Unveiling nonlinear site response through time-frequency analysis of earthquake records

SUMMARY It is well known that nonlinear site effects may arise in soils during strong ground motion. This translates into a decrease in propagation velocity, shift of resonance frequencies, increased material damping and lessened ground motion amplification. In this study, we introduce a time-frequency resonance analysis (TFRA) technique to unveil nonlinear site response by computing broad-band resonance frequencies derived from waveforms recorded across a wide range of ground motions at 567 stations of the Kiban Kyoshin network (KiK-net) in Japan. The found resonance frequencies follow closely those computed from surface to borehole spectral ratios. Furthermore, we quantify the coseismic frequency changes, which shift towards lower values as the earthquake ground shaking increases. At some stations, the extracted resonance frequencies attain up to a 60 per cent decrease, representing a shear modulus reduction ($\mu /\mu _{\rm max}$) of 0.16 (84 per cent decrease) assuming a homogeneous layer over a half-space model. To ensure independence from specific seismic events, we establish peak ground acceleration (${\rm PGA}$) thresholds corresponding to 5 per cent and 10 per cent frequency shifts to identify regions where sites are prone to soil nonlinearity. We find that for a 5 per cent frequency shift, some sites require a relatively small ${\rm PGA}$ ($\sim$ 30 $\rm cm\,s^{-2}$) to trigger this effect, with most places needing a ${\rm PGA}\, \sim$ 50 $\rm cm\,s^{-2}$. Furthermore, the computed $\mu /\mu _{\rm max}$ values are categorized by the time-averaged shear-wave velocity to a depth of 30 and 5 m ($V_{S30}$ and $V_{S05}$), which are proxies commonly used in earthquake engineering studies for characterizing site effects. We do not observe a clear correlation between the time-averaged shear-wave velocity to a certain depth and the computed shear modulus reduction (nonlinear site effect). Furthermore, no evident correlation was found between the nonlinear site effect and the earthquake magnitude, the distance from the earthquake to the site. This study suggests that nonlinear soil behaviour is site-specific. This complicates the use of proxies or equations to take into account these effects, making it difficult to include soil nonlinearity in regional seismic hazard studies.