A Spectral Estimate of Average Slip in Earthquakes

Abstract:

We demonstrate that the high-frequency acceleration spectral level a_o of an ω-square source spectrum is directly proportional to the average slip of the earthquake ∆u divided by the travel time to the station r/β

a_o = 1.37 F^s (β/r) ∆u

and multiplied by the radiation pattern F^s. This simple relation is robust but depends implicitly on the assumed relation between the corner frequency and source radius, which we take from the Brune (1970, JGR) model.

We use this relation to estimate average slip by fitting spectral ratios with smaller earthquakes as empirical Green’s functions. For a pair of M_w = 1.8 and 1.2 earthquakes in Parkfield, we fit the spectral ratios published by Nadeau et al. (1994, BSSA) to obtain 0.39 and 0.10 cm. For the M_w= 3.9 earthquake that occurred on Oct 29, 2012, at the Pinnacles, we fit spectral ratios formed with respect to an M_d = 2.4 aftershock to obtain 4.4 cm. Using the Sato and Hirasawa (1973, JPE) model instead of the Brune model increases the estimates of average slip by 75%.

These estimates of average slip are factors of 5-40 (or 3-23) times less than the average slips of 3.89 cm and 23.3 cm estimated by Nadeau and Johnson (1998, BSSA) from the slip rates, average seismic moments and recurrence intervals for the two sequences to which they associate these earthquakes. The most reasonable explanation for this discrepancy is that the stress release and rupture processes of these earthquakes is strongly heterogeneous. However, the fits to the spectral ratios do not indicate that the spectral shapes are distorted in the first two octaves above the corner frequency.