267 research outputs found
Statistical properties of seismicity of fault zones at different evolutionary stages
We perform a systematic parameter space study of the seismic response of a large fault with different levels of heterogeneity, using a 3-D elastic framework within the continuum limit. The fault is governed by rate-and-state friction and simulations are performed for model realizations with frictional and large scale properties characterized by different ranges of size scales. We use a number of seismicity and stress functions to characterize different types of seismic responses and test the correlation between hypocenter locations and the employed distributions of model parameters. The simulated hypocenters are found to correlate significantly with small L values of the rate-and-state friction. The final sizes of earthquakes are correlated with physical properties at their nucleation sites. The obtained stacked scaling relations are overall self-similar and have good correspondence with properties of natural earthquakes
Dynamical system analysis and forecasting of deformation produced by an earthquake fault
We present a method of constructing low-dimensional nonlinear models
describing the main dynamical features of a discrete 2D cellular fault zone,
with many degrees of freedom, embedded in a 3D elastic solid. A given fault
system is characterized by a set of parameters that describe the dynamics,
rheology, property disorder, and fault geometry. Depending on the location in
the system parameter space we show that the coarse dynamics of the fault can be
confined to an attractor whose dimension is significantly smaller than the
space in which the dynamics takes place. Our strategy of system reduction is to
search for a few coherent structures that dominate the dynamics and to capture
the interaction between these coherent structures. The identification of the
basic interacting structures is obtained by applying the Proper Orthogonal
Decomposition (POD) to the surface deformations fields that accompany
strike-slip faulting accumulated over equal time intervals. We use a
feed-forward artificial neural network (ANN) architecture for the
identification of the system dynamics projected onto the subspace (model space)
spanned by the most energetic coherent structures. The ANN is trained using a
standard back-propagation algorithm to predict (map) the values of the observed
model state at a future time given the observed model state at the present
time. This ANN provides an approximate, large scale, dynamical model for the
fault.Comment: 30 pages, 12 figure
Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults
The statistics of earthquakes in a heterogeneous fault zone is studied
analytically and numerically in the mean field version of a model for a
segmented fault system in a three-dimensional elastic solid. The studies focus
on the interplay between the roles of disorder, dynamical effects, and driving
mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of
dynamical weakening (or ``overshoot'') effects (epsilon) and the normal
distance (L) of the driving forces from the fault. In general, small epsilon
and small L are found to produce Gutenberg-Richter type power law statistics
with an exponential cutoff, while large epsilon and large L lead to a
distribution of small events combined with characteristic system-size events.
In a certain parameter regime the behavior is bistable, with transitions back
and forth from one phase to the other on time scales determined by the fault
size and other model parameters. The implications for realistic earthquake
statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps
Statistics of Earthquakes in Simple Models of Heterogeneous Faults
Simple models for ruptures along a heterogeneous earthquake fault zone are
studied, focussing on the interplay between the roles of disorder and dynamical
effects. A class of models are found to operate naturally at a critical point
whose properties yield power law scaling of earthquake statistics. Various
dynamical effects can change the behavior to a distribution of small events
combined with characteristic system size events. The studies employ various
analytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps
Statistical properties of seismicity of fault zones at different evolutionary stages
We perform a systematic parameter space study of the seismic response of a large fault with different levels of heterogeneity, using a 3-D elastic framework within the continuum limit. The fault is governed by rate-and-state friction and simulations are performed for model realizations with frictional and large scale properties characterized by different ranges of size scales. We use a number of seismicity and stress functions to characterize different types of seismic responses and test the correlation between hypocenter locations and the employed distributions of model parameters. The simulated hypocenters are found to correlate significantly with small L values of the rate-and-state friction. The final sizes of earthquakes are correlated with physical properties at their nucleation sites. The obtained stacked scaling relations are overall self-similar and have good correspondence with properties of natural earthquake
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
Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems
An effective characterization of chaotic conservative Hamiltonian systems in
terms of the curvature associated with a Riemannian metric tensor derived from
the structure of the Hamiltonian has been extended to a wide class of potential
models of standard form through definition of a conformal metric. The geodesic
equations reproduce the Hamilton equations of the original potential model
through an inverse map in the tangent space. The second covariant derivative of
the geodesic deviation in this space generates a dynamical curvature, resulting
in (energy dependent) criteria for unstable behavior different from the usual
Lyapunov criteria. We show here that this criterion can be constructively used
to modify locally the potential of a chaotic Hamiltonian model in such a way
that stable motion is achieved. Since our criterion for instability is local in
coordinate space, these results provide a new and minimal method for achieving
control of a chaotic system
Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes
We present a new method of data clustering applied to earthquake catalogs,
with the goal of reconstructing the seismically active part of fault networks.
We first use an original method to separate clustered events from uncorrelated
seismicity using the distribution of volumes of tetrahedra defined by closest
neighbor events in the original and randomized seismic catalogs. The spatial
disorder of the complex geometry of fault networks is then taken into account
by defining faults as probabilistic anisotropic kernels, whose structures are
motivated by properties of discontinuous tectonic deformation and previous
empirical observations of the geometry of faults and of earthquake clusters at
many spatial and temporal scales. Combining this a priori knowledge with
information theoretical arguments, we propose the Gaussian mixture approach
implemented in an Expectation-Maximization (EM) procedure. A cross-validation
scheme is then used and allows the determination of the number of kernels that
should be used to provide an optimal data clustering of the catalog. This
three-steps approach is applied to a high quality relocated catalog of the
seismicity following the 1986 Mount Lewis () event in California and
reveals that events cluster along planar patches of about 2 km, i.e.
comparable to the size of the main event. The finite thickness of those
clusters (about 290 m) suggests that events do not occur on well-defined
euclidean fault core surfaces, but rather that the damage zone surrounding
faults may be seismically active at depth. Finally, we propose a connection
between our methodology and multi-scale spatial analysis, based on the
derivation of spatial fractal dimension of about 1.8 for the set of hypocenters
in the Mnt Lewis area, consistent with recent observations on relocated
catalogs
Crack-Like Processes Governing the Onset of Frictional Slip
We perform real-time measurements of the net contact area between two blocks
of like material at the onset of frictional slip. We show that the process of
interface detachment, which immediately precedes the inception of frictional
sliding, is governed by three different types of detachment fronts. These
crack-like detachment fronts differ by both their propagation velocities and by
the amount of net contact surface reduction caused by their passage. The most
rapid fronts propagate at intersonic velocities but generate a negligible
reduction in contact area across the interface. Sub-Rayleigh fronts are
crack-like modes which propagate at velocities up to the Rayleigh wave speed,
VR, and give rise to an approximate 10% reduction in net contact area. The most
efficient contact area reduction (~20%) is precipitated by the passage of slow
detachment fronts. These fronts propagate at anomalously slow velocities, which
are over an order of magnitude lower than VR yet orders of magnitude higher
than other characteristic velocity scales such as either slip or loading
velocities. Slow fronts are generated, in conjunction with intersonic fronts,
by the sudden arrest of sub-Rayleigh fronts. No overall sliding of the
interface occurs until either of the slower two fronts traverses the entire
interface, and motion at the leading edge of the interface is initiated. Slip
at the trailing edge of the interface accompanies the motion of both the slow
and sub-Rayleigh fronts. We might expect these modes to be important in both
fault nucleation and earthquake dynamics.Comment: 19 page, 5 figures, to appear in International Journal of Fractur
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