The Importance of Corner Frequency in Site-Based Stochastic Ground Motion Models

TL;DR

This paper emphasizes the critical role of the corner frequency in site-based stochastic ground motion models and demonstrates how explicitly fitting this parameter improves the accuracy of synthetic ground motions in matching recorded data.

Contribution

It introduces a method to incorporate and optimize the corner frequency as a key parameter in stochastic models, enhancing their ability to replicate recorded seismic spectra and correlations.

Findings

Fitting the corner frequency improves spectral amplitude accuracy.

Optimized models better capture spectral variability and correlation.

Variance in corner frequency explains 26% of long-period spectral variability.

Abstract

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., $Sa(T)$ for $T \geq 1$s) 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 $\log(Sa(T))$), and the correlation structure (i.e., correlation of $\log(Sa(T))$ 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 ($\log(Sa(T))$) to seven 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.