HELMSTETTER , A.

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...

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...

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...

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...

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...

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...

Accelerating displacements preceding some catastrophic landslides have been found empirically to follow a time-to-failure power law, corresponding to a finite-time singularity of the velocity $v \\sim 1/(t_c-t)$ [{\\it Voight}, 1988]. Here, we provide a physical basis for this phenomenological law based on a slider-block model using a state and...

In a previous work [Helmstetter, 2003], we have proposed a simple physical model to explain the accelerating displacements preceding some catastrophic landslides, based on a slider-block model with a state and velocity dependent friction law. This model predicts two regimes of sliding, stable and unstable leading to a critical finite-time...

A dense, local network of 30 geodetic markers covering a 50 × 60 km2 area in the southwestern European Alps (Briançon region) has been temporarily surveyed in 1996, 2006 and 2011 by GPS. The aim is to measure the current deformation in this seismically active area. The study zone is characterized by a majority of extensional and dextral focal...