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.

Fractal behaviour of distances between consecutive aftershocks: the examples of Landers, Northridge and Hector Mine Southern California mainshocks

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.

Aftershock sequences of three seismic crises at southern California, USA, simulated by a cellular automata model based on self-organized criticality

Marisol Monterrubio,Xavier Lana,Maria Dolors Martínez 한국지질과학협의회 2015 Geosciences Journal Vol.19 No.1

Several properties of aftershock series related to themain shocks of Landers, Northridge and Hector Mine (southern California, USA) are reproduced by theDynamic Fiber Bundle Model, DFBM. Optimum values for the three parameters governing DFBM aredetermined by searching for the best agreement of real aftershock series properties and those ofsynthetic sequences gen- erated by this model. The analysis of the model parameter values providesdetails on the underlying physical mechanism of the after- shock sequence generation. First, theratio of seismic energy radiated as seismic waves and transferred as stress-strain to adjacentfaults; second, the degree of stress heterogeneity reproducing the complex behavior of realaftershock series. Additionally, the results of simula- tions support the coexistence of two typesof relaxation processes. One of them is associated with the well-known modified Omori’s (MO) law,which involves elapsed times between consecutive after- shocks monotonically increasing; the otheris manifested by episodes of sudden stress release, with inter-event times much shorter than thosepredicted by MO law. These episodes are assumed to be a consequence of the complex distribution oftectonic stresses and fault geometry. The first process is associated to events designed as leadingaftershocks, LA. The second process generates series of events which are designed as cascades, CA. It is worth of mention that several properties con- cerning CAs can be reasonably related tocritical changes on stressfield along the simulation process.

Two complementary stress release processes based on departures from Omori’s law

Marisol Monterrubio,Maria-Dolors Martínez,Xavier Lana 한국지질과학협의회 2016 Geosciences Journal Vol.20 No.1

Three aftershock series in Southern California, associated with the mainshocks of Landers (1992), Northridge (1994) and Hector Mine (1999) are interpreted as the superposition of a long stress relaxation process, in agreement with the Omori’s law, and a number of short episodes with sudden stress release. These short episodes are detected as departures from the expected Omori’s law. Aftershocks following a long stress relaxation process are designed as leading aftershocks (LA) and their generation rate fits well to the modified Omori’s law (MOL). The rest of aftershocks correspond to the different episodes of sudden stress release, every one designed as a cascade (CA). Cascades are found to be characterized by four basic properties. First, although the number of aftershocks NC belonging to every cascade fluctuates greatly along the stress relaxation process, a clear positive trend of NC with the elapsed time since the mainshock is observed in the initial phase of the aftershock sequence. After a critical elapsed time, very short in comparison with the aftershock sequence length, this positive trend diminishes significantly or even becomes negative. Second, the aftershock generation rate, GR, for every cascade, is almost constant. Third, GR for the successive CAs, represented as a function of its starting time measured since the mainshock, decreases according to a power-law. Four, the validity of the Gutenberg-Richter law is preserved for the sequence of all aftershocks belonging to cascades, with values of the b-parameter quite similar to those deduced for the complete aftershock series. Additionally, some statistical and fractal (self-affine) properties of CAs are analyzed. Given that the number of aftershocks with minimum magnitudes assuring catalogue completeness ranges, for the three seismic crises, from 6,000 up to 20,000, properties concerning LA and CA can be established with a high degree of confidence. As a conclusion, a single stress relaxation process following the Omori’s law should be discarded. A physical explanation, based on the complex spatial patterns of the stress field and tectonic fractures, as well as on the two proposed relaxation processes, is qualitatively discussed.