436 research outputs found
Andrade, Omori and Time-to-failure Laws from Thermal Noise in Material Rupture
Using the simplest possible ingredients of a rupture model with thermal
fluctuations, we provide an analytical theory of three ubiquitous empirical
observations obtained in creep (constant applied stress) experiments: the
initial Andrade-like and Omori-like decay of the rate of deformation and
of fiber ruptures and the critical time-to-failure behavior of
acoustic emissions just prior to the macroscopic rupture. The lifetime of the
material is controlled by a thermally activated Arrhenius nucleation process,
describing the cross-over between these two regimes. Our results give further
credit to the idea proposed by Ciliberto et al. that the tiny thermal
fluctuations may actually play an essential role in macroscopic deformation and
rupture processes at room temperature. We discover a new re-entrant effect of
the lifetime as a function of quenched disorder amplitude.Comment: 4 pages with 1 figur
Bath's law Derived from the Gutenberg-Richter law and from Aftershock Properties
The empirical Bath'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 Bath's law is to be found in the selection procedure
used to define mainshocks and aftershocks rather than in any difference in the
mechanisms controlling the magnitude of the mainshock and of the aftershocks.
We use the ETAS model of seismicity, which provides a more realistic model of
aftershocks, based on (i) a universal Gutenberg-Richter (GR) law for all
earthquakes, and on (ii) the increase of the number of aftershocks with the
mainshock magnitude. Using numerical simulations of the ETAS model, we show
that this model is in good agreement with Bath's law in a certain range of the
model parameters.Comment: major revisions, in press in Geophys. Res. Let
Correlations and invariance of seismicity under renormalization-group transformations
The effect of transformations analogous to those of the real-space
renormalization group are analyzed for the temporal occurrence of earthquakes.
The distribution of recurrence times turns out to be invariant under such
transformations, for which the role of the correlations between the magnitudes
and the recurrence times are fundamental. A general form for the distribution
is derived imposing only the self-similarity of the process, which also yields
a scaling relation between the Gutenberg-Richter b-value, the exponent
characterizing the correlations, and the recurrence-time exponent. This
approach puts the study of the structure of seismicity in the context of
critical phenomena.Comment: Short paper. I'll be grateful to get some feedbac
Anomalous Power Law Distribution of Total Lifetimes of Branching Processes Relevant to Earthquakes
We consider a branching model of triggered seismicity, the ETAS
(epidemic-type aftershock sequence) model which assumes that each earthquake
can trigger other earthquakes (``aftershocks''). An aftershock sequence results
in this model from the cascade of aftershocks of each past earthquake. Due to
the large fluctuations of the number of aftershocks triggered directly by any
earthquake (``productivity'' or ``fertility''), there is a large variability of
the total number of aftershocks from one sequence to another, for the same
mainshock magnitude. We study the regime where the distribution of fertilities
is characterized by a power law and the bare
Omori law for the memory of previous triggering mothers decays slowly as , with relevant for earthquakes. Using the tool
of generating probability functions and a quasistatic approximation which is
shown to be exact asymptotically for large durations, we show that the density
distribution of total aftershock lifetimes scales as when the average branching ratio is critical ().
The coefficient quantifies the interplay between the
exponent of the Gutenberg-Richter magnitude distribution and the increase of the number of aftershocks
with the mainshock magnitude (productivity) with . More
generally, our results apply to any stochastic branching process with a
power-law distribution of offsprings per mother and a long memory.Comment: 16 pages + 4 figure
Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing of Ruptures
We perform a comparative statistical analysis between the acoustic-emission time series from the ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparent association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distributions for acoustic-emission and earthquake time series are described by a unique scaling law indicating self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the aging process of the temple and the local seismic activit
Universal mean moment rate profiles of earthquake ruptures
Earthquake phenomenology exhibits a number of power law distributions
including the Gutenberg-Richter frequency-size statistics and the Omori law for
aftershock decay rates. In search for a basic model that renders correct
predictions on long spatio-temporal scales, we discuss results associated with
a heterogeneous fault with long range stress-transfer interactions. To better
understand earthquake dynamics we focus on faults with Gutenberg-Richter like
earthquake statistics and develop two universal scaling functions as a stronger
test of the theory against observations than mere scaling exponents that have
large error bars. Universal shape profiles contain crucial information on the
underlying dynamics in a variety of systems. As in magnetic systems, we find
that our analysis for earthquakes provides a good overall agreement between
theory and observations, but with a potential discrepancy in one particular
universal scaling function for moment-rates. The results reveal interesting
connections between the physics of vastly different systems with avalanche
noise.Comment: 13 pages, 5 figure
"Universal" Distribution of Inter-Earthquake Times Explained
We propose a simple theory for the ``universal'' scaling law previously
reported for the distributions of waiting times between earthquakes. It is
based on a largely used benchmark model of seismicity, which just assumes no
difference in the physics of foreshocks, mainshocks and aftershocks. Our
theoretical calculations provide good fits to the data and show that
universality is only approximate. We conclude that the distributions of
inter-event times do not reveal more information than what is already known
from the Gutenberg-Richter and the Omori power laws. Our results reinforces the
view that triggering of earthquakes by other earthquakes is a key physical
mechanism to understand seismicity.Comment: 4 pages with two figure
Avalanches, Scaling and Coherent Noise
We present a simple model of a dynamical system driven by externally-imposed
coherent noise. Although the system never becomes critical in the sense of
possessing spatial correlations of arbitrarily long range, it does organize
into a stationary state characterized by avalanches with a power-law size
distribution. We explain the behavior of the model within a time-averaged
approximation, and discuss its potential connection to the dynamics of
earthquakes, the Gutenberg-Richter law, and to recent experiments on avalanches
in rice piles.Comment: 17 pages, 4 Postscript figures, written in LaTeX using RevTeX and
epsfig.st
A model for the distribution of aftershock waiting times
In this work the distribution of inter-occurrence times between earthquakes
in aftershock sequences is analyzed and a model based on a non-homogeneous
Poisson (NHP) process is proposed to quantify the observed scaling. In this
model the generalized Omori's law for the decay of aftershocks is used as a
time-dependent rate in the NHP process. The analytically derived distribution
of inter-occurrence times is applied to several major aftershock sequences in
California to confirm the validity of the proposed hypothesis.Comment: 4 pages, 3 figure
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