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Rupture Pulse Characterization: Self-Healing, Self-Similar, Expanding Solutions in a Continuum Model of Fault Dynamics

Universita'degli
Studi di Napoli "Federico II"
Dpto. di Scienze Fisiche
Dpto. di Geofisica e Vulcanólogia
(S. B. N.)
Department of Physics
University of California
Santa Barbara, California 93106
(J. M. C.)

We investigate the dynamics of self-healing rupture pulses on a stressed fault, embedded in a three-dimensional scalar medium. A state-dependent friction law that incorporates rate-weakening acts at the interface. When the system is sufficiently large that the solutions are not influenced by edge effects, 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 displays self-similarity, akin to the classic crack solution. We define a dimensionless parameter, H, which depends on the friction, the prestress, and properties of the medium. Numerical results reveal that H controls the transition 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 pulse properties to cases with well-defined heterogeneities in the prestress. In this case, the pulse width is sensitive to the local variations, expanding or contracting as it runs into low- or high-stress regions, respectively.

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