Calculation of aftershock accumulation from observed postseismic deformation: M6 2004 Parkfield, California, earthquake

The postseismic stress accumulation τ(t) over the interval 0.004 to 880 days following the 2004 Parkfield earthquake (M6) can be inferred from GPS measurements of postseismic deformation. The stress relaxation τ(t) − τ′lt, where τ′l is the interseismic loading rate and t is the time after the earthquake, plotted as a function of the number of M > 1.5 aftershocks Na(t) that have occurred by time t is bilinear with the slope of the fit to the first half of the aftershock sequence less than the slope of the fit to the second half. Thus, the aftershock seismicity rate is not proportional to the stress relaxation rate τ′(t) − τ′l over the entire sequence, but rather exhibits two distinct proportionalities. The observed postearthquake accumulation of M > 1.5 earthquakes in the aftershock zone as a function of time can be explained with the rate‐and‐state friction relation proposed by Dieterich (1994) between the cumulative number of earthquakes and τ(t).