Characteristics of earthquake sequences: comparison from 0D to 3D

2021 ◽  
Author(s):  
Meng Li ◽  
Casper Pranger ◽  
Ylona van Dinther
Keyword(s):  
Stress Drop ◽  
Dynamic Models ◽  
Numerical Models ◽  
Recurrence Interval ◽  
Staggered Grid ◽  
Earthquake Parameters ◽  
Higher Dimensional ◽  
Dimensional Models ◽  
As Stress ◽  
Earthquake Sequences

<p>Numerical models are well-suited to overcome limited spatial-temporal observations to understand earthquake sequences, which is fundamental to ultimately better assess seismic hazard. However, high-resolution numerical models in 3D are computationally time and memory consuming. This is not optimal if the aspects of lateral or depth variations within the results are not needed to answer a particular objective. In this study we quantify and summarize the limitations and advantages for simulating earthquake sequences in all spatial dimensions.</p><p> </p><p>We simulate earthquake sequences on a strike-slip fault with rate-and-state friction from 0D to 3D using both quasi-dynamic and fully dynamic approaches. This cross-dimensional comparison is facilitated by our newly developed, flexible code library <em>Garnet</em>, which adopts a finite difference method with a fully staggered grid. We have validated our models using problems BP1-QD & FD and BP4-QD & FD of the SEAS (Sequences of Earthquakes and Aseismic Slip) benchmarks from the Southern California Earthquake Center.</p><p> </p><p>Our results demonstrate that lower-dimensional/quasi-dynamic models are qualitatively similar in terms of earthquake cycle characteristics to their higher-dimensional/fully-dynamic counterparts, while they could be hundreds to millions times faster at the same time. Quantitatively, we observe that certain earthquake parameters, such as stress drop and fracture energy release, can be accurately reproduced in each of these simpler models as well. However, higher dimensional models generally produce lower maximum slip velocities and hence longer coseismic durations. This is mainly due to lower rupture speeds, which result from increased energy consumption along added rupture front directions. In the long term, higher dimensional models produce shorter recurrence interval and hence smaller total slip, which is mainly caused by the higher interseismic stress loading rate inside the nucleation zone. The same trend is also observed when comparing quasi-dynamic models to fully dynamic ones. We extend a theoretical calculation that to first order approximates the aforementioned physical observables in 3D to all other dimensions. These theoretical considerations confirm the same trend as what is observed for stress drop, recurrence interval and total slip across dimensions. These findings on similarities and differences of different dimensional models and a corresponding quantification of computational efficiency can guide model design and facilitate result interpretation in future studies.</p>

Dynamic and quasi-dynamic modelling of earthquake sequences from zero to three dimensions: choose model complexity as needed

2020 ◽  
Author(s):  
Meng Li ◽  
Casper Pranger ◽  
Luca Dal Zilio ◽  
Ylona van Dinther
Keyword(s):  
Dynamic Models ◽  
Model Complexity ◽  
Computational Time ◽  
Cycle Period ◽  
Seismic Cycle ◽  
Cycle Simulation ◽  
Higher Dimensional ◽  
Dimensional Models ◽  
Earthquake Sequences ◽  
Lower Dimensional

<p>Earthquake sequences reflect the repetitive dynamic processes of stress accumulation and release on a fault. Understanding earthquake sequences is fundamental for the research of induced and natural earthquakes and may ultimately help to better assess long-term seismic hazard. Numerical models are well-suited to overcome limited spatiotemporal observations and improve our understanding on this topic. However, large models in 3D are still computational time and memory consuming. Moreover, this may not be optimal if the aspects of lateral or depth variations within the results are not needed to answer a particular objective. This motivated us to investigate the advantages and limitations of various dimensional models by simulating earthquake sequences in 0D, 1D, 2D and ultimately 3D. We applied a C++ numerical library GARNET [1] to deal with the various dimensional models in one simulator. This library uses a fully staggered finite difference scheme with a rectilinear adaptive grid. It also incorporates an automatic discretization algorithm and combines different physical ingredients such as visco-elasto-plastic rheology and quasi- and fully dynamic approaches into one algorithm.</p><p>Here we present numerical experiments of a strike-slip fault under rate-and-state friction, surrounded by an elastic medium with constant tectonic loading and, test them under different parameters and initial conditions. By adding one dimension at a time, we simulate a more detailed structure of the seismic cycle. The higher dimensional models present both the validity and the limitations of the lower dimensional ones. For example, inertial waves are not possible to present in 0D while a quasi-dynamic radiation damping term can be added here instead. Another example is that due to lack of grid extension along the fault, both 0D and 1D model fail to reveal an earthquake nucleation phase. However, some important observables, such as the seismic cycle period, maximum/minimum stress and slip rates, are calculated accurately in lower dimensional models, which are much faster than higher dimensional models. We also implemented and compared quasi- and fully dynamic models in the same way. Our results indicate that both the size of simulated seismic events and their interval are reduced in quasi-dynamic models. This could provide us with guidance to identify the appropriate model complexity for various problems. We will also present 3D modeling results, which will be compared to their 2D equivalent. Finally, we present our results for the SCEC SEAS benchmarks [2] and compare them to other participating codes.</p><p>[1] Pranger, C. C., L. Le Pourhiet, D. May, Y. van Dinther, and T. Gerya (2016). “Self- consistent seismic cycle simulation in a three-dimensional continuum model: method- ology and examples.” AGU Fall Meeting Abstracts.</p><p>[2] Erickson, B. A., et al. (2019). The Community Code Verification Exercise for Simulating Sequences of Earthquakes and Aseismic Slip (SEAS). Poster Presentation at 2019 SCEC Annual Meeting.</p>

LOW TEMPERATURE MODELS OF METAL OXIDE SEMICONDUCTOR FIELD-EFFECT TRANSISTORS

1995 ◽  
Vol 06 (02) ◽  
pp. 317-373 ◽  
Author(s):  
G. GILDENBLAT ◽  
D. FOTY
Keyword(s):  
Low Temperature ◽  
Field Effect Transistors ◽  
Numerical Models ◽  
Three Dimensional ◽  
Oxide Semiconductor ◽  
Characteristic Time Scale ◽  
Mos Transistors ◽  
Short Channel ◽  
Temperature Range ◽  
Dimensional Models

We review the modeling of silicon MOS devices in the 10–300 K temperature range with an emphasis on the specifics of low-temperature operation. Recently developed one-dimensional models of long-channel transistors are discussed in connection with experimental determination and verification of the effective channel mobility in a wide temperature range. We also present analytical pseudo-two-dimensional models of short-channel devices which have been proposed for potential use in circuit simulators. Several one-, two-, and three-dimensional numerical models are discussed in order to gain insight into the more subtle details of the low-temperature device physics of MOS transistors and capacitors. Particular attention is paid to freezeout effects which, depending on the device design and the ambient temperature range, may or may not be important for actual device operation. The numerical models are applied to study the characteristic time scale of freezeout transients in the space-charge regions of silicon devices, to the analysis and suppression of delayed turn-off in MOS transistors with compensated channel, and to the temperature dependence of three-dimensional effects in short-channel, narrow-channel MOSFETs.

The relations between the corner frequency, seismic moment and source dynamic parameters derived from the spontaneous rupture of a circular fault

2021 ◽  
Vol 228 (1) ◽  
pp. 134-146
Author(s):  
Jian Wen ◽  
Jiankuan Xu ◽  
Xiaofei Chen
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Dynamic Models ◽  
Scaling Law ◽  
Boundary Integral ◽  
Corner Frequency ◽  
Dynamic Parameters ◽  
Zone Size ◽  
Dynamic Rupture ◽  
Scaling Relationships

SUMMARY The stress drop is an important dynamic source parameter for understanding the physics of source processes. The estimation of stress drops for moderate and small earthquakes is based on measurements of the corner frequency ${f_c}$, the seismic moment ${M_0}$ and a specific theoretical model of rupture behaviour. To date, several theoretical rupture models have been used. However, different models cause considerable differences in the estimated stress drop, even in an idealized scenario of circular earthquake rupture. Moreover, most of these models are either kinematic or quasi-dynamic models. Compared with previous models, we use the boundary integral equation method to simulate spontaneous dynamic rupture in a homogeneous elastic full space and then investigate the relations between the corner frequency, seismic moment and source dynamic parameters. Spontaneous ruptures include two states: runaway ruptures, in which the rupture does not stop without a barrier, and self-arresting ruptures, in which the rupture can stop itself after nucleation. The scaling relationships between ${f_c}$, ${M_0}$ and the dynamic parameters for runaway ruptures are different from those for self-arresting ruptures. There are obvious boundaries in those scaling relations that distinguish runaway ruptures from self-arresting ruptures. Because the stress drop varies during the rupture and the rupture shape is not circular, Eshelby's analytical solution may be inaccurate for spontaneous dynamic ruptures. For runaway ruptures, the relations between the corner frequency and dynamic parameters coincide with those in the previous kinematic or quasi-dynamic models. For self-arresting ruptures, the scaling relationships are opposite to those for runaway ruptures. Moreover, the relation between ${f_c}$ and ${M_0}$ for a spontaneous dynamic rupture depends on three factors: the dynamic rupture state, the background stress and the nucleation zone size. The scaling between ${f_c}$ and ${M_0}$ is ${f_c} \propto {M_0^{ - n}}$, where n is larger than 0. Earthquakes with the same dimensionless dynamic parameters but different nucleation zone sizes are self-similar and follow a ${f_c} \propto {M_0^{ - 1/3}}$ scaling law. However, if the nucleation zone size does not change, the relation between ${f_c}$ and ${M_0}$ shows a clear departure from self-similarity due to the rupture state or background stress.

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 Experimental validation of numerical structural dynamic models for metal plate joining techniques

2017 ◽  
Vol 24 (15) ◽  
pp. 3348-3369 ◽  
Author(s):  
L Van Belle ◽  
D Brandolisio ◽  
E Deckers ◽  
S Jonckheere ◽  
C Claeys ◽  
...  
Keyword(s):  
Adhesive Bonding ◽  
Dynamic Models ◽  
Numerical Models ◽  
Metal Plate ◽  
Joint Models ◽  
Structural Dynamic ◽  
Single Plate ◽  
Power Injection ◽  
Stiffness And Damping ◽  
Good Agreement

Joined structures are of great industrial relevance. The dynamic effects of joints are, however, often practically difficult to accurately account for in numerical models, as they often lead to local changes in stiffness and damping. This paper discusses the comparison between measurements and simulations of joined panels considering four different joining techniques: adhesive bonding, metal inert gas welding, resistance spot welding and flow drill screwing. An experimental modal analysis is performed on the different systems and the power injection method is applied to determine the loss factors of single plate systems and their joined counterparts. The joined panels are modeled in a holistic simulation environment with particular focus on the joining region, by the application of predefined and generic joint models. A very good agreement is obtained between the simulated dynamic behavior and the experimental results, showing that an accurate representation of the joints has been obtained.

2D Numerical Simulation of Intraoceanic Subduction during the Upper Jurassic Closure of the Vardar Tethys

2020 ◽  
Author(s):  
Nikola Stanković ◽  
Vesna Cvetkov ◽  
Vladica Cvetković
Keyword(s):  
Numerical Simulations ◽  
Late Cretaceous ◽  
Stokes Equations ◽  
Numerical Models ◽  
Upper Jurassic ◽  
Staggered Grid ◽  
Parameter Study ◽  
Ongoing Research ◽  
Magmatic Complex ◽  
Vardar Zone

<p>In this study we report interim results of our ongoing research that involves the application of numerical modeling for constraining the geodynamic conditions associated with the closure of the Vardar branch of the Tethys Ocean. The study is aimed at better understanding the ultimate fate of the Balkan ophiolites, namely at addressing the question whether these ophiolites represent relicts of an ocean that completely closed during Upper Jurassic/lowermost Cretaceous time (Vardar Tethys) or they also contain remnants of the ocean floor of a Late Cretaceous oceanic realm (Sava – Vardar) [Schmid et al., 2008].</p><p>In our numerical models we try to simulate a single intraoceanic subduction that commences in the Lower/Mid Jurassic and ends in the Lower Cretaceous, transitioning into oceanic closure processes and subsequent collision between Adria and Eurasia plates. These convergent-collision events should have led to the formation of ophiolite-like igneous rocks of the so-called Sava - Vardar zone.</p><p>A series of numerical simulations were performed with varying parameters. In the scope of our numerical simulations, the set of equations is solved: the continuity equation, the Navier-Stokes equations and the temperature equation. Marker in cell method was incorporated in solving this system with finite difference discretization of the equations on a staggered grid. To utilize this numerical method a thermo-mechanical code I2VIS [Gerya et al., 2000; Gerya & Yuen, 2003] was used for obtaining the final results. </p><p>Our actual 2D thermo-mechanical models cover the crust and the upper portion of the mantle with varying starting widths of the Vardar Ocean in the Lower Jurassic. The ocean is modeled with two segments: the western subducting slab and the eastern overriding slab. Slabs with different ages and thicknesses were used and the convergence rate is varied. The intraoceanic subduction is assumed to have been initiated along the mid oceanic ridge. Two continents (i.e. Adria and Eurasia) with different thicknesses of the continental lithosphere and crust are also modeled adjacent to a single oceanic realm between them.</p><p>The parameter study is in function of defining conditions under which the hypothesized scenario occurs. So far, we have succeeded in reproducing westward obduction onto the Adriatic margin, which is in accordance with the geological observations, i.e., with the top-west emplaced West Vardar ophiolites [see Schmid et al., 2008 for references]. However, our model is yet to produce sufficient amounts of back-arc extension along the Eurasian active margin and that is crucial for explaining the formation of the igneous provinces occurring within the Late Cretaceous Sava – Vardar zone and the Timok Magmatic Complex.</p>

Sign in / Sign up

Export Citation Format

Share Document