scholarly journals The evolving interaction of low-frequency earthquakes during transient slip

2016 ◽  
Vol 2 (4) ◽  
pp. e1501616 ◽  
Author(s):  
William B. Frank ◽  
Nikolaï M. Shapiro ◽  
Allen L. Husker ◽  
Vladimir Kostoglodov ◽  
Alexander A. Gusev ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Poisson Process ◽  
Point Process ◽  
Autocorrelation Function ◽  
Collective Behavior ◽  
Low Frequency ◽  
Slow Slip ◽  
Plate Interface ◽  
Single Asperity ◽  
Seismogenic Faults

Observed along the roots of seismogenic faults where the locked interface transitions to a stably sliding one, low-frequency earthquakes (LFEs) primarily occur as event bursts during slow slip. Using an event catalog from Guerrero, Mexico, we employ a statistical analysis to consider the sequence of LFEs at a single asperity as a point process, and deduce the level of time clustering from the shape of its autocorrelation function. We show that while the plate interface remains locked, LFEs behave as a simple Poisson process, whereas they become strongly clustered in time during even the smallest slow slip, consistent with interaction between different LFE sources. Our results demonstrate that bursts of LFEs can result from the collective behavior of asperities whose interaction depends on the state of the fault interface.

On the rate of Poisson process approximation to a Bernoulli process

1997 ◽  
Vol 34 (4) ◽  
pp. 898-907 ◽  
Author(s):  
Aihua Xia
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Discrete Time ◽  
Wasserstein Distance ◽  
Stein’S Method ◽  
Upper Bounds ◽  
Stein's Method ◽  
Bernoulli Process ◽  
Logarithmic Factor ◽  
Process Approximation

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

scholarly journals Slow slip rate and excitation efficiency of deep low-frequency tremors beneath southwest Japan

2018 ◽  
Vol 722 ◽  
pp. 314-323 ◽  
Author(s):  
Kumiko Daiku ◽  
Yoshihiro Hiramatsu ◽  
Takanori Matsuzawa ◽  
Tomoyuki Mizukami
Keyword(s):  
Low Frequency ◽  
Slip Rate ◽  
Slow Slip ◽  
Southwest Japan ◽  
Excitation Efficiency

Statistical analysis of seismic data on earthquakes in the area of the Vrancea focus

1970 ◽  
Vol 60 (4) ◽  
pp. 1089-1099
Author(s):  
Ion Săcuiu ◽  
Dan Zorilescu
Keyword(s):  
Statistical Analysis ◽  
Poisson Process ◽  
Seismic Data ◽  
Time Interval ◽  
Generation Process ◽  
Present Contribution ◽  
Important Conclusion ◽  
Distribution Laws ◽  
Frequency Magnitude

abstract The present contribution deals with distribution laws of the earthquake's magnitude, the number of earthquakes (by modelling the generation process as a Poisson process) and the time interval between two successive earthquakes. The most important conclusion arrived at is that in the area of the Vrancea focus the distribution of the magnitudes is lognormal and brings forth a frequency-magnitude relation of the form log λ ( Μ ) = a + b log M + c ( log M ) 2 , not a linear one. A correlation between the magnitude and the time interval of two successive earthquakes is considered and a series of seismic indices are introduced.

Variance reducing modifications for estimators of standardized moments of random sets

2000 ◽  
Vol 32 (03) ◽  
pp. 682-700
Author(s):  
Jeffrey D. Picka
Keyword(s):  
Statistical Analysis ◽  
Point Process ◽  
Random Sets ◽  
Boolean Models ◽  
Asymptotic Regime ◽  
Estimation Strategy ◽  
Moment Estimation ◽  
Second Moments ◽  
Simulation Results ◽  
Variance Result

In the statistical analysis of random sets, it is useful to have simple statistics that can be used to describe the realizations of these sets. The cumulants and several other standardized moments such as the correlation and second cumulant can be used for this purpose, but their estimators can be excessively variable if the most straightforward estimation strategy is used. Through exploitation of similarities between this estimation problem and a similar one for a point process statistic, two modifications are proposed. Analytical results concerning the effects of these modifications are found through use of a specialized asymptotic regime. Simulation results establish that the modifications are highly effective at reducing estimator standard deviations for Boolean models. The results suggest that the reductions in variance result from a balanced use of information in the estimation of the first and second moments, through eliminating the use of observations that are not used in second moment estimation.

Observing seismic signatures of slow slip events with unsupervised learning

2021 ◽  
Author(s):  
Leonard Seydoux ◽  
Michel Campillo ◽  
René Steinmann ◽  
Randall Balestriero ◽  
Maarten de Hoop
Keyword(s):  
Clustering Algorithm ◽  
Low Frequency ◽  
Seismic Signal ◽  
Geodetic Data ◽  
Slow Slip ◽  
Slow Slip Events ◽  
Slow Slip Event ◽  
Intermittent Behavior ◽  
Slow Earthquakes ◽  
Slip Event

<p>Slow slip events are observed in geodetic data, and are occasionally associated with seismic signatures such as slow earthquakes (low-frequency earthquakes, tectonic tremors). In particular, it was shown that swarms of slow earthquake can correlate with slow slip events occurrence, and allowed to reveal the intermittent behavior of several slow slip events. This observation was possible thanks to detailed analysis of slow earthquakes catalogs and continuous geodetic data, but in every case, was limited to particular classes of seismic signatures. In the present study, we propose to infer the classes of seismic signals that best correlate with the observed geodetic data, including the slow slip event. We use a scattering network (a neural network with wavelet filters) in order to find meaningful signal features, and apply a hierarchical clustering algorithm in order to infer classes of seismic signal. We then apply a regression algorithm in order to predict the geodetic data, including slow slip events, from the occurrence of inferred seismic classes. This allow to (1) identify seismic signatures associated with the slow slip events as well as (2) infer the the contribution of each classes to the overall displacement observed in the geodetic data. We illustrate our strategy by revisiting the slow-slip event of 2006 that occurred beneath Guerrero, Mexico.</p>

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