Observations and modeling of the rupture development based on the analysis of Source Time Functions

2020 ◽  
Author(s):  
Julien Renou ◽  
Martin Vallée ◽  
Hideo Aochi
Keyword(s):  
Dynamic Models ◽  
Large Population ◽  
Time Function ◽  
Development Phase ◽  
Rupture Velocity ◽  
Source Time Function ◽  
Generic Properties ◽  
Dynamic Source ◽  
Source Models ◽  
The Moment

<p>Our knowledge of earthquake source physics, giving rise to events of very different magnitudes, requires observations of a large population of earthquakes. The development of systematic analysis tools for the global seismicity meets these expectations, and allows us to extract the generic properties of earthquakes, which can then be integrated into models of the rupture process. Following this approach, the SCARDEC method is able to retrieve source time functions of events over a large range of magnitude (Mw > 5.7). The source time function (which describes the temporal evolution of the moment rate) is suitable for the analysis of transient rupture properties which provide insights into the generation of earthquakes of various sizes. Our study aims at observing the rupture development of such earthquakes in order to add better constraints on dynamic source models. We first focus on the development of earthquakes through the analysis of the SCARDEC catalog. The phase leading to the peak of the source time function ("development phase'') is extracted to characterize its evolution. From the computation of moment accelerations at prescribed moment rates, we observe that the evolution of the moment rate during the developement phase is independent of the final magnitude. A quantitative analysis of the moment rate increase as a function of time further indicates that this phase does not respect the steady t² self-similar growth. These observations are then compared with dynamic source models. We develop heterogeneous dynamic models which take into consideration rupture physics. Heterogeneous distributions of the friction parameter and the initial stress contribute to generate highly realistic rupture scenarios. Rupture propagation is strongly influenced by these two dynamic parameters which induce a clear preferential direction of propagation together with a local variability of the rupture velocity. Variability of the kinematic parameters also tends to correlate rupture velocity and slip velocity, which is a key feature for the transient behavior of the development phase previously observed. These findings are expected to put further constraints on future realistic dynamic rupture scenarios.</p>

Deriving source-time functions using principal component analysis

1989 ◽  
Vol 79 (3) ◽  
pp. 711-730
Author(s):  
D. W. Vasco
Keyword(s):  
Principal Component Analysis ◽  
Moment Tensor ◽  
Principal Component ◽  
Singular Values ◽  
Singular Value ◽  
Time Function ◽  
Basis Functions ◽  
Single Source ◽  
Source Time Function ◽  
The Moment

Abstract Factors such as source complexity, microseismic noise, and lateral heterogeneity all introduce nonuniqueness into the source-time function. The technique of principal component analysis is used to factor the moment tensor into a set of orthogonal source-time functions. This is accomplished through the singular value decomposition of the time-varying moment tensor. The adequacy of assuming a single source-time function may then be examined through the singular values of the decomposition. The F test can also be used to assess the significance of the various principal component basis functions. The set of significant basis functions can be used to test models of the source-time functions, including multiple sources. Application of this technique to the Harzer nuclear explosion indicated that a single source-time function was found to adequately explain the moment tensor. It consists of a single pulse appearing on the diagonal elements of the moment-rate tensor. The decomposition of the moment tensor for a deep teleseism in the Bonin Islands revealed three basis functions associated with relatively large singular values. The F test indicated that only two of the principal components were significant. The principal component associated with the largest singular value consists of a large pulse followed 16-sec later by a diminished pulse. The second principal component, a long-period oscillation, appears to be a manifestation of the poor resolution of the moment-rate tensor at low frequencies.

Seismic moment and long-period radiation of underground nuclear explosions

1973 ◽  
Vol 63 (3) ◽  
pp. 847-857
Author(s):  
Gerhard Müller
Keyword(s):  
Point Source ◽  
Seismic Moment ◽  
Time Function ◽  
Moment Function ◽  
P Wave ◽  
Underground Explosion ◽  
Source Time Function ◽  
Nuclear Explosions ◽  
Long Period ◽  
The Moment

abstract The moment function of an explosion is introduced, using the equivalence of an explosive point source and three mutually perpendicular linear dipoles. The seismic moment of an explosion is the final value, for large times, of the moment function. Its relation to source parameters is similar to that of the moment of an earthquake: M1 = (λ + 2μ)S1D1 (λ, μ = Lamé's parameters, S1 = surface area of a sphere surrounding the explosion in the elastic zone, D1 = static radial displacement on this sphere). From strain observations of other authors (Romig et al., 1969; Smith et al., 1969), the moment of the underground nuclear explosion BENHAM is estimated to be about 1024 dyne cm. This moment value supports the assumption that the source-time function for the long-period radiation from large nuclear explosions (periods greater than about 10 sec) is essentially a step-function. On the other hand, a quantitative estimate of the long-period P-wave spectrum of the explosions JORUM, HANDLEY and MILROW and a comparison with observed spectra of Molnar (1971) for JORUM and HANDLEY and Wyss et al. (1971) for MILROW support the assumption of an impulsive source-time function. This discrepancy, which is typical of current opinions among seismologists, is not resolved. It is concluded that an explosive point source is possibly not a sufficient model for the long-time radiation and the static displacement field of a nuclear underground explosion whose elastic radius is about equal to its depth and which is detonated in a prestressed medium.

scholarly journals Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

2013 ◽  
Vol 5 (2) ◽  
pp. 1125-1162 ◽  
Author(s):  
S. C. Stähler ◽  
K. Sigloch
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Practical Importance ◽  
Principal Component ◽  
Seismic Source ◽  
Empirical Orthogonal Functions ◽  
Time Function ◽  
Source Inversion ◽  
Source Time Function ◽  
Earthquake Parameters

Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves, but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits to propagate these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

SIMULATION OF DOOR MOVEMENT WITH A CLOSING MECHANISM

2021 ◽  
Vol 2021 (11) ◽  
pp. 4-10
Author(s):  
Aleksandr Reutov
Keyword(s):  
Mechanical Characteristics ◽  
Dynamic Models ◽  
Quality Criteria ◽  
Strong Impact ◽  
Closing Time ◽  
Door Opening ◽  
Air Resistance ◽  
The Moment ◽  
Moment Of Resistance ◽  
Closing Mechanism

The work objective is to determine the parameters of the closing mechanism that provide the specified characteristics of the door movement. Research method: computer simulation of the movement of a door with a lock mechanism as a multi-mass dynamic system, taking into account the mechanical characteristics and contact interaction of the lock mechanism. Research results and novelty. Computer dynamic models of a door with a door closer and a door with a spring have been developed. The moments of the door opening force, the closing time of the door, the angular velocity of the door at the time of impact with the frame are considered as the criteria for the quality of the door closing mechanism. Formulas are obtained that determine the permissible values of stiffness and deformation of the door closer spring according to the specified moments of the door opening force. The movement of doors with a door closer and with a spring is compared. The parameters of the closing mechanism providing the specified characteristics of the door movement of the considered example are determined. It is shown that with the same values of the opening force moments, the speed of impact with the frame in the case of the door closer is less than the door with a spring. Conclusions: The developed computer dynamic models of a door with a door closer and a door with a spring make it possible to determine the characteristics of the door movement taking into account the inertial and mechanical characteristics of the door closer and spring mechanisms. The permissible values of stiffness and deformation of the door closer spring can be determined by the specified moments of the door opening force in two positions. It is established that the forces of air resistance and friction in the hinges of the door cannot create the moment of resistance necessary for smooth closing of the door without a strong impact on the frame with a limited closing time. The quality criteria that minimize the closing time and the speed of impact of the door with the frame are contradictory. The choice of optimal parameters of the door closing mechanism is possible if one of the criteria is replaced by a restriction. The developed formulas and computer models are recommended for use in the design of devices that restrict the movement of doors.

The 14 September 1995 (M = 7.3) Copala, Mexico, earthquake: A source study using teleseismic, regional, and local data

1997 ◽  
Vol 87 (4) ◽  
pp. 999-1010
Author(s):  
F. Courboulex ◽  
M. A. Santoyo ◽  
J. F. Pacheco ◽  
S. K. Singh
Keyword(s):  
Time Window ◽  
Time Function ◽  
Source Process ◽  
Source Time Function ◽  
Nonlinear Method ◽  
Local Data ◽  
Plate Interface ◽  
Linear Inversion ◽  
Field Source ◽  
Mexico Earthquake

Abstract We analyze source characteristics of the 14 September 1995, Copala, Mexico, earthquake (M = 7.3) using teleseismic, regional, and local seismograms. In the analysis of the teleseismic and the regional seismic waves, we apply the empirical Green's function (EGF) technique. The recording of an appropriate aftershock is taken as the EGF and is used to deconvolve the mainshock seismogram, thus obtaining an apparent far-field source-time function at each station. The deconvolution has been done using surface waves. For teleseismic data, we apply a spectral deconvolution method that enables us to obtain 37 apparent source-time functions (ASTFs) at 29 stations. In the analysis of the regional broadband seismograms, we use two different aftershocks as EGF, and the deconvolution is performed in the time domain with a nonlinear method, imposing a positivity constraint, and the best azimuth for the directivity vector is obtained through a grid-search approach. We also analyze two near-source accelerograms. The traces are inverted for the slip distribution over the fault plane by applying a linear inversion technique. With the aid of a time-window analysis, we obtain an independent estimation of the source-time function and a more detailed description of the source process. The analysis of the three datasets permits us to deduce the main characteristics of the source process. The rupture initiated at a depth of 16 km and propagated in two directions: updip along the plate interface toward 165° N and toward 70° N. The source duration was between 12 and 14 sec, with the maximum of energy release occurring 8 sec after the initiation of the rupture. The estimated rupture dimension of 35 × 45 km is about one-fourth of the aftershock area. The average dislocation over the fault was 1.4 m (with a maximum dislocation of 4.1 m located 10 km south of the hypocenter), which gives roughly 1 MPa as the average static stress drop.

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