Does aftershock duration scale with mainshock size?

It has been claimed that aftershock duration scales with the mainshock recurrence interval [Dieterich, 1994]. This implies a scaling between aftershock duration and mainshock magnitude. To see if such a scaling exist, we compare properties of aftershock sequences associated with mainshocks whose size span several magnitude units. Earthquake properties were examined along two northern California fault segments, one is the Calaveras fault, another is a northern segment of the San Andreas fault. The first study area contains the rupture area of the M6.2, 1984 Morgan Hill, and the latter is adjacent the southern end of the M7.1, 1989 Loma Prieta rupture. Both the Morgan Hill and the Loma Prieta aftershock activities lasted 1-3 × 10⁸ seconds. On the other hand, aftershock activities of small-to-moderate mainshocks lasted about 1-2 × 10⁶ seconds. Nevertheless, there is no evidence for scaling between mainshock size and aftershock duration for moderate-to-small mainshocks. It thus seems that large earthquakes, because they break the entire seismogenic depth and interact with deeper parts of the crust, trigger a relaxation mechanism that is inactive during aftershock activity due to moderate-to-small quakes, and whose characteristic relaxation time is much longer than that of the brittle crust. Current seismicity models do not provide explanation for these observations.