## Two empirical double-corner frequency source spectra and their physical implications

Chen Ji, & Ralph J. ArchuletaPublished December 22, 2020, SCEC Contribution #10893

We introduce double-corner-frequency (DCF) source spectral models JA19 and JA19_2S, which in conjunction with a stochastic ground-motion model, can reproduce the mean peak ground acceleration (PGA) and mean peak ground velocity (PGV) of the NGA West-2 database for magnitudes 3.3 to 7.3. Their displacement amplitude spectrum remains constant for frequencies less than f_c1, decays as f^(-1) between f_c1 and f_c2, and decays as f^(-2) for frequencies greater than f_c2.The model JA19 is self-similar. Its two corner frequencies f_c1 and f_c2 scale with moment magnitude (M) as (1) 〖log(f〗_c1 (M))=1.754-0.5M and (2) 〖log(f〗_c2 (M))=3.250-0.5M. We find that relation (1) is consistent with the known self-similar scaling relations of the rupture duration (T_d), where T_d=1⁄((πf_c1)). Relation (2) may reflect the scaling relation of the average rise time (T_R), where T_R~0.8⁄((f_c2)). Stochastic simulations of ground motion using JA19 cannot reproduce the sharp change in magnitude dependence of PGA and PGV at M 5.3, suggesting a breakdown of self-similarity. The magnitude dependence of PGA and PGV and this change in slope is well explained by JA19_2S, which results from perturbing the f_c1 scaling relationship in JA19. For JA19_2S: log(f_c1 (M))=1.474-0.415 M for M≤5.3; log(f_c1 (M))=2.375-0.585 M for M>5.3. The scaling relation for f_c2 is unchanged. When f_c1≪f_c2, the scaled energy (ratio of radiated energy and seismic moment) scales with M_0 〖f_c1〗^2 f_c2. The scaled energy of JA19 is 2.2×10^(-5), independent of magnitude. Because JA19_2S is not self-similar, its scaled energy is 2.2-4.87×10^(-5), increasing 2.2 times when magnitude increases from 3.3 to 5.3 and subsequently decreasing 2.2 times as magnitude further increases from 5.3 to 7.3. Both agree with the global average (~3×10^(-5)) reported previously. Using our proposed empirical models, the standard deviation of average static stress drop from seismological studies can be significantly greater than the standard deviation of the stress parameter used to estimate PGA and PGV.

**Citation**

Ji, C., & Archuleta, R. J. (2020). Two empirical double-corner frequency source spectra and their physical implications. *Bulletin of the Seismological Society of America*, 111(2), 737-761. https://pubs.geoscienceworld.org/ssa/bssa/article/111/2/737/593421/Two-Empirical-Double-Corner-Frequency-Source

**Related Projects & Working Groups**

UCSB BROADBAND KINEMATIC RUPTURE SIMULATION WITH A DOUBLE CORNER SOURCE SPECTRUM, Seismology, Ground Motion Simulation Validation