Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Abe, Yuta; Kato, Naoyuki

doi:10.1007/s00024-011-0450-8

Cited by 43 publications

(19 citation statements)

References 36 publications

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“…This is similar to the chaotic motions in a two-degree-of-freedom system studied by numerous researches [e.g., Turcotte, 1990a,b, 1992;de Sousa Viera, 1999;and Abe and Kato, 2013]. Figures 11-13 show the simulation results for η 1 =10 and η 2 =10, η 1 =10 and η 2 =2, and η 1 =10 and η 2 =20, respectively, when the values of other model parameters are the same as those in Figure 7.…”

Section: Effect Due To Static Frictional Forcesupporting

confidence: 75%

“…The details can be seen in Thompson and Stewart [1986] or other nonlinear literatures. Chaotic motion in a two-degree-of-freedom system have been studied by numerous researches [e.g., Turcotte, 1990a,b, 1992;de Sousa Viera, 1999;and Abe and Kato, 2013]. However, only the friction law was considered in those studies.…”

Section: Friction Due To Thermal Pressurizationmentioning

confidence: 99%

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Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

Wang

2017

Annals of Geophysics

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Section: Effect Due To Static Frictional Forcesupporting

confidence: 75%

Section: Friction Due To Thermal Pressurizationmentioning

confidence: 99%

Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

Wang

2017

Annals of Geophysics

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“…Numerous solutions, developments, and applications exist (e.g. Burridge and Knopoff, 1967;Cao and Aki, 1984;Schmittbuhl et al, 1996;Carlson and Langer, 1989;Carlson et al, 1991;Gu and Wong, 1991;Kawamura, 2006, 2008;Wang, 2012;Erickson et al, 2011;Abe and Kato, 2013;Aragon and Jagla, 2013). Burridge and Knopoff (1967) developed the simple spring-slider model into one-and twodimensional models, both experimentally and numerically.…”

Section: Spring-slider Modelsmentioning

confidence: 99%

“…Several authors implemented different forms of the friction laws, e.g. time dependence (Dieterich, 1972a), displacement dependence (Cao and Aki, 1984), and rate and state dependence (Gu and Wong, 1991;Erickson et al, 2011;Abe and Kato, 2013). Several developments were aimed at including additional effects such as seismic waves (Wang, 2012) or stress relaxation (Aragon and Jagla, 2013).…”

Section: Spring-slider Modelsmentioning

confidence: 99%

Analogue earthquakes and seismic cycles: experimental modelling across timescales

2017

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Abstract. Earth deformation is a multi-scale process ranging from seconds (seismic deformation) to millions of years (tectonic deformation). Bridging short-and long-term deformation and developing seismotectonic models has been a challenge in experimental tectonics for more than a century. Since the formulation of Reid's elastic rebound theory 100 years ago, laboratory mechanical models combining frictional and elastic elements have been used to study the dynamics of earthquakes. In the last decade, with the advent of high-resolution monitoring techniques and new rock analogue materials, laboratory earthquake experiments have evolved from simple spring-slider models to scaled analogue models. This evolution was accomplished by advances in seismology and geodesy along with relatively frequent occurrences of large earthquakes in the past decade. This coincidence has significantly increased the quality and quantity of relevant observations in nature and triggered a new understanding of earthquake dynamics. We review here the developments in analogue earthquake modelling with a focus on those seismotectonic scale models that are directly comparable to observational data on short to long timescales. We lay out the basics of analogue modelling, namely scaling, materials and monitoring, as applied in seismotectonic modelling. An overview of applications highlights the contributions of analogue earthquake models in bridging timescales of observations including earthquake statistics, rupture dynamics, ground motion, and seismic-cycle deformation up to seismotectonic evolution.

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“…This periodic orbit then undergoes a period doubling cascade into a strange attractor, recognized as broadband noise in the power spectrum. From numerical simulations of earthquake ruptures using a twobody model with a rate-and state-friction law, Abe and Kato (2013) observed various slip patterns, including the periodic recurrence of seismic and aseismic slip events, and several types of chaotic behavior. The system exhibits typical perioddoubling sequences for some parameter ranges, and attains chaotic motion.…”

mentioning

confidence: 99%

Multistable slip of a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

Wang

2017

Nonlin. Processes Geophys.

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Abstract. This study is focused on multistable slip of earthquakes based on a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity by using the normalized equation of motion of the model. The major model parameters are the normalized characteristic displacement, U c , of the friction law and the normalized viscosity coefficient, η, between the slider and background plate. Analytic results at small slip suggest that there is a solution regime for η and γ (= 1/U c ) to make the slider slip steadily. Numerical simulations exhibit that the time variation in normalized velocity, V /V max (V max is the maximum velocity), obviously depends on U c and η. The effect on the amplitude is stronger due to η than due to U c . In the phase portrait of V /V max versus the normalized displacement, U/U max (U max is the maximum displacement), there are two fixed points. The one at large V /V max and large U/U max is not an attractor, while that at small V /V max and small U/U max can be an attractor for some values of η and U c . When U c <0.55, unstable slip does not exist. When U c ≥ 0.55, U c and η divide the solution domain into three regimes: stable, intermittent, and unstable (or chaotic) regimes. For a certain U c , the three regimes are controlled by a lower bound, η l , and an upper bound, η u , of η. The values of η l , η u , and η u − η l all decrease with increasing U c , thus suggesting that it is easier to yield unstable slip for larger U c than for smaller U c or for larger η than for smaller η. When U c <1, the Fourier spectra calculated from simulation velocity waveforms exhibit several peaks, thus suggesting the existence of nonlinear behavior of the system. When U c >1, the related Fourier spectra show only one peak, thus suggesting linear behavior of the system.

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Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Cited by 43 publications

References 36 publications

Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

Analogue earthquakes and seismic cycles: experimental modelling across timescales

Multistable slip of a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

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