Rupture pulse characterization: Self-healing, self-similar, expanding solutions in a continuum model of fault dynamics

We investigate the dynamics of self-healing rupture pulses on a stressed fa ult, embedded in a three-dimensional scalar medium. A state-dependent frict ion law that incorporates rate-weakening acts at the interface. When the sy stem is sufficiently large that the solutions are not influenced by edge ef fects, we observe three distinct regimes numerically: (1) expanding cracks, (2) expanding pulses, and (3) arresting pulses. We demonstrate that when a persistent pulse exists (regime 2), it expands as it propagates and displa ys self-similarity, akin to the classic crack solution. We define a dimensi onless parameter, H, which depends on the friction, the prestress, and prop erties of the medium. Numerical results reveal that H controls the transiti on between regimes where both crack and pulse solutions are allowed and the regime where only arresting pulses are possible. The boundary that divides expanding crack and pulse solutions depends on local properties associated with the initiation of rupture. Finally, we extend the investigation of pu lse propel-ties to cases with well-defined heterogeneities in the prestress . In this case, the pulse width is sensitive to the local variations, expan ding or contracting as it runs into low- or high-stress regions, respective ly.