Average Static Stress Drop of Crustal Earthquakes Inferred From Source Spectra

Chen Ji, & Ralph J. Archuleta

Submitted August 16, 2021, SCEC Contribution #11586, 2021 SCEC Annual Meeting Poster #237

Most estimates of an earthquake’s average static stress drop ∆σ_s, particularly for small and even moderate magnitude earthquakes, have been made using observed source spectra following the seminal work of Brune (1970). However, depending on which theoretical model is used, ∆σ_s for the same source spectrum can differ by a factor of 5.56. A review of a collection of theoretical source spectral models revealed: i) in spite of this large, model-dependent discrepancy in predicting stress drop, all models suggest that earthquakes radiate about half of the available strain energy to the surrounding medium. For crack models with circular and elliptical fault geometry 0.5 is the theoretical uppermost apparent seismic radiation efficiency: η_R^A=2σ_a/Δσ_s; σ_a and Δσ_s are apparent stress and average static stress drop, respectively; ii) there is a significant discrepancy between the apparent stress inferred from theoretical energy partitioning and the apparent stress predicted using spherical mean corner frequency based on a point source approximation. Their ratio c_p varies from 1.0 for the Brune (1970, 1971) model to 6.38 for the Madariaga (1976) model. This must be considered if one uses these spectral models to predict the ground motion; iii) the constancy of the “stress parameter” ((∆σ) ̃) found in engineering seismology is similar to having constant apparent stress σ_a (e.g., Ide and Beroza, 2001). The observation that (∆σ) ̃ is generally larger than average static stress drop Δσ_s implies that M>5 shallow crustal earthquakes radiate more seismic energy, on average, than what is predicted from conventional dynamic crack models. These earthquakes are consistent with the growing pulse and steady-state slip-pulse models of Wang and Day (2017) in terms of both η_R^A and average rupture velocity. The observation (∆σ) ̃>Δσ_s also implies that either the average source spectra of an earthquake cannot be well modeled using a classic single-corner, omega-square model or the inferred average stress drop overestimates the true Δσ_s. For a single-corner spectrum, the Brune model provides the closest approximation to Δσ_s among the spectral models we reviewed. A modified Snoke’s (Snoke, 1987) method that is consistent with steady-state slip-pulse model is developed and used to estimate Δσ_s of 2019 Ridgecrest earthquake sequence.

Key Words
static stress drop, apparent stress, source spectra

Ji, C., & Archuleta, R. J. (2021, 08). Average Static Stress Drop of Crustal Earthquakes Inferred From Source Spectra. Poster Presentation at 2021 SCEC Annual Meeting.

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