Calculation of the local rupture speed of dynamically propagating earthquakes

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. In this paper the problem of the determination of the rupture speed (v__r) is considered. The comparison of different numerical schemes to compute v_r from the rupture time (t__r) shows 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. It is also shown how the determination of t__r can affect v_{_r} ; numerical results indicate that if the fault slip velocity threshold (v__l) used to define t__r is too high (v_{_l} ≥ 0.1 m/s) the details of the rupture are missed, for instance the rupture tip bifurcation occurring for 2–D supershear rupture. On the other hand, for v__l ≤ 0.01 m/s the results appear to be stable and independent on the choice of v__l . Finally, it is demonstrated that in the special case of the linear slip–weakening friction law the definitions of t__r from the threshold criterion on the fault slip velocity and from the achievement of the maximum yield stress are practically equivalent.