  We analyze 21 aftershock sequences of California to test for evidence of
space-time diffusion. Aftershock diffusion may result from stress diffusion and
is also predicted by any mechanism of stress weakening. Here, we test an
alternative mechanism to explain aftershock diffusion, based on multiple
cascades of triggering. In order to characterize aftershock diffusion, we
develop two methods, one based on a suitable time and space windowing, the
other using a wavelet transform adapted to the removal of background
seismicity. Both methods confirm that diffusion of seismic activity is very
weak, much weaker than reported in previous studies. A possible mechanism
explaining the weakness of observed diffusion is the effect of geometry,
including the localization of aftershocks on a fractal fault network and the
impact of extended rupture lengths which control the typical distances of
interaction between earthquakes.
