Earthquake “Quanta” as an explanation for observed magnitudes and stress drops

1995 ◽  
Vol 85 (3) ◽  
pp. 808-813
Author(s):  
I. Selwyn Sacks ◽  
Paul A. Rydelek
Keyword(s):  
Computer Simulation ◽  
Linear Relation ◽  
Stress Drop ◽  
Constant Stress ◽  
Similar Process ◽  
Self Similar ◽  
Stress Drops

Abstract The familiar linear relation (Gutenberg-Richter) between the logarithm of the number of earthquakes and their magnitude is commonly ascribed to the distribution (fractal) of fault sizes in a self-similar process. We show that a concept of earthquake quanta whose failure is governed by simple physics and suggested by observations explains not only the Gutenberg-Richter relation but also the relatively constant stress drop for larger magnitude events. Results from computer simulation are consistent with observations from detailed seismicity studies.

A kinematic self-similar rupture process for earthquakes

1994 ◽  
Vol 84 (4) ◽  
pp. 1216-1228 ◽  
Author(s):  
A. Herrero ◽  
P. Bernard
Keyword(s):  
Stress Drop ◽  
Numerical Models ◽  
Kinematic Model ◽  
Body Waves ◽  
Partial Slip ◽  
Wave Radiation ◽  
Similar Process ◽  
Dislocation Model ◽  
Radiation Spectra ◽  
Self Similar

Abstract The basic assumption that the self-similarity and the spectral law of the seismic body-wave radiation (e.g., ω-square model) must find their origin in some simple self-similar process during the seismic rupture led us to construct a kinematic, self-similar model of earthquakes. It is first assumed that the amplitude of the slip distribution high-pass filtered at high wavenumber does not depend on the size of the ruptured fault. This leads to the following “k-square” model for the slip spectrum, for k > 1/L: Δ~uL(k)=CΔσμLk2, where L is the ruptured fault dimension, k the radial wavenumber, Δσ the mean stress drop, μ the rigidity, and C an adimensional constant of the order of 1. The associated stress-drop spectrum, for k > 1/L, is approximated by Δ~σL(k)=ΔσLk. The rupture front is assumed to propagate on the fault plane with a constant velocity v, and the rise time function is assumed to be scale dependent. The partial slip associated to a given wavelength 1/k is assumed to be completed in a time 1/kv, based on simple dynamical considerations. We therefore considered a simple dislocation model (instantaneous slip at the final value), which indeed correctly reproduces this self-similar characteristic of the slip duration at any scale. For a simple rectangular fault with isochrones propagating in the x direction, the resulting far-field displacement spectrum is related to the slip spectrum as u˜(ω)=FΔ~u(kx=1Cdωv,ky=0), where the factor F includes radiation pattern and distance effect, and Cd is the classical directivity coefficient 1/[1 − v/c cos (θ)]. The k-square model for the slip thus leads to the ω-square model, with the assumptions above. Independently of the adequacy of these assumptions, which should be tested with dynamic numerical models, such a kinematic model has several important applications. It may indeed be used for generating realistic synthetics at any frequency, including body waves, surface waves, and near-field terms, even for sites close to the fault, which is often of particular importance; it also provides some clues for estimating the weighting factors for the empirical Green's function methods. Finally, the slip spectrum may easily be modified in order to model other power-law decay of the radiation spectra, as well as composite earthquakes.

scholarly journals MODELLING SELF-SIMILAR TRAFFIC OF MULTISERVICE NETWORKS

2019 ◽  
Vol 1 ◽  
pp. 46-54
Author(s):  
Zakir Maharramov ◽  
Vugar Abdullayev ◽  
Tamilla Mammadova
Keyword(s):  
Computer Simulation ◽  
Simulation Modelling ◽  
Similar Process ◽  
Load Factor ◽  
Queuing Systems ◽  
Weibull Distributions ◽  
Time Intervals ◽  
Multiservice Networks ◽  
Self Similar ◽  
Service Duration

Simulation modelling is carried out, which allows adequate describing the traffic of multiservice networks with the commutation of packets with the characteristic of burstiness. One of the most effective methods for studying the traffic of telecommunications systems is computer simulation modelling. By using the theory of queuing systems (QS), computer simulation modelling of packet flows (traffic) in modern multi-service networks is performed as a random self-similar process. Distribution laws such as exponential, Poisson and normal-logarithmic distributions, Pareto and Weibull distributions have been considered. The distribution of time intervals between arrivals of packages and the service duration of service of packages at different system loads has been studied. The research results show that the distribution function of time intervals between packet arrivals and the service duration of packages is in good agreement with the Pareto and Weibull distributions, but in most cases the Pareto distribution prevails. The queuing systems with the queues M/Pa/1 and Pa/M/1 has been studied, and the fractality of the intervals of requests arriving have been compared by the properties of the estimates of the system load and the service duration. It has been found out that in the system Pa/M/1, with the parameter of the form a> 2, the fractality of the intervals of requests arriving does not affect the average waiting time and load factor. However, when 𝑎≤2, as in the M/Pa/1 system, both considered statistical estimates differ. The application of adequate mathematical models of traffic allows to correctly assess the characteristics of the quality of service (QoS) of the network.

Source dimensions and stress drops of small earthquakes near Parkfield, California

1984 ◽  
Vol 74 (1) ◽  
pp. 27-40
Author(s):  
M. E. O'Neill
Keyword(s):  
Stress Drop ◽  
Small Region ◽  
Static Stress ◽  
Depth Range ◽  
Zero Crossing ◽  
Source Dimensions ◽  
Duration Magnitude ◽  
Short Period ◽  
Static Stress Drop ◽  
Stress Drops

Abstract Source dimensions and stress drops of 30 small Parkfield, California, earthquakes with coda duration magnitudes between 1.2 and 3.9 have been estimated from measurements on short-period velocity-transducer seismograms. Times from the initial onset to the first zero crossing, corrected for attenuation and instrument response, have been interpreted in terms of a circular source model in which rupture expands radially outward from a point until it stops abruptly at radius a. For each earthquake, duration magnitude MD gave an estimate of seismic moment MO and MO and a together gave an estimate of static stress drop. All 30 earthquakes are located on a 6-km-long segment of the San Andreas fault at a depth range of about 8 to 13 km. Source radius systemically increases with magnitude from about 70 m for events near MD 1.4 to about 600 m for an event of MD 3.9. Static stress drop ranges from about 2 to 30 bars and is not strongly correlated with magnitude. Static stress drop does appear to be spatially dependent; the earthquakes with stress drops greater than 20 bars are concentrated in a small region close to the hypocenter of the magnitude 512 1966 Parkfield earthquake.

Existence, uniqueness and stability of impulsive stochastic neutral functional differential equations driven by Rosenblatt process with varying-time delays

2019 ◽  
Vol 27 (4) ◽  
pp. 213-223
Author(s):  
El Hassan Lakhel ◽  
Abdelmonaim Tlidi
Keyword(s):  
Differential Equations ◽  
Fixed Point Theory ◽  
Functional Differential Equations ◽  
Point Theory ◽  
Uniqueness Result ◽  
Similar Process ◽  
Neutral Functional Differential Equations ◽  
Rosenblatt Process ◽  
Self Similar ◽  
Functional Differential

Abstract Hermite processes are self-similar processes with stationary increments; the Hermite process of order 1 is fractional Brownian motion (fBm) and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of impulsive neutral stochastic functional differential equations with variable delays driven by Rosenblatt process with index {H\in(\frac{1}{2},1)} , which is a special case of a self-similar process with long-range dependence. More precisely, we prove an existence and uniqueness result, and we establish some conditions, ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

Large Uncertainties in Earthquake Stress-Drop Estimates and Their Tectonic Consequences

2020 ◽  
Vol 91 (4) ◽  
pp. 2320-2329 ◽  
Author(s):  
James S. Neely ◽  
Seth Stein ◽  
Bruce D. Spencer
Keyword(s):  
Seismic Hazard ◽  
Stress Drop ◽  
Hazard Analysis ◽  
Earthquake Hazards ◽  
Teleseismic Data ◽  
Tectonic Environment ◽  
Zero Correlation ◽  
Environment Stress ◽  
Stress Drops ◽  
Erroneous Inferences

Abstract Earthquake stress drop, the stress change on a fault due to an earthquake, is important for seismic hazard analysis because it controls the level of high-frequency ground motions that damage structures. Numerous studies report that stress drops vary by tectonic environment, providing insight into a region’s seismic hazard. Here, we show that teleseismic stress-drop estimates have large uncertainties that make it challenging to distinguish differences between the stress drops of different earthquakes. We compared stress drops for ∼900 earthquakes derived from two independent studies using teleseismic data and found practically zero correlation. Estimates for the same earthquake can differ by orders of magnitude. Therefore, reported stress-drop differences between earthquakes may not reflect true differences. As a result of these larger uncertainties, some tectonic environment stress-drop patterns that appear in one study do not appear in the other analysis of the same earthquakes. These large uncertainties in teleseismic estimates might lead to erroneous inferences about earthquake hazards. In many applications, it may be more appropriate to assume that earthquakes in different regions have approximately the same average stress drop.

Moment–Area Scaling Relationship Assuming Constant Stress Drop for Crustal Earthquakes

2020 ◽  
Vol 110 (1) ◽  
pp. 241-249
Author(s):  
Kazuhito Hikima ◽  
Akihiro Shimmura
Keyword(s):  
Stress Drop ◽  
Constant Stress ◽  
Event Data ◽  
Scaling Relation ◽  
Seismogenic Layer ◽  
Crustal Earthquakes ◽  
Rupture Area ◽  
Scaling Relationship ◽  
Static Stress Drop ◽  
Good Agreement

ABSTRACT For crustal earthquakes, the scaling relationship between the seismic moment M0 and rupture area S varies with the size of the earthquake, due to the limited thickness of the seismogenic layer. In those M0–S scaling relations, in most cases, the calculated static stress drop is altered with the size of earthquake, although the change depends on the assumed fault model. However, it is not clear whether the dependence of the stress drop on M0 is physically reasonable. In this study, the scaling relation between M0 and S, which assumes a constant stress drop over a wide M0 range, is discussed based on the analytical stress drop formula of a rectangular strike-slip fault. In the proposed relation, M0 is proportional to S3/2 for small and medium faults and to S1 for long faults. In addition, the relation between M0 and S varies in the intermediate range, depending on the aspect ratio. The scaling relation showed good agreement with past event data when the saturated rupture width was set to around 15–20 km and the stress drop was set to about 3 MPa.

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