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 (<em>v_<sub>r</sub></em>) is considered. The comparison of different numerical schemes to compute <em>v<sub>r</sub></em> from the rupture time (<em>t_<sub>r</sub></em>) 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 <em>t_<sub>r</sub></em> can affect <em>v<sub>_r </sub></em>; numerical results indicate that if the fault slip velocity threshold (<em>v_<sub>l</sub></em>) used to define <em>t_<sub>r</sub></em> is too high (<em>v<sub>_l</sub></em> ≥ 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 <em>v_<sub>l</sub></em> ≤ 0.01 m/s the results appear to be stable and independent on the choice of <em>v_<sub>l </sub></em>. Finally, it is demonstrated that in the special case of the linear slip–weakening friction law the definitions of <em>t_<sub>r</sub></em> from the threshold criterion on the fault slip velocity and from the achievement of the maximum yield stress are practically equivalent.
Highlights
Spontaneous dynamic models provide the spatial distribution of the rupture times, which namely define the location of the rupture front during the dynamic propagation of the ruptures
To compare the results obtained by adopting the different numerical approaches described in Section 2.1, instead of comparing the spatial distribution of the resulting rupture speed over the whole fault plane, we select four profiles, which are at the hypocentral depth and aligned along the strike direction (x1), at the strike coordinate of the imposed hypocenter and aligned along the dept (x3) and along two mixed–mode directions, having azimuth angles of 45° and 30° with respect to x1
In this paper we have considered the problem of the determination of the rupture speed vr characterizing a fully dynamic, spontaneous earthquake
Summary
A well–constrained value of vr is important in spontaneous dynamic rupture models (as such considered by Bizzarri and Das [2012] and in the present study), and in the case of kinematic models of earthquakes In these models the analytical evolution of the fault slip velocity is a priori specified and this requires the exact determination of the rupture times (see for instance Ide and Takeo [1997], among many others). We will discuss the determination of the tr, which affects, by definition, the calculation of vr
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