SORNETTE , D.

We present exploratory analogies and speculations on the mechanisms underlying the organization of faulting and earthquake in the earth crust. The mechanical properties of the brittle lithosphere at scales of the order or larger than a few kilometers are proposed to be analogous to those of non-cohesive granular media, since both systems...

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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...

The epidemic-type aftershock sequence (ETAS) model is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power-law decay ∼1/t1+θ of seismicity after an earthquake) and Gutenberg-Richter law (power-law distribution of earthquake energies). In order to describe also the space...

We study a 2D quasi-static discrete crack anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transferred to all elements through elastic forces. This model can be considered as belonging to the class of self-organized models which may exhibit spontaneous...

Systems with long-range persistence and memory are shown to exhibit different precursory as well as recovery patterns in response to shocks of exogeneous versus endogeneous origins. By endogeneous, we envision either fluctuations resulting from an underlying chaotic dynamics or from a stochastic forcing origin which may be external or be an...

The empirical Ba°th's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones' [1969] and Console et al. [2003], we show that the origin of Ba°th's law is to be found in the selection procedure used to define mainshocks and aftershocks...

Using the simple ETAS branching model of seismicity, which assumes that each earthquake can trigger other earthquakes, we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source.We show that, in...

We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by a single mainshock decreases with the time from the mainshock according to the modified Omori law...

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are taken Gaussian. Here, we offer an important...

We review the "critical point" concept for large earthquakes and enlarge it in the framework of so-called "finite-time singularities". The singular behavior associated with accelerated seismic release is shown to result from a positive feedback of the seismic activity on its release rate. The most important mechanisms for such positive feedback...

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The model predicts the...

We analyze 21 aftershock sequences of California to test for evidence of space-time diffusion. Aftershock diffusion may result from stress diffusion and is also predicted by any mechanism of stress weakening. Here, we test an alternative mechanism to explain aftershock diffusion, based on multiple cascades of triggering. In order to...

We consider a general stochastic branching process, which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered...

Following Hergarten and Neugebauer [1] 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...

The classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal...

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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...

We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995)). The discrete scaling symmetries which may be present at smaller scales are shown to be...

Finance is about how the continuous stream of news gets incorporated into prices. But not all news have the same impact. Can one distinguish the effects of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 from financial crashes such as Oct. 1987 as well as smaller volatility bursts? Using a parsimonious...

The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ∝ 1/(tc − t)p ′ of the time to the mainshock occurring at tc. Here, we show that this law results from the direct Omori law for aftershocks describing the power law decay ∼ 1/(t − tc)p of...

We present creep experiments on fiber composite materials with controlled heterogeneity. Recorded strain rates and acoustic emission rates exhibit a power law relaxation in the primary creep regime (Andrade law) followed by a power law acceleration up to rupture over up to four decades in time. We discover that the failure time is proportional...

We present creep experiments on fiber composite materials. Recorded strain rates and acoustic emission (AE) rates exhibit both a power law relaxation in the primary creep regime and a power-law acceleration before global failure. In particular, we observe time-to-failure power laws in the tertiary regime for acoustic emissions over four decades...

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