Steady-state solutions of rupture propagation in an earthquake simulator governed by rate and state dependent friction
1 Institute of Mathematics, Am Neuen Palais 10, 14469 Potsdam, Germany
2 Deutsches GeoForschungsZentrum Potsdam, Telegrafenberg, 14473 Potsdam, Germany
a e-mail: email@example.com
Revised: 23 December 2010
Published online: 18 February 2011
Earthquake simulators become increasingly important with respect to seismic hazard assessment. It is, therefore, a crucial question whether the imposed simplifications, e.g. reducing fully dynamic to quasi-dynamic rupture propagation, may lead to unrealistic results. In the present study, we focus on the role of rupture velocity vr in an earthquake simulator governed by rate-and-state dependent friction as proposed by . In particular, we investigate the range of possible values of vr within the model. As an end-member scenario, we consider the existence of a steady-state solution of a one-dimensional rupture front propagating with vr on an idealized two-dimensional fault of infinite dimension discretized into uniform cells. We find that, in principle, values of vr between 0 and ∞ are possible depending on the values of slip speed δ0 and pre-stress τ0 ahead of the rupture front. In this view, values of δ0 close to the slip speed during an earthquake δEQ lead to small values of the time-to-failure and can thus generate ruptures with unrealistic high values of vr, if the model is close to the steady-state conditions. These results are useful to provide constraints for the parameter space of a reasonable earthquake simulator.
© EDP Sciences, Springer-Verlag, 2011