Double corner frequency spectrum and its implications for the physics of the earthquake source

Chen Ji, & Ralph J. Archuleta

In Preparation March 1, 2020, SCEC Contribution #10937

We introduce a self-similar double-corner-frequency (DCF) source spectrum model (JA19), which in conjunction with a stochastic ground-motion model, can reasonably 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. 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 greater 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. We find that the relation is consistent with the known self-similar scaling relations of the rupture duration (τ_d), if relating τ_d with f_c1 as τ_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)). The sharp change in magnitude dependence of PGA and PGV at magnitude 5.3 cannot be reproduced by the stochastic simulation with JA19, suggesting a breakdown of self-similarity. The magnitude dependence of PGA and PGV is much better explained by model JA19_2S, which results from perturbing the f_c1 scaling relationship in JA19 model for two magnitude ranges: M≤5.3, log⁡(f_c1 (M))=2.3745-0.585 M; M>5.3, log⁡(f_c1 (M))=1.4735-0.415 M. These two relations are equivalent to the source duration τ_d increasing with seismic moment as 〖M_0〗^(1/(3+ε)), with ε~0.614 for 3.3<M<5.3 and ε~-0.436 for 5.3<M<7.3. The JA19_2S model predicts that the scaled energy increases by a factor of 2.2 from 2.2×10^(-5) for M 3.3 events to 4.8×10^(-5) for M 5.3 events, and subsequently decreases by a factor of 2.2 to 2.2×10^(-5) for M 7.3 events. Using the relationship τ_d=1/(πf_c1) we find that f_c1 predicts the duration (±19%) of large magnitude earthquakes as found in the global CMT catalog (Ekström et al., 2005). The stress drop inferred from f_c1 is similar to that found for the global average (Allmann and Shearer, 2009). Model JA19_2S prediction of the high-frequency level of the acceleration Fourier amplitude spectrum is very similar to that derived by Atkinson and Silva (2000) using an additive DCF spectrum. If one were to convert the DCF spectrum to a single corner frequency model, the inferred stress drop would be approximately twice the global average. Thus, the stress parameter that characterizes the high frequency level of the acceleration spectrum is not the same as a stress drop inferred from the duration of an earthquake.

Ji, C., & Archuleta, R. J. (2020, 03). Double corner frequency spectrum and its implications for the physics of the earthquake source. Oral Presentation at IASPEI Effects of Surface Geology.