## Empirical Self-similar Double-corner Frequency Spectrum as a Model for the Earthquake Source

Ralph J. Archuleta, & Chen JiPublished August 15, 2019, SCEC Contribution #9857, 2019 SCEC Annual Meeting Poster #002

We introduce a self-similar double-corner-frequency (DCF) source spectrum. Its displacement spectrum amplitude remains constant for frequency less than f_c1, decays as f^(-1) between f_c1 and f_c2, and f^(-2) for frequency larger than f_c2. The two corner frequencies f_c1 and f_c2 scale with magnitude (M) as (1) log(f_c1(M))=1.754-0.5M and (2) log(f_c2(M)) =3.250-0.5M. The apparent single corner frequency (f_c)^A of the classic ω^(-2) model, defined as (f_c)^A=√(f_c1 f_c2 ), satisfies (3) log(f_c)^A (M)=2.502-0.5M. These three scaling relations are not independent. We find that the relation (1) is consistent with the known self-similar scaling relations of the rupture duration (τ_d), if relating the τ_d with f_c1 as τ_d=1⁄((πf_c1)). The relation (3) is tightly related with the constant “stress parameter”, previously noticed in strong motion community (Boore, 1983, Baltay and Hanks, 2014). Our DCF model reveals that to simultaneously satisfy long and short period seismic observations using such a point source approximation requires (f_c)^A~k⁄τ_d ,k=1.78, rather than 0.6 to 1.0 used in previous analysis. We show that in conjunction with a stochastic ground-motion model, this spectrum can reasonably reproduce the peak ground acceleration (PGA) and peak ground velocity (PGV) of the NGA West-2 data set for magnitudes 3.3 to 7.7. Its predicted radiated energy and apparent stress agree with global estimates of these parameters. Such an empirical model explains why the average stress drop from seismological studies is different from the stress parameter used to estimate PGA and PGV. The physical explanation of the high corner frequency f_c2, which is a consequence of relations (1) and (3), is not clear yet. We report that (a) the inferred characteristic time is much smaller than the rupture duration of asperities, predicted using the empirical scaling relation of asperity size (Somerville et al., 1999); (b) f_c2 may be related with the average rise time <(T_r )> on the fault surface, inferred from the slip models (Somerville et al., 1999), as <(T_r )>=0.8⁄f_c2 . This is close to the relation of the Brune time function. (c) f_c2 might be associated with the average peak time of the fault slip on asperities. This source spectrum will be incorporated with UCSB broadband simulation algorithm.

**Key Words**

Earthquake Source Spectrum

**Citation**

Archuleta, R. J., & Ji, C. (2019, 08). Empirical Self-similar Double-corner Frequency Spectrum as a Model for the Earthquake Source. Poster Presentation at 2019 SCEC Annual Meeting.

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