Variability of Spectral Estimates of Stress Drop Reconciled by Radiated Energy

A review of a collection of theoretical source spectral models revealed: (1) Despite the well-known variation in predicting static stress drop Delta sigma(s) from the seismic moment and corner frequency, all models, especially the three conventional models, suggest that earthquakes radiate about half of the available strain energy into the surrounding medium. This similarity justifies a less model-dependent approach to estimate Delta sigma(s), though estimates for natural earthquakes rely on apparent seismic radiation efficiency ( = 2 sigma(a)/Delta sigma(s); sigma(a) is apparent stress of an earthquake). (2) When one attempts to use Delta sigma(s) and spectral models to make predictions, such as apparent stress sigma(a), there is a model-dependent discrepancy between the sigma(a) inferred from theoretical energy partitioning and the sigma(a) predicted using spherical mean corner frequency. Their ratio c(p) varies significantly from1.0 for the Brune (1970, 1971) model to 6.38 for the Madariaga (1976) model. If one uses spectral models to predict the ground motion, c(p) must be considered. (3) We infer that the constancy of the "stress parameter" ((Delta sigma) over tilde) found in engineering seismology (e.g., Boore, 1983; Atkinson and Beresnev, 1998) is similar to having constant apparent stress, sigma(a) (e.g., Ide and Beroza, 2001). The observation that (Delta sigma) over tilde is generally larger than the average static stress drop Delta sigma(s) for global M > 5.5 shallow crustal earthquakes in active tectonic regions implies that these earthquakes radiate, on average, more seismic energy than predicted from the conventional dynamic crack models.