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Xavier Lana,Dolors Martínez,Carina Serra,Amir Hosseini 한국지질과학협의회 2020 Geosciences Journal Vol.24 No.2
Distances between consecutive aftershocks are analysed by means of mono- and multifractal theory with the aim of quantifying the complexity of the physical mechanism governing them, as well as their predictability and predictive instability. Hausdorff, Ha, and Hurst, H, exponents are determined by semivariograms and rescaled analysis, respectively. The exponent β of the power law describing power spectral contents is also quantified. These three parameters permit a generation of fractional Gaussian noise, fGn, simulating distances. The complexity and predictive instability of physical mechanism generating the series of distances is quantified by means of the correlation dimension, μ*, the Kolmogorov entropy, κ, and the Lyapunov exponents, λi, which are based on the reconstruction theorem formulation. Additionally, the multifractal detrended fluctuation analysis, MF-DFA, contributes with a different point of view to quantify the complexity of the series, in terms of fractal spectral width, W, spectral asymmetry, B, and the critical Hölder exponent, a0. By one hand, the MF-DFA is applied to the complete set of distances characterising the whole aftershock process. By the other hand, the MF-DFA is applied to segments of the series of distances with the aim of determining the evolution of the complexity since the mainshock up to the end of the stress relaxation process. Finally, an ARIMA multilinear regression process is applied to obtain some improvements, in comparison with fGn simulations, on the prediction of distances. The database for this analysis is obtained from the Southern California Seismic Network (SCSN) catalogue. Three series of aftershocks equalling to or exceeding magnitudes of 2.0, assuring seismic catalogue completeness, and associated with Landers (06/28/1992), Northridge (01/17/1994) and Hector Mine (10/16/1999) mainshocks are obtained. It is worth mentioning that common mono-multifractal behaviour for the three aftershocks series is not detected, whatever aftershock periods or segments of them are considered.
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Fractal analysis and statistics of seismic generation rates: the example of the southern California
Xavier Lana,Maria Dolors Martínez,Seyed Amir Hosseini,Carina Serra 한국지질과학협의회 2017 Geosciences Journal Vol.21 No.3
The seismic generation rate, SGR, at southern California along the 1981–2007 recording period is analysed with the main purpose of finding out whether there exist some correlations between seismic activity before, after and along aftershock sequences triggered by mainshocks of high magnitude. The possibility that a mainshock could be triggered by another neighbouring mainshock and its aftershock sequence is also investigated. The analyses are based on monthly SGR series, obtained as the number of events detected every month along the recording period considered. These monthly SGR series are derived for three aftershock areas associated with Landers (June 28, 1992, Mw = 7.3), Northridge (January 17, 1994, Mw = 6.7) and Hector Mine (October 16, 1999, Mw = 7.1) mainshocks. The most relevant features of SGR series are investigated through various techniques: 1) the rescaled range analysis and the interpretation of the Hurst exponent in terms of persistence, anti-persistence and randomness; 2) time trend estimation by the Kendall-tau algorithm and assessment of their statistical significance by the Mann-Kendall test; 3) the self-affine character, derived from semivariograms, and the Hausdorff measure; 4) autocorrelation and power spectra; 5) cross-correlation and cross-power spectra; 6) the search for the statistical distribution best reproducing the empirical probability of SGR series. Additionally, a close look at plots of epicenters within the aftershock areas, distinguishing between periods of background and aftershock activity, permits detecting some features of the seismicity. Changes on spatial patterns of seismicity suggest that the effects of tectonic stress redistribution could persist beyond an aftershock period, at short and medium distances of the mainshock. This possibility would be also in agreement with cross-correlation results for SGR series.
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