We study the propagation of seismic ruptures along a fault surface using a
fourth-order finite difference program. When prestress is uniform, rupture
propagation is simple but presents essential differences with the circular
self-similar shear crack models of Kostrov. The best known is that rupture
can only start from a finite initial patch (or asperity). The other is that
the rupture front becomes elongated in the in-plant direction. Finally, if
the initial stress is sufficiently high, the rupture front in the in-plane
direction becomes super-shear and the rupture front develops a couple of "
ears" in the in-plane direction. We show that we can understand these featu
res in terms of single nondimensional parameter kappa that is roughly the r
atio of available strain energy to energy release rate. For low values of k
appa rupture does not occur because Griffith's criterion is not satisfied.
A bifurcation occurs when kappa is larger than a certain critical value, ka
ppa (c). For even larger values of kappa rupture jumps to super-shear speed
s. We then carefully study spontaneous rupture propagation along a long str
ike-slip fault and along a rectangular asperity. As for the simple uniform
fault, we observe three regimes: no rupture for subcritical values of kappa
, sub-shear speeds for a narrow range of supercritical values of kappa, and
super-shear speeds for kappa > 1.3 kappa (c). Thus, there seems to be a ce
rtain universality in the behavior of seismic ruptures.