The decay of the aftershock density with distance plays an important role in the discussion of the dominant underlying cause of earthquake triggering. Here, we provide evidence that its form is more complicated than typically assumed and that in particular a transition in the power law decay occurs at length scales comparable to the thickness of the crust. This is supported by an analysis of a high-resolution catalogue for Southern California and surrogate catalogues generated by the Epidemic-Type Aftershock Sequence (ETAS) model, which take into account short-term aftershock incompleteness, anisotropic triggering and variations in the observational magnitude threshold. Our findings indicate specifically that the asymptotic decay in the aftershock density with distance is characterized by an exponent larger than 2.0, which is much bigger than the observed exponent of approximately 1.35 observed for shorter distances. This has also important consequences for time-dependent seismic hazard assessment based on the ETAS model.