Dynamics of simple earthquake model with time delay and variation of friction strength

Abstract

Abstract. We examine the dynamical behaviour of the phenomenological Burridge-Knopoff-like model with one and two blocks, where the friction term is supplemented by the time delay τ and the variable friction strength c. Time delay is assumed to reflect the initial quiescent period of the fault healing, considered to be a function of history of sliding. Friction strength parameter is proposed to mimic the impact of fault gouge thickness on the rock friction. For the single-block model, interplay of the introduced parameters c and τ is found to give rise to oscillation death, which corresponds to aseismic creeping along the fault. In the case of two blocks, the action of c 1 , c 2 , τ 1 and τ 2 may result in several effects. If both blocks exhibit oscillatory motion without the included time delay and frictional strength parameter, the model undergoes transition to quasiperiodic motion if only c 1 and c 2 are introduced. The same type of behaviour is observed when τ 1 and τ 2 are varied under the condition c 1 = c 2 . However, if c 1 , and τ 1 are fixed such that the given block would lie at the equilibrium while c 2 and τ 2 are varied, the (c 2 , τ 2 ) domains supporting quasiperiodic motion are interspersed with multiple domains admitting the stationary solution. On the other hand, if (c 1 , τ 1 ) warrant oscillatory behaviour of one block, under variation of c 2 and τ 2 the system's dynamics is predominantly quasiperiodic, with only small pockets of (c 2 , τ 2 ) parameter space admitting the periodic motion or equilibrium state. For this setup, one may also find a transient chaos-like behaviour, a point corroborated by the positive value of the maximal Lyapunov exponent for the corresponding time series.

A study of earthquake recurrence based on a one-body spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

“…The fluid density ρ f and the porosity n depend on T and p. Although there are numerous studies on such dependence (Lachenbruch, 1980;Bizzarri, 2012b; and cited references therein), observed data and theoretical analyses about the values of ρ f and n during a seismic cycle are rare.…”

“…The one-, two-, three-, and few-body models with various friction laws have also been applied to approach fault dynamics (see Turcotte, 1992). The studies for various friction laws based on spring-slider models are briefly described below: (1) for rate-and state-dependent friction (e.g., Rice and Tse, 1986;Ryabov and Ito, 2001;Erickson et al, 2008Erickson et al, , 2011He et al, 2003;Mitsui and Hirahara, 2009;Bizzarri, 2012a;Abe and Kato, 2013;Kostić et al, 2013a;Bizzarri and Crupi, 2014;Franović et al, 2016); (2) for velocity-weakening friction (e.g., Carlson and Langer, 1989;Huang and Turcotte, 1992;Brun and Gomez, 1994;Wang and Hwang, 2001;Wang, 2003;Kostić et al, 2013b); (3) for simple static-dynamic friction (e.g., Abaimov et al, 2007;Hasumi, 2007).…”

“…Some results concerning earthquake recurrence are simply explained below. Erickson et al (2008) suggested that aperiodicity in earthquake dynamics is due to either the nonlinear friction law (Huang and Turcotte, 1990) or the heterogeneous stress distribution (Lapusta and Rice, 2003). Wang and Hwang (2001) emphasized the importance of heterogeneous frictional strengths.…”

“…The frictional force F (u, v) is controlled by several factors (see Wang, 2016, and cited references therein). An effect combined from temperature and fluids in a fault zone can result in thermal pressurization (abbreviated as TP hereafter) which would yield a shear stress (resistance) on the fault plane (Sibson, 1973;Lachenbruch, 1980;Rice, 2006;Wang, 2009Wang, , 2011Wang, , 2016Wang, , 2017aBizzarri, 2009). Rice (2006) proposed two end-member models of TP, i.e., the adiabatic undrained deformation (AUD) model and slip-on-aplane (SOP) model.…”

A Study of Earthquake Recurrence based on a One-body Spring-slider Model in the Presence of Thermal-pressurized Slip-weakening Friction and Viscosity

“…The frictional force F (u, v) is controlled by several factors (see Wang, 2016, and cited references therein). An effect combined from temperature and fluids in a fault zone can result in thermal pressurization (abbreviated as TP hereafter) which would yield a shear stress (resistance) on the fault plane (Sibson, 1973;Lachenbruch, 1980;Rice, 2006;Wang, 2009Wang, , 2011Wang, , 2016Wang, , 2017aBizzarri, 2009). Rice (2006) proposed two end-member models of TP, i.e., the adiabatic undrained deformation (AUD) model and slip-on-aplane (SOP) model.…”