3,589 research outputs found
Spatiotemporal correlations of earthquakes in the continuum limit of the one-dimensional Burridge-Knopoff model
Spatiotemporal correlations of the one-dimensional spring-block
(Burridge-Knopoff) model of earthquakes, either with or without the viscosity
term, are studied by means of numerical computer simulations. The continuum
limit of the model is examined by systematically investigating the model
properties with varying the block-size parameter a toward a\to 0. The Kelvin
viscosity term is introduced so that the model dynamics possesses a sensible
continuum limit. In the presence of the viscosity term, many of the properties
of the original discrete BK model are kept qualitatively unchanged even in the
continuum limit, although the size of minimum earthquake gets smaller as a gets
smaller. One notable exception is the existence/non-existence of the
doughnut-like quiescence prior to the mainshock. Although large events of the
original discrete BK model accompany seismic acceleration together with a
doughnut-like quiescence just before the mainshock, the spatial range of the
doughnut-like quiescence becomes narrower as a gets smaller, and in the
continuum limit, the doughnut-like quiescence might vanish altogether. The
doughnut-like quiescence observed in the discrete BK model is then a phenomenon
closely related to the short-length cut-off scale of the model
Simulation study of the two-dimensional Burridge-Knopoff model of earthquakes
Spatiotemporal correlations of the two-dimensional spring-block
(Burridge-Knopoff) model of earthquakes are extensively studied by means of
numerical computer simulations. The model is found to exhibit either
``subcritical'' or ``supercritical'' behavior, depending on the values of the
model parameters. Transition between these regimes is either continuous or
discontinuous. Seismic events in the ``subcritical'' regime and those in the
``supercritical'' regime at larger magnitudes exhibit universal scaling
properties. In the ``supercritical'' regime, eminent spatiotemporal
correlations, {\it e.g.}, remarkable growth of seismic activity preceding the
mainshock, arise in earthquake occurrence, whereas such spatiotemporal
correlations are significantly suppressed in the ``subcritical'' regime.
Seismic activity is generically suppressed just before the mainshock in a close
vicinity of the epicenter of the upcoming event while it remains to be active
in the surroundings (the Mogi doughnut). It is also observed that, before and
after the mainshock, the apparent -value of the magnitude distribution
decreases or increases in the ``supercritical'' or ``subcritical'' regimes,
respectively. Such distinct precursory phenomena may open a way to the
prediction of the upcoming large event
Prediction of Large Events on a Dynamical Model of a Fault
We present results for long term and intermediate term prediction algorithms
applied to a simple mechanical model of a fault. We use long term prediction
methods based, for example, on the distribution of repeat times between large
events to establish a benchmark for predictability in the model. In comparison,
intermediate term prediction techniques, analogous to the pattern recognition
algorithms CN and M8 introduced and studied by Keilis-Borok et al., are more
effective at predicting coming large events. We consider the implications of
several different quality functions Q which can be used to optimize the
algorithms with respect to features such as space, time, and magnitude windows,
and find that our results are not overly sensitive to variations in these
algorithm parameters. We also study the intrinsic uncertainties associated with
seismicity catalogs of restricted lengths.Comment: 33 pages, plain.tex with special macros include
Simulation study of spatio-temporal correlations of earthquakes as a stick-slip frictional instability
Spatio-temporal correlations of earthquakes are studied numerically on the
basis of the one-dimensional spring-block (Burridge-Knopoff) model. As large
events approach, the frequency of smaller events gradually increases, while,
just before the mainshock, it is dramatically suppressed in a close vicinity of
the epicenter of the upcoming mainshock, a phenomenon closely resembling the
``Mogi doughnut'
Predictability of Self-Organizing Systems
We study the predictability of large events in self-organizing systems. We
focus on a set of models which have been studied as analogs of earthquake
faults and fault systems, and apply methods based on techniques which are of
current interest in seismology. In all cases we find detectable correlations
between precursory smaller events and the large events we aim to forecast. We
compare predictions based on different patterns of precursory events and find
that for all of the models a new precursor based on the spatial distribution of
activity outperforms more traditional measures based on temporal variations in
the local activity.Comment: 15 pages, plain.tex with special macros included, 4 figure
Recommended from our members
Intrinsic properties of a Burridge-Knopoff model of an earthquake fault
We present a detailed numerical study of certain fundamental aspects of a one-dimensional homogeneous, deterministic Burridge-Knopoff model. The model is described by a massive wave equation, in which the key nonlinearity is associated with the stick-slip velocity-weakening friction force at the interface between tectonic plates. In this paper, we present results for the statistical distribution of slipping events in the limit of a very long fault and infinitesimally slow driving rates. Typically, we find that the magnitude distribution of smaller events is consistent with the Gutenberg-Richter law, while the larger events occur in excess of this distribution. The crossover from smaller to larger events is identified with a correlation length describing the transition from localized to delocalized events. We also find that there is a sharp upper cutoff describing the maximum large event. We identify how the correlation length and this upper cutoff scale with the parameters in the model. We find that both are independent of system size, while both do depend on the spatial discretization. In addition to the magnitude distribution, we present a series of measurements of other seismologically relevant quantities, including the event duration, the size of the rupture zone, and the energy release, and discuss the relationship between our measurements and the corresponding empirical laws in seismology
Mary Pauper: A Historical Exploration of Early Care and Education Compensation, Policy, and Solutions
The Early Educator Investment Collaborative is committed in our work to recognizing and understanding the historical context in which structural racism continues to present in the early childhood workforce and eliminating the systemic oppression that keeps many early childhood educators living in poverty. In 2021, Child Trends was selected to conduct a literature review and develop a policy and practice report to map the history of systemic racism in the U.S. and how it has influenced early childhood education (ECE) policy and practice, with a particular focus on educator pay and benefits, preparation, and workforce stability.This report articulates a landscape analysis and a set of recommendations for policy, practice, and future research to improve the professional status of early childhood educators. The intent of this work is to build a common understanding of the biggest equity issues impacting early childhood educators—historically and in the present day
Model quakes in the two-dimensional wave equation
This paper presents a new two-dimensional wave equation model of an earthquake fault. The model generates a complex sequence of slip events on a fault with uniform properties when there is a frictional weakening instability. Previous models of long faults in one and two dimensions had the driving in the bulk, giving the Klein-Gordon equation in the bulk. Here, I place the driving on the boundary; giving the wave equation in the bulk. The different models are, however, shown to behave similarly. I examine a whole range of frictions, with slip weakening as one end-member case and velocity weakening as the other end-member case, and show that they display a generic type of slip complexity: there is an exponential distribution of the largest events and, for sufficient weakening, a power law distribution of small events. With the addition of a viscous-type friction term on the fault, I show that the results are independent of grid resolution, indicating that continuum limit complexity is achieved
Dynamics of earthquake nucleation process represented by the Burridge-Knopoff model
Dynamics of earthquake nucleation process is studied on the basis of the
one-dimensional Burridge-Knopoff (BK) model obeying the rate- and
state-dependent friction (RSF) law. We investigate the properties of the model
at each stage of the nucleation process, including the quasi-static initial
phase, the unstable acceleration phase and the high-speed rupture phase or a
mainshock. Two kinds of nucleation lengths L_sc and L_c are identified and
investigated. The nucleation length L_sc and the initial phase exist only for a
weak frictional instability regime, while the nucleation length L_c and the
acceleration phase exist for both weak and strong instability regimes. Both
L_sc and L_c are found to be determined by the model parameters, the frictional
weakening parameter and the elastic stiffness parameter, hardly dependent on
the size of an ensuing mainshock. The sliding velocity is extremely slow in the
initial phase up to L_sc, of order the pulling speed of the plate, while it
reaches a detectable level at a certain stage of the acceleration phase. The
continuum limits of the results are discussed. The continuum limit of the BK
model lies in the weak frictional instability regime so that a mature
homogeneous fault under the RSF law always accompanies the quasi-static
nucleation process. Duration times of each stage of the nucleation process are
examined. The relation to the elastic continuum model and implications to real
seismicity are discussed.Comment: Title changed. Changes mainly in abstract and in section 1. To appear
in European Physical Journal
Initiation propagation and termination of elastodynamic ruptures associated with segmentation of faults and shaking hazard
Using a model of a complex fault system, we examine the initiation, propagation, and termination of ruptures and their relationship to fault geometry and shaking hazard. We find concentrations of epicenters near fault step overs and ends; concentrations of terminations near fault ends; and persistent propagation directivity effects. Taking advantage of long sequences of dynamic events, we directly measure shaking hazards, such as peak ground acceleration exceedance probabilities, without need for additional assumptions. This provides a new tool for exploring shaking hazard from a physics-based perspective, its dependence on various physical parameters, and its correlation with other geological and seismological observables. Using this capability, we find some significant aspects of the shaking hazard can be anticipated by measures of the epicenters. In particular, asymmetries in the relative peak ground motion hazard along the faults appear well correlated with asymmetries in epicentral locations
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