Scaling properties of the Parkfield aftershock sequence

Aftershock sequences present a unique opportunity to study the physics of earthquakes. Important questions concern the fundamental origin of three widely applicable scaling laws: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Omori's law for aftershock decay rates, and (3) Bath's law for the difference between the magnitude of the largest aftershock and a mainshock. The high-resolution Parkfield seismic network provided the opportunity for detailed studies of the aftershock sequence following the 28 September 2004, M 6.0 Parkfield earthquake. In this article it is shown that aftershocks satisfy the Gutenberg-Richter scaling relation only for relatively large times after the mainshock. There is a systematic time delay for the establishment of this scaling law. The temporal evolution of the rates of occurrence of aftershocks is quantified using the generalized Omori's law. This scaling law contains two characteristic times c and c. The analysis suggests that the parameter c plays the role of a characteristic time for the establishment of GutenbergRichter scaling. This time increases systematically with a decreasing lower magnitude cutoff. The systematic time delay is attributed to a cascade of energy from long wavelengths to short wavelengths. The parameterr is a measure of the average time until the first aftershock occurs. We find that tau slightly varies with the lower magnitude cutoff of the sequence. We also note that the largest aftershock inferred from an extrapolation of Gutenberg-Richter scaling, M 5.0, is equal to the largest observed aftershock. This scaling associated with the universal applicability of Bath's law is attributed to a constant partitioning of energy between a mainshock and its associated aftershock sequence. We also give in this article the distribution of interoccurrence times between successive aftershocks. We show that this distribution is well approximated by a nonhomogeneous Poissons process driven by the modified Omori's law. The self-consistency between interoccurrence statistics and decay rates is taken as further evidence for the applicability of our studies.