Apparent stress of moderate sized earthquakes in southern California

Using S-wave records at epicentral distances less than 60 km we determine the apparent stress for 62 Mw≥4.5 earthquakes in southern California since 2000. All earthquakes have reliable network moment tensor solutions. We compute seismic radiated energy with two methods: a time domain method by Kanamori et al. (2020) and a frequency domain method by Boatwright et al. (2002). The Kanamori approach (GR) is a modified Gutenberg-Richter in which attenuation and near surface effects are not considered. The Boatwright method uses path attenuation, near surface kappa0, and a station specific radiation pattern. With Boatwright we compute seismic energy 1) with an average radiation pattern (F0) and 2) with station specific radiation pattern (F1). The geometric means of apparent stress are 0.48, 0.40 and 0.57 MPa for GR, F0 and F1, respectively. Apparent stress is independent of seismic moment for these earthquakes. Converting apparent stress to Brune’s stress drop (Andrews, 1986), we find stress drops of 2.1, 1.7 and 2.5 MPa for GR, F0 and F1, respectively. From the perspective of seismic radiated energy, a Brune stress drop is nearly the same as that when using Madariaga (1976) and Kaneko and Shearer (2014) models (Ji, Archuleta and Wang, 2022). The standard deviation of stress drop (log10) is 0.35—almost the same for GR, F0 and F1. Cotton et al. (2013) show the standard deviation from stochastic vibration theory used in ground motion prediction equations is 0.15 for Mw>5.5 earthquakes. Seismic moment/corner frequency methods produce a standard deviation of 0.61, though the magnitude range is larger in some studies. Apparent stress (and consequently stress drop) shows a statistically significant depth dependence (~0.05 MPa/km).