The importance of corner frequency in site-based stochastic ground motion models

Synthetic ground motions (GMs) play a fundamental role in both deterministic and probabilistic seismic engineering assessments. This paper shows that the family of filtered and modulated white noise stochastic GM models overlooks a key parameter—the high-pass filter's corner frequency, $f_c$. In the simulated motions, this causes significant distortions in the long-period range of the linear-response spectra and in the linear-response spectral correlations. To address this, we incorporate $f_c$ as an explicitly fitted parameter in a site-based stochastic model. We optimize $f_c$ by individually matching the long-period linear-response spectrum (i.e., $Sa\left(T\right)$ for $T\ge 1s$) of synthetic GMs with that of each recorded GM. We show that by fitting $f_c$ the resulting stochastically simulated GMs can precisely capture the spectral amplitudes, variability (i.e., variances of $\log \left(Sa\right(T\left)\right)$), and the correlation structure (i.e., correlation of $\log \left(Sa\right(T\left)\right)$ between distinct periods $T_1$ and $T_2$) of recorded GMs. To quantify the impact of $f_c$, a sensitivity analysis is conducted through linear regression. This regression relates the logarithmic linear-response spectrum ($\log \left(Sa\right(T\left)\right)$) to 7 GM parameters, including the optimized $f_c$. The results indicate that the variance of $f_c$ observed in natural GMs, along with its correlation with the other GM parameters, accounts for 26% of the spectral variability in long periods. Neglecting either the $f_c$ variance or $f_c$ correlation typically results in an important overestimation of the linear-response spectral correlation.