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In order to investigate the effects of fault zones on earthquake
ruptures that are geometrically complex, we focus on the dynamic
formation process of secondary branch faults (BFs) distributed
along principle slip planes based on multi- scale model
introducing hierarchical fault geometry inside fault zones.
Employing a model analyzed by the boundary integral equation
method, we observe sequential bifurcations of the tip of
main-fault (MF) as it is dynamically propagated. Farther, if the
propagation distance of the MF is smaller than a critical length,
BFs are arrested soon after the initiation and their lengths
become proportional to the MF length (self-similar distribution);
we refer the BFs as mesoscopic BFs. The rupture velocity of the MF
becomes constant here, due to energy dissipation on the mesoscopic
BFs being proportional to the length of MF. However, once the MF
is propagated beyond the critical distance, therefore a BF exceeds
a critical length, a BF starts to grow spontaneously into a scale
comparable to the MF length; we refer this BF as a macroscopic BF.
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