Scaling of earthquake rupture growth in the Parkfield area: Self-similar growth and suppression by the finite seismogenic layer

We propose a new framework on the scaling of earthquake rupture growth time history, and we scale the moment rate and the cumulative moment functions of earthquakes over a wide magnitude range (M-w 1.7-6.0) in Parkfield, California. The moment rate and the cumulative moment functions of the small and medium earthquakes (M-w 1.7-4.6) are derived by slip inversion analyses with the empirical Green's function technique. The moment rate functions of the investigated earthquakes, except the M-w 6.0 event, are similar to each other, increasing rapidly in the first half (growth stage) and decelerating in the latter half (decline stage). In the growth stage, the cumulative moment functions are approximated by M-o (t) [Nm] = 2 x 10(17) (t [s])(3) independent of the final size of the earthquakes. The proportionality of the cumulative moment to the cube of time implies self-similarity during earthquake rupture growth. In the decline stage, the cumulative moment function veers off the common rupture curve. The M-w 6.0 event also grows along the same rupture curve until 1 s, after which the cumulative moment function is proportional to time from the onset itself. This is because the finite seismogenic layer limits the vertical extent of dynamic rupture. Our method and results contribute to our understanding of earthquake source physics, especially on earthquake rupture growth processes, which may help to improve earthquake early warning techniques.