated time-series of earthquakes

This study introduces a new approach (based on the Continuous Wavelet Transform Modulus Maxima method) to describe qualitatively and quantitatively the complex temporal patterns of seismicity, their multifractal and clustering properties in particular. Firstly, we analyse the temporal characteristics of intermediate-depth seismic activity (M >= 2.6 events) in the Vrancea region, Romania, from 1974 to 2002. The second case studied is the shallow, crustal seismicity (M >= 1.5 events), which occurred from 1976 to 1995 in a relatively large region surrounding the epicentre of the 1995 Kobe earthquake (Mw = 6.9). In both cases we have declustered the earthquake catalogue and selected only the events with M >= Mc (where Mc is the magnitude of completeness) before analysis. The results obtained in the case of the Vrancea region show that for a relatively large range of scales, the process is nearly monofractal and random (does not display correlations). For the second case, two scaling regions can be readily noticed. At small scales (i.e. hours to days) the series display multifractal behaviour, while at larger scales (days to several years) we observe monofractal scaling. The Holder exponent for the monofractal region is around 0.8, which would indicate the presence of long-range dependence (LRD). This result might be the consequence of the complex oscillatory or power-law trends of the analysed time-series. In order to clarify the interpretation of the above results, we consider two 'artificial' earthquake sequences. Firstly, we generate a 'low productivity' earthquake catalogue, by using the epidemic-type aftershock sequence (ETAS) model. The results, as expected, show no significant LRD for this simulated process. We also generate an event sequence by considering a 70 kin long and 17.5 km deep fault, which is divided into square cells with dimensions of 550 in and is embedded in a 3-D elastic half-space. The simulated catalogue of this study is identical to the case (A), described by Eneva & Ben-Zion. The series display clear quasi-periodic behaviour, as revealed by simple statistical tests. The result of the wavelet-based multifractal analysis shows several distinct scaling domains. We speculate that each scaling range corresponds to a different periodic trend of the time-series.