Steady-state solutions of rupture propagation in an earthquake simulator governed by rate and state dependent friction

Abstract

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 vr 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 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 speedδ0 and pre-stress τ0 ahead of the rupture front. In this view, values ofδ0 close to the slip speed during an earthquakeδEQ 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. IntroductionIn recent decades, numerical models for simulating earthquake occurrence have been used to improve the understanding of the earthquake process and to estimate the resulting seismic hazard in the future. Different models cover a broad range between two end-member classes; first, detailed physical simulations of the dynamic rupture process [2,4] of a specific event and second, calculations of thousands of years of earthquake evolution in models with reduced complexity. The pros and cons are obvious: The first model class allows for realistic description of a particular event, but is related with high numerical effort and several poorly-constrained parameters. In contrast the latter class provides less realistic simulations; these models, however, allow for robust statistics, because a large number of events may be generated. Models of this type, generally labeled as "earthquake simulators" [3,8,11,13,17,18,20,21], become increasingly popular for seismic hazard calculations, since they overcome the problem of small data sets (earthquake catalogs), at least to some degree. The tightrope walk is now to find the most relevant mechanisms that govern the dynamics of the earthquake process and to keep the model as simple as possible, simultaneously. Less important processes may be neglected or plugged into a stochastic component [11,12,20] leading to a hybrid-model (deterministic/stochastic). We note that purely stochastic models are also widely applied; here, the empirical knowledge of a