Properties of Foreshocks and Aftershocks of the Non-Conservative SOC Olami-Feder-Christensen Model: Triggered or Critical Earthquakes?

Following Hergarten and Neugebauer [2002] who discovered aftershock and foreshock sequences in the Olami-Feder-Christensen (OFC) discrete block-spring earthquake model, we investigate to what degree the simple toppling mechanism of this model is sufficient to account for the properties of earthquake clustering in time and space. Our main finding is that synthetic catalogs generated by the OFC model share practically all properties of real seismicity at a qualitative level, with however significant quantitative differences. We find that OFC catalogs can be in large part described by the concept of triggered seismicity but the properties of foreshocks depend on the mainshock magnitude, in qualitative agreement with the critical earthquake model and in disagreement with simple models of triggered seismicity such as the Epidemic Type Aftershock Sequence (ETAS) model [Ogata, 1988]. Many other features of OFC catalogs can be reproduced with the ETAS model with a weaker clustering than real seismicity, i.e. for a very small average number of triggered earthquakes of first generation per mother-earthquake.Comment: revtex, 19 pages, 8 eps figure

Statistical analysis of rockfall volume distributions: implications for rockfall dynamics.

International audienceWe analyze the volume distribution of natural rockfalls on different geological settings (i.e., calcareous cliffs in the French Alps, Grenoble area, and granite Yosemite cliffs, California Sierra) and different volume ranges (i.e., regional and worldwide catalogs). Contrary to previous studies that included several types of landslides, we restrict our analysis to rockfall sources which originated on subvertical cliffs. For the three data sets, we find that the rockfall volumes follow a power law distribution with a similar exponent value, within error bars. This power law distribution was also proposed for rockfall volumes that occurred along road cuts. All these results argue for a recurrent power law distribution of rockfall volumes on subvertical cliffs, for a large range of rockfall sizes (102–1010 m3), regardless of the geological settings and of the preexisting geometry of fracture patterns that are drastically different on the three studied areas. The power law distribution for rockfall volumes could emerge from two types of processes. First, the observed power law distribution of rockfall volumes is similar to the one reported for both fragmentation experiments and fragmentation models. This argues for the geometry of rock mass fragment sizes to possibly control the rockfall volumes. This way neither cascade nor avalanche processes would influence the rockfall volume distribution. Second, without any requirement of scale-invariant quenched heterogeneity patterns, the rock mass dynamics can arise from avalanche processes driven by fluctuations of the rock mass properties, e.g., cohesion or friction angle. This model may also explain the power law distribution reported for landslides involving unconsolidated materials. We find that the exponent values of rockfall volume on subvertical cliffs, 0.5 ± 0.2, is significantly smaller than the 1.2 ± 0.3 value reported for mixed landslide types. This change of exponents can be driven by the material strength, which controls the in situ topographic slope values, as simulated in numerical models of landslides [Densmore et al., 1998; Champel et al., 2002]. INDEX TERMS: 5104 Physical Properties of Rocks: Fracture and flow; 1815 Hydrology: Erosion and sedimentation; 8122 Tectonophysics: Dynamics, gravity and tectonics

Scale free networks of earthquakes and aftershocks

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent $\gamma = 2.0(1)$. The original Omori law with $p=1$ emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte

Response Functions to Critical Shocks in Social Sciences: An Empirical and Numerical Study

We show that, provided one focuses on properly selected episodes, one can apply to the social sciences the same observational strategy that has proved successful in natural sciences such as astrophysics or geodynamics. For instance, in order to probe the cohesion of a policy, one can, in different countries, study the reactions to some huge and sudden exogenous shocks, which we call Dirac shocks. This approach naturally leads to the notion of structural (as opposed or complementary to temporal) forecast. Although structural predictions are by far the most common way to test theories in the natural sciences, they have been much less used in the social sciences. The Dirac shock approach opens the way to testing structural predictions in the social sciences. The examples reported here suggest that critical events are able to reveal pre-existing ``cracks'' because they probe the social cohesion which is an indicator and predictor of future evolution of the system, and in some cases foreshadows a bifurcation. We complement our empirical work with numerical simulations of the response function (``damage spreading'') to Dirac shocks in the Sznajd model of consensus build-up. We quantify the slow relaxation of the difference between perturbed and unperturbed systems, the conditions under which the consensus is modified by the shock and the large variability from one realization to another

Universal features of correlated bursty behaviour

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution in a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

On the Occurrence of Finite-Time-Singularities in Epidemic Models of Rupture, Earthquakes and Starquakes

We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks, based solely on the most solidly documented stylized facts of seismicity (clustering in space and in time and power law Gutenberg-Richter distribution of earthquake energies). This theory accounts for the main observations (power law acceleration and discrete scale invariant structure) of critical rupture of heterogeneous materials, of the largest sequence of starquakes ever attributed to a neutron star as well as of earthquake sequences.Comment: Revtex document of 4 pages including 1 eps figur

An observational test of the origin of accelerating moment release before large earthquakes

International audience[1] A progressive increase of seismic activity distributed over a wide region around a future earthquake epicenter is termed accelerating moment release (AMR). This phenomenon has been observed in several studies over the last 15 years, although there is no consensus about the physical origin of the effect. In a recent hypothesis known as the stress accumulation (SA) model, the AMR is thought to result from the last stage of loading in the earthquake cycle. In this view, the increasing seismicity is due to minor stress release as the whole region becomes sufficiently stressed for the major event to occur. The stress accumulation model makes specific predictions about the distribution of events in an AMR sequence. Because the AMR is predicted to be a result of loading on the main fault, the precursory activity should be concentrated in the positive lobes of the far-field stresses calculated by a backslip dislocation model of the main shock. To test this model, AMR is first found in optimal circular regions around the epicenters of each of the M w ! 6.5 earthquakes in central and southern California since 1950. A backslip dislocation model is then used to determine which of the precursory events occur in the regions predicted by stress accumulation. AMR is shown to occur preferentially in the lobes of the backslip stress field predicted by the stress accumulation model

Characterization of rockfalls from seismic signal: insights from laboratory experiments

International audienceThe seismic signals generated by rockfalls can provide information on their dynamics and location. However, the lack of field observations makes it difficult to establish clear relationships between the characteristics of the signal and the source. In this study, scaling laws are derived from analytical impact models to relate the mass and the speed of an individual impactor to the radiated elastic energy and the frequency content of the emitted seismic signal. It appears that the radiated elastic energy and frequencies decrease when the impact is viscoelastic or elasto-plastic compared to the case of an elastic impact. The scaling laws are validated with laboratory experiments of impacts of beads and gravels on smooth thin plates and rough thick blocks. Regardless of the involved materials, the masses and speeds of the impactors are retrieved from seismic measurements within afactor of 3. A quantitative energy budget of the impacts is established. On smooth thin plates, the lost energy is either radiated in elastic waves or dissipated in viscoelasticity when the impactor is large or small with respect to the plate thickness, respectively. In contrast, on rough thick blocks, theelastic energy radiation represents less than 5% of the lost energy. Most of the energy is lost in plastic deformation or rotation modes of the bead owingto surface roughness. Finally, we estimate the elastic energy radiated during field scale rockfalls experiments. This energy is shown to be proportional to the boulder mass, in agreement with the theoretical scaling laws

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa