Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate‐ and state‐dependent friction

Abstract

Abstract. We present an efficient and rigorous numerical procedure for calculating the elastodynamic response of a fault subjected to slow tectonic loading processes of long duration within which them are episodes of rapid earthquake failure. This is done for a general class of rate-and state-dependent friction laws with positive direct velocity effect. The algorithm allows us to treat accurately, within a single computational procedure, loading intervals of thousands of years and to calculate, for each earthquake episode, initially aseismic accelerating slip prior to dynamic rupture, the rupture propagation itself, rapid post seismic deformation which follows, and also ongoing creep slippage throughout the loading period in velocity-strengthening fault regions. The methodology is presented using the two-dimensional (2-D) antiplane spectral formulation and can be readily extended to the 2-D in-plane and 3-D spectral formulations and, with certain modifications, to the space-time boundary integral formulations as well as to their discretized development using finite difference or finite element methods. The methodology can be used to address a number of important issues, such as fault operation under low overall stress, interaction of dynamic rupture propagation with pore pressure development, patterns of rupture propagation in events nucleated naturally as a part of a sequence, the earthquake nucleation process, earthquake sequences on faults with heterogeneous frictional properties and/or normal stress, and others. The procedure is illustrated for a 2-D crustal strike-slip fault model with depth-variable properties. For lower values of the state-evolution distance of the friction law, small events appear. The nucleation phases of the small and large events are very similar, suggesting that the size of an event is determined by the conditions on the fault segments the event is propagating into rather than by the nucleation process itself. We demonstrate the importance of incorporating slow tectonic loading with elastodynamics by evaluating two simplified approaches, one with the slow tectonic loading but no wave effects and the other with all dynamic effects included but much higher loading rate.

Rate and state dependent friction and the stability of sliding between elastically deformable solids

“…It is now generally assumed to be descended from an Arrhenius activated rate process describing creep at asperity contacts. That interpretation had been mentioned earlier by Stesky (1977), was implicit in Chester (1994), and was suggested explicitly, in the rate and state framework, by Heslot et al (1994), Brà echet and Estrin (1994), Baumberger (1997), Sleep (1997), Persson (1998), Baumberger et al (1999), Lapusta et al (2000), and Nakatani (2001). In such an interpretation, for the simple case of a single activated process, we write the slip rate as…”

“…That is, for rapid enough changes in V so as for the surfaces to be at the same population of asperity contacts (i.e., at a constant value of the state variable), the variation of friction strength with slip rate V is generally found to involve a positive proportionality to ln(V ). This dependence is plausibly attributed to the presence of a thermally activated creep process at stressed asperity contacts (Stesky, 1977;Heslot et al, 1994;Chester, 1994;Brà echet and Estrin, 1994;Baumberger, 1997;Sleep, 1997;Persson, 1998;Baumberger et al, 1999;Lapusta et al, 2000;Nakatani, 2001) as discussed further. We also demonstrate how compromises from the full rate and state constitutive framework, in the direction of classical friction laws like pure velocity-dependent friction, of velocity-weakening type, do not allow a quasi-static range and, in fact, lead to paradoxical prediction of supersonic propagation of slip pulses (as recognized already by Weertman, 1969, andKnopo andLandoni, 1998), or to ill-posedness, depending on the strength of the velocity weakening.…”

“…A simple remedy, which regularizes the law at V =0, is to include backward jumps by replacing exp( c =k B T )= exp( =a ) with 2 sinh( =a ). Such a procedure, motivated by the thermal activation concept, is in standard use in formulating crustal scale earthquake models with rate and state constitutive laws (e.g., Rice and Ben-Zion, 1996; Ben-Zion and Rice, 1997;Lapusta et al, 2000).…”

Seismic variability of subduction thrust faults: Insights from laboratory models

“…The gelatin is characterized by a Maxwell time of ∼45 s. The material thus responds as a viscoelastic solid during the interseimic phase, and it is mainly elastic during the few seconds characterizing the slip phase. The rheological properties of gelatin are a fundamental factor to obtain a comprehensive model throughout the entire earthquake cycle including the interseismic viscoelastic deformation [e.g., Rice, 1993;Lapusta et al, 2000]. Tuning the lithospheric viscosity to higher values would increase the timescale without changing the essence of the physical process.…”

Stable creeping fault segments can become destructive as a result of dynamic weakening

“…It starts at a time when the interseismic fault slip rate distribution is as expected for the slow-rate friction properties adopted in the model: patch A is mostly locked and patch B is creeping with the long-term plate rate, like the creeping areas that surround the two patches. During the following interseismic period, the locked region of patch A shrinks by penetration of creep from the surrounding areas, which occurs due to stress concentration at the boundary between creeping and locked regions (e.g., Tse and Rice, 1986;Lapusta et al, 2000). Earthquake rupture nucleates when the creeping region within patch A becomes comparable to the nucleation size estimates (Rice and Ruina, 1983;Rice et al, 2001;Rubin and …”