Eur. Phys. J. Special Topics 191, 105-115 (2010)
https://doi.org/10.1140/epjst/e2010-01344-6

Regular article

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: zoeller@uni-potsdam.de

Received: 22 November 2010
Revised: 23 December 2010
Published online: 18 February 2011

Abstract

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 v_r in an earthquake simulator governed by rate-and-state dependent friction as proposed by [8]. In particular, we investigate the range of possible values of v_r 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 v_r on an idealized two-dimensional fault of infinite dimension discretized into uniform cells. We find that, in principle, values of v_r 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 δ_EQ lead to small values of the time-to-failure and can thus generate ruptures with unrealistic high values of v_r, 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.