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.

翻译：合成地震动在确定性和概率性地震工程评估中均发挥着基础作用。本文表明，滤波和调制白噪声随机地震动模型家族忽略了一个关键参数——高通滤波器的角频率$f_c$。这导致模拟地震动在线性反应谱的长周期范围及线性反应谱相关性中出现显著畸变。为解决此问题，我们将$f_c$作为显式拟合参数纳入基于场地的随机模型。通过使每次记录地震动的长周期线性反应谱（即$T \geq 1$s时的$Sa(T)$）与合成地震动逐一匹配，优化$f_c$。研究表明，通过拟合$f_c$，随机模拟生成的地震动能够精确捕捉记录地震动的谱幅值、变异性（即$\log(Sa(T))$的方差）以及相关性结构（即不同周期$T_1$和$T_2$之间$\log(Sa(T))$的相关性）。为量化$f_c$的影响，通过线性回归进行了灵敏度分析。该回归将对数线性反应谱（$\log(Sa(T))$）与七个地震动参数（包括优化后的$f_c$）关联。结果表明，天然地震动中观测到的$f_c$方差及其与其他地震动参数的相关性，可解释长周期谱变异的26%。忽略$f_c$方差或$f_c$相关性通常会导致线性反应谱相关性的严重高估。