Peak ground motions and site response at Anza and Imperial Valley, California

Power spectra of shear-waves for eighteen earthquakes from the Anza-Imperial Valley region were inverted for source, mid-path Q, site attenuation and site response. The motivation was whether differences in site attenuation (parameterized as t*, r/cQ, where r is distance along ray path near the site, c is shear velocity and Q is the quality factor that parameterizes attenuation) and site response could be correlated with residuals in peak values of velocity or acceleration after removing the affect of distance-dependent attenuation. We decomposed spectra of S-waves from horizontal components of 18 earthquakes from 2010 to 2018 into a common source for each event with ω⁻² spectral fall-off at high frequencies and then projected the residuals onto path and site terms following the methodology of Boatwright et al. (Bull Seismol Soc Am 81:1754–1782, 1991). The site terms were constrained to have an amplification at a particular frequency governed by V_S30 at two of the sites which had downhole shear-wave logs. The 18 events, 3 < M < 4, had moments between approximately 10²⁰ and 10²² dyne-cm, and stress drops between 1 and 100 bars. Average mid-crust attenuation had a Q of 844 reflecting the average path through the crystalline rock of the San Jacinto Mountains. t* for each station corresponded to the geologic environment such that stations on hard rock had low t* (e.g. stations KNW, PFO and RDM) a station in the San Jacinto fault zone (station SND) had a moderate t* of 0.035 s and stations in the Imperial Valley usually had higher t*s. Generally t* correlated with average amplification suggesting that sites characterized by low surface velocities and higher attenuation also have more amplification in the 1–6 Hz band. Residuals of peak values were determined by subtracting the prediction of Boore and Atkinson (2008). There is a correlation between average amplification and peak velocity, but not peak acceleration. Interestingly, there is less scatter at high values of amplification although there is also less data. Scatter in values of peak velocity and peak acceleration are higher at shorter compared to longer durations. When using a frequency-dependent form for Q, variances are higher, sometimes much higher; the dataset does not support frequency-dependent Q, which is not similar to results from the Imperial Valley and northeastern North America.