Multifractal and Chaotic Analysis of Vrancea (Romania) Intermediate-depth Earthquakes: Investigation of the Temporal Distribution of Events

Abstract

The Vrancea seismic region contains an isolated cluster of events beneath the Carpathian Arc Bend in Romania, dipping to about 200 km depth. Seismic activity mainly occurs at intermediate depths (h > 60 km). The main goal of the paper is to perform an in-depth, complex analysis of the occurrence times of these intermediate-depth events. We also try to show the versatility of the methods used to characterize different aspects of the seismicity evolution and to offer a user-friendly software toolbox to do most of the related computations. The earthquake catalog used in this study spans from 1974 to 2002 and includes only the intermediate-depth events. In the first part of the paper, we analyze the multifractal characteristics of the temporal distribution of earthquakes. The study reveals two distinct scaling regimes. At small scales we found a clear nonhomogeneous, multifractal pattern, while at large scales the temporal distribution of events shows a monofractal, and close to Poissonian (random), behavior. The multifractal behavior at small scales (minutes-hours) is shown to be clearly an effect of the ''short'' aftershock sequences that occurred after some major Vrancea earthquakes. In the second part of the paper we analyze whether our temporal series shows a persistent (or anti-persistent) long-term behavior, by using the Detrended Fluctuation Analysis (DFA) method. The results suggest that the analyzed temporal series of Vrancea earthquakes is a non-correlated process. In part three of the paper we seek to determine whether the dynamics of our earthquake system (described by the occurrence time of Vrancea earthquakes) is deterministically chaotic, deriving from a rather simple evolution law, or whether it is stochastic and is generated by a system that possesses many degrees of freedom. The results suggest that our signal is stochastic (probably does not possess an attractor). The limited time-span of the catalog and the analysis performed in this paper cannot rule out the emergence of an interesting, quasideterministic and low-dimensional structure in the case of major Vrancea earthquakes.

Temporal properties of seismicity and largest earthquakes in SE Carpathians

“…We extend previous studies (e.g. Marza et al, 1991;Mantyniemi et al, 2003;Enescu et al, 2005) by the estimation of the hazard rate distribution of the largest events on the basis of various statistical approaches.…”

“…Seismicity returns to the background seismicity rate approximately 100 days after the main shock. Enescu et al (2005), in their multi-fractal study of Vrancea seismicity, came to the conclusion that with exception of the aftershocks, the recurrence times of events M w >2.8 are distributed according to a Poisson process. These results are complementary to those presented in our study.…”

“…These results are complementary to those presented in our study. The exponential distribution of the smaller events can most probably be explained by the fact that in the study of Enescu et al (2005), the recurrence time distribution was obtained for the whole Vrancea area, thus the local distribution functions were averaged. The spatial averaging can account for the exponential distribution of the resulting recurrence times.…”

“…An extended recurrence time analysis for earthquakes in the Vrancea area was recently performed by Enescu et al (2005). These authors used a data catalogue beginning in 1974 and found that, with the exception of aftershock activity, the recurrence times of small and intermediate size events were distributed according to a Poisson process.…”

“…The unified scaling law of Bak et al (2002) states however that the statistics of the small and large events are self-similar within a characteristic space range. The results of Enescu et al (2005) were obtained by averaging the distribution of smaller events over the whole area of observation. The exponential distribution of recurrence times is possibly a consequence of spatial averaging.…”