Omori's Power Law aftershock sequences of microfracturing in rock fracture experiment

AbstractIn the proposed study, non-linear behavioral patterns in the seismic regime for earthquakes in the Himalayan basin have been studied using a complete, verified EQ catalogue comprised of all major events and their aftershock sequences in the Himalayan basin for the past 110 years [1900–2010]. The dataset has been analyzed to give better decision making criteria for impending earthquakes. A series of statistical tests based on multi-dimensional rigorous statistical studies, inter-event distance analyses, and statistical time analyses have been used to obtain correlation dimensions. The time intervals of earthquakes within a seismic regime have been used to train the neural network to analyze the nature of earthquake patterns in the different clusters. The results obtained from descriptive statistics show high correlation with previously conducted gravity studies and radon anomaly variation. A study of the time of recurrence of the numerical properties of the regime for 60 years from 1950 to 2010 for the Himalayan belt for analysis of significant EQ failure events has been done to find the best fit for an empirical data probability distribution. The distribution of waiting time of swarm events occurring in the Himalayan basin follows a power-law model, while independent events do not fit the power-law distribution. This suggests that probability of the occurrence of swarm events [M ⩽ 6.0] with frequent shaking may be more frequent than that of the occurrence of independent events of magnitude [M >6.0] in the Himalayan belt. We propose a three-layer feed forward neural network model to identify factors, with the actual occurrence of the maximum earthquake level M as input and target vectors in Himalayan basin area. We infer through a series of statistical results and evaluations that probabilistic forecasting of earthquakes can be achieved by finding the meta-stable cluster zones of the Himalayan clusters for the spatio-temporal distribution of earthquakes in the area.

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Self-organization of spatio-temporal earthquake clusters

Nonlinear Processes in Geophysics ◽

10.5194/npg-7-21-2000 ◽

2000 ◽

Vol 7 (1/2) ◽

pp. 21-29 ◽

Cited By ~ 26

Author(s):

S. Hainzl ◽

G. Zöller ◽

J. Kurths

Keyword(s):

Power Law ◽

Transient Creep ◽

Waiting Time Distribution ◽

Power Law Distribution ◽

Aftershock Activity ◽

Omori Law ◽

Aftershock Sequences ◽

Spatio Temporal ◽

Large Earthquakes ◽

Earthquake Clusters

Abstract. Cellular automaton versions of the Burridge-Knopoff model have been shown to reproduce the power law distribution of event sizes; that is, the Gutenberg-Richter law. However, they have failed to reproduce the occurrence of foreshock and aftershock sequences correlated with large earthquakes. We show that in the case of partial stress recovery due to transient creep occurring subsequently to earthquakes in the crust, such spring-block systems self-organize into a statistically stationary state characterized by a power law distribution of fracture sizes as well as by foreshocks and aftershocks accompanying large events. In particular, the increase of foreshock and the decrease of aftershock activity can be described by, aside from a prefactor, the same Omori law. The exponent of the Omori law depends on the relaxation time and on the spatial scale of transient creep. Further investigations concerning the number of aftershocks, the temporal variation of aftershock magnitudes, and the waiting time distribution support the conclusion that this model, even "more realistic" physics in missed, captures in some ways the origin of the size distribution as well as spatio-temporal clustering of earthquakes.

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Analysis of power law assumptions for short-period comets and Kuiper bodies

International Astronomical Union Colloquium ◽

10.1017/s0252921100031584 ◽

1999 ◽

Vol 173 ◽

pp. 289-293 ◽

Cited By ~ 1

Author(s):

J.R. Donnison ◽

L.I. Pettit

Keyword(s):

Power Law ◽

Pareto Distribution ◽

Limited Data ◽

Short Period ◽

Probability Plots ◽

Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

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Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

Journal of Speech and Hearing Research ◽

10.1044/jshr.1101.169 ◽

1968 ◽

Vol 11 (1) ◽

pp. 169-178 ◽

Cited By ~ 4

Author(s):

Alan Gill ◽

Charles I. Berlin

Keyword(s):

Power Law ◽

Response Magnitude ◽

Single Units ◽

Spectral Content ◽

Hearing Sensitivity ◽

Subjective Magnitude ◽

Orderly Fashion ◽

Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

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510 Heart rate variability (power-law-regression) and age in patients with decompensated chronic heart failure

European Journal of Heart Failure Supplements ◽

10.1016/s1567-4215(04)90376-1 ◽

2004 ◽

Vol 3 (1) ◽

pp. 131

Author(s):

H SCHMIDT

Keyword(s):

Heart Failure ◽

Heart Rate ◽

Heart Rate Variability ◽

Chronic Heart Failure ◽

Power Law

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