Variability of Spectral Estimates of Stress Drop Reconciled by Radiated Energy

Abstract

ABSTRACT A review of a collection of theoretical source spectral models revealed: (1) Despite the well-known variation in predicting static stress drop Δσs 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 Δσs, though estimates for natural earthquakes rely on apparent seismic radiation efficiency (=2σa/Δσs; σa is apparent stress of an earthquake). (2) When one attempts to use Δσs and spectral models to make predictions, such as apparent stress σa, there is a model-dependent discrepancy between the σa inferred from theoretical energy partitioning and the σa predicted using spherical mean corner frequency. Their ratio cp varies significantly from 1.0 for the Brune (1970, 1971) model to 6.38 for the Madariaga (1976) model. If one uses spectral models to predict the ground motion, cp must be considered. (3) We infer that the constancy of the “stress parameter” (Δσ˜) found in engineering seismology (e.g., Boore, 1983; Atkinson and Beresnev, 1998) is similar to having constant apparent stress, σa (e.g., Ide and Beroza, 2001). The observation that Δσ˜ is generally larger than the average static stress drop Δσs 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.