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Variability of Spectral Estimates of Stress Drop Reconciled by Radiated Energy

Chen Ji, Ralph J. Archuleta, & Yongfei Wang

Published June 17, 2022, SCEC Contribution #11870

A review of a collection of theoretical source spectral models revealed: i) Despite the well-known variation in predicting static stress drop 〖Δσ〗_s from the seismic moment and corner frequency, all models, especially 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 〖Δσ〗_s, though estimates for natural earthquakes rely on apparent seismic radiation efficiency (=2 σ_a⁄〖Δσ〗_s , σ_a is apparent stress of an earthquake). ii) When one attempts to use 〖Δσ〗_s and spectral models to make predictions, such as apparent stress σ_a, there is a model-dependent discrepancy between the σ_a inferred from theoretical energy partitioning and the σ_a predicted using spherical mean corner frequency. Their ratio, c_p, 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, c_p must be considered. iii) We infer that the constancy of the “stress parameter” ((∆σ) ̃) found in engineering seismology (e.g., Boore, 1983; Atkinson and Beresnev, 1998) is similar to having constant apparent stress, σ_a (e.g., Ide and Beroza, 2001). The observation that (∆σ) ̃ is generally larger than the average static stress drop Δσ_s for global M>5.5 shallow crustal earthquakes (SCEs) in active tectonic regions implies that these earthquakes radiate, on average, more seismic energy than predicted from conventional dynamic crack models.

Ji, C., Archuleta, R. J., & Wang, Y. (2022). Variability of Spectral Estimates of Stress Drop Reconciled by Radiated Energy. Bulletin of the Seismological Society of America,. doi: 10.1785/0120210321.