Observations demonstrate that faults are fractal surfaces with deviations from planarity at all scales. We study dynamic rupture propagation on self-similar faults having root mean square (rms) height fluctuations of order 10-3 to 10-2 times the profile length. Our 2D plane strain models feature strongly rate-weakening fault friction and off-fault Drucker–Prager viscoplasticity. The latter bounds otherwise unreasonably large stress concentrations in the vicinity of bends. Our choice of a cohesionless yield function prevents tensile stress states and thus fault opening. A consequence of strongly rate-weakening friction is the existence of a critical background stress level above which self-sustaining rupture propagation, in the form of self-healing slip pulses, first becomes possible. Around this level, at which natural faults are expected to operate, ruptures become extremely sensitive to fault roughness and exhibit substantial fluctuations in rupture velocity. Except for shallow inclinations of the maximum compressive stress to the fault (less than about 20°), the fluctuations are anticorrelated with the local fault slope. These accelerations and decelerations of the rupture, together with naturally emerging slip heterogeneity, excite waves of all wavelengths and result in ground acceleration spectra that are flat at high frequency, consistent with observed strong motion records.

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