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Authors: Bizzarri, A 
Title: Calculation of the local rupture speed of dynamically propagating earthquakes
Issue Date: Dec-2013
Series/Report no.: 5/56(2013)
DOI: 10.4401/ag-6279
Keywords: Rupture speed
Subject Classification04. Solid Earth::04.06. Seismology::04.06.03. Earthquake source and dynamics 
Abstract: The velocity at which a propagating earthquake advances on the fault surface is of pivotal importance in the contest of the source dynamics and in the modeling of the ground motions generation. The rupture speed (vr ) is one of the results provided by spontaneous dynamic models of ruptures, in that it is a part of the solution and it is not imposed a priori, like in non spontaneous models or in kinematic models. Since vr is numerically retrieved from the spatial distribution of the rupture times (tr ), a well– constrained value of vr in a given fault node is important. In this paper we focus on the numerical determination of vr. By comparing different numerical schemes to compute vr from tr we show that, in general, central finite differences schemes are more accurate than forward or backward schemes, regardless the order of accuracy. Overall, the most efficient and accurate algorithm is the five–points stencil method at the second–order of accuracy. These conclusions hold for homogeneous and heterogeneous configurations and for different constitutive models, such as the slip– weakening law and the rate– and state–friction governing equations. It is also shown how the determination of tr can affect vr; numerical results indicate that if the fault slip velocity threshold (vl ) used to define tr is too high (vl ≥ 0.1 m/s) the details of the rupture are missed, for instance the jump of the rupture front eventually occurring for 2–D supershear ruptures. On the other hand, for vl ≤ 0.01 m/s the results appear to be stable and independent on the choice of vl. Finally, it is confirmed that in the special case of the linear slip–weakening friction law the computation of vr from the threshold criterion on the fault slip velocity and from the achievement of the maximum yield stress are equivalent.
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