Corner Frequency vs Finite-Source Stress Drop Estimates

Abstract:

To estimate stress drop common practice is to use a variety of signal processing methods to measure corner frequencies and then use the corner frequency and a mechanical model (e.g. Brune, 1970; Sato and Hirasawa, 1973; Madariaga, 1976; Kaneko and Shearer, 2014) to estimate the stress drop. These methods can suffer from sampling bias in accounting for the significant effects of directivity on corner frequency. Coda methods (Mayeda and Walter, 1996) avoid the sampling bias issue by making use of the averaging properties of seismic coda. Nevertheless all such corner frequency methods have a factor of 5.57 uncertainty in estimated stress drops due to the differences in the mechanical models. Finite-source models account for directivity effects through the modeling of waveforms and spectra to develop the kinematic slip models of rupture. The derived slip models are then mapped to stress change using Ripperger and Mai (2004) therefore avoiding the choice of a simplified mechanical model to map corner frequency to stress drop. In this study we simulate broadband time histories for the Wald et al. (1996) strong motion kinematic slip model and perform spectral fitting of the Brune model to estimate corner frequencies and stress drop. We examine bias introduced by subsampling the focal sphere, and investigate the relationship of the various corner-frequency/mechanical model estimates of stress drop to the stress change computed for the input slip model. Initial results indicate there is a very strong bias in corner frequency estimates with limited data sets. Considering the full azimuthal data set we find that the Brune stress drop recovers the average determined from the finite-source slip model. The other mechanical model estimates have values that are larger and more consistent with the peak stress drop.