Nonuniversality and scaling breakdown in a nonconservative earthquake model

Asperity characteristics of the Olami-Feder-Christensen model of earthquakes

Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibited "asperity"-like phenomena, i.e., the same region ruptures many times near periodically [T. Kotani, Phys. Rev. E 77, 010102(R) (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, e.g., the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space.

Entropy production and self-organized (sub)criticality in earthquake dynamics

We derive an analytical expression for entropy production in earthquake populations based on Dewar's formulation, including flux (tectonic forcing) and source (earthquake population) terms, and apply it to the Olami-Feder-Christensen numerical model for earthquake dynamics. Assuming the commonly observed power-law rheology between driving stress and remote strain rate, we test the hypothesis that maximum entropy production (MEP) is a thermodynamic driver for self-organized 'criticality' (SOC) in the model. MEP occurs when the global elastic strain is near-critical, with small relative fluctuations in macroscopic strain energy expressed by a low seismic efficiency, and broad-bandwidth power-law scaling of frequency and rupture area. These phenomena, all as observed in natural earthquake populations, are hallmarks of the broad conceptual definition of SOC (which has, to date, often included self-organizing systems in a near but strictly subcritical state). In the MEP state, the strain field retains some memory of past events, expressed as coherent 'domains', implying a degree of predictability, albeit strongly limited in practice by the proximity to criticality and our inability to map the natural stress field at an equivalent resolution to the numerical model.

Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen (OFC) to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the OFC model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.

Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes

Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp delta -function-like peak corresponding to rhythmic recurrence of events with a fixed "period" uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology.

Transient and stationary behavior of the Olami-Feder-Christensen model

Using long-term computer simulations and mean-field-like arguments, we investigate the transient time and the properties of the stationary state of the Olami-Feder-Christensen model as function of the coupling parameter alpha and the system size N. The most important findings are that the transient time increases with a nonuniversal exponent of the system size, and that the avalanche size distribution will not approach a power law with increasing system size.

Quasiperiodic events in an earthquake model

We introduce a modification of the Olami-Feder-Christensen earthquake model [Phys. Rev. Lett. 68, 1244 (1992)10.1103/PhysRevLett.68.1244] in order to improve the resemblence with the Burridge-Knopoff mechanical model and with possible laboratory experiments. A constant and finite force continually drives the system, resulting in instantaneous relaxations. Dynamical disorder is added to the thresholds following a narrow distribution. We find quasiperiodic behavior in the avalanche time series with a period proportional to the degree of dissipation of the system. Periodicity is not as robust as criticality when the threshold force distribution widens, or when an increasing noise is introduced in the values of the dissipation.

Criticality and universality in a generalized earthquake model

We propose that an appropriate prototype for modeling self-organized criticality in dissipative systems is a generalized version of the two-variable cellular automata model introduced by Hergarten and Neugebauer [Phys. Rev. E 61, 2382 (2000)]. We show that the model predicts exponents for the event size distribution which are consistent with physically observed results for dissipative phenomena such as earthquakes. In addition we provide evidence that the model is critical based on both scaling analyses and direct observation of the distribution and behavior of the two variables in the interior of the lattice. We further argue that for reasonably large lattices the results are universal for all dissipative choices of the model parameters.

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the q-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.