What stress drop do seismic waveforms reveal when the stress distribution on a finite fault is complex?

Abstract:

What stress drop are we estimating when we fit a Brune model (1970, 1971) to the moment-rate spectrum of a complex earthquake source? To answer this question we used the slip-rate distributions from more than 30 dynamic rupture simulations (Schmedes et al., 2010) as kinematic sources. We propagate the intermediate- and far-field S-wave to stations between 10-100 km from the fault. For each source, the initial stress field on the fault is a stochastic realization with 2-point statistics consistent with a power law. The resulting models have complex final slip distributions due to the heterogeneity of the initial stress field. This also leads to complex waveforms, even though we use a whole-space as the medium. Preliminary results suggest that the corner frequency in the near-field is dominated by the closest asperity to the point of observation; in the far-field, the largest slip asperity dominates the waveforms. This implies that the stress drop we compute with a Brune model might reflect the stress drop on a particular asperity on the fault, as opposed to an average stress drop on the fault. This will lead to a larger stress drop estimate, because the seismic moment would correspond to the entire earthquake, while the corner frequency would relate to a smaller area (Δσ=M₀(f_c/(0.42β)³)). In the dynamic rupture simulations we see stress relaxation on the fault as the medium adjusts to the final state. This can lead to a static stress drop larger than the dynamic stress drop. We compare estimates of dynamic stress drops determined from corner frequencies and static stress drops from the near field stations, to better understand the relationship between these two parameters. We also provide a relationship between corner frequency and an average stress drop computed from the dynamic rupture simulations as proposed by Shao et al. (2012). Finally we show inverted stress drops from the 2011 Virginia earthquake (Shao et al., 2011) and conclude that the large observed stress drop is related to two asperities, which are the main contributors to the observed corner frequency. This unique dynamic dataset also allows us to investigate the discrepancies between the stress drop estimates based on near-fault and teleseismic data. We will calculate body wave seismograms at teleseismic distances and estimate their Brune stress drops.