Postseismic relaxation and aftershocks

[1] Perfettini et al. (2005) suggested that the temporal dependence of surface displacements u(t) measured in the epicentral area following an earthquake is related to N(t), the cumulative number of aftershocks, by the equation u(t) = a + bt + cN(t) + d(1 − e^−αt), where a, b, c, d, and α are constants chosen to fit the data and t is the postearthquake time. N(t) appears in the expression for u(t) because both the aftershocks and a portion of u(t) are thought to be driven by the same source, postseismic fault creep at subseismogenic depths on the downdip extension of the coseismic rupture. We show that this equation with the actually observed N(t) fits the postseismic displacements recorded on several baselines following each of five earthquakes: 1999 M7.6 Chi-Chi (Taiwan), 1999 M7.1 Hector Mine (southern California), 2002 M7.9 Denali (central Alaska), 2003 M6.5 San Simeon (central California), and 2004 M6.0 Parkfield (central California) earthquakes. Although there are plausible physical interpretations for each of the terms in the expression for u(t), the large number of adjustable constants (a, b, c, d, and α) involved in fitting the rather simple postseismic displacements diminishes the significance of the fit. Because the observed N(t) is well fit by the modified Omori's law, fault creep at depth presumably exhibits the same temporal dependence. That dependence could be explained if the rheology of the fault downdip from the coseismic rupture is consistent with ordinary transient creep. Montesi (2004) demonstrated that power law creep across a shear zone at depth would also produce that temporal signal.