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, fc$f_c$. 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 fc$f_c$ as an explicitly fitted parameter in a site-based stochastic model. We optimize fc$f_c$ by individually matching the long-period linear-response spectrum (i.e., Sa(T)$Sa(T)$ for T >= 1s$T \ge 1\,{\rm {s}}$) of synthetic GMs with that of each recorded GM. We show that by fitting fc$f_c$ the resulting stochastically simulated GMs can precisely capture the spectral amplitudes, variability (i.e., variances of log(Sa(T))$\log (Sa(T))$), and the correlation structure (i.e., correlation of log(Sa(T))$\log (Sa(T))$ between distinct periods T1$T_1$ and T2$T_2$) of recorded GMs. To quantify the impact of fc$f_c$, a sensitivity analysis is conducted through linear regression. This regression relates the logarithmic linear-response spectrum (log(Sa(T))$\log (Sa(T))$) to 7 GM parameters, including the optimized fc$f_c$. The results indicate that the variance of fc$f_c$ 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 fc$f_c$ variance or fc$f_c$ correlation typically results in an important overestimation of the linear-response spectral correlation.