Ground motion time series recorded at stations separated by up to about 50 km show a frequency-dependent spatial coherency structure, and the corresponding ground motion intensity measures are found to be correlated. As omitting this correlation can result in underestimation of seismic losses in risk analysis, it is critical to quantify the spatial correlation structure for ground motion Fourier spectra estimated at different sites during a single event within a region. Toward this goal, we have developed an empirical frequency-dependent spatial correlation model for the within-event residuals of effective Fourier amplitude spectra from the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation (NGA) West2 database. The correlation model shows slower decrease of the spatial correlation with distance at lower frequencies compared with higher frequencies, in agreement with the underlying ground motion data, and no significant dependence on the magnitude of the earthquakes is observed. We use this empirical model to incorporate frequency-dependent spatial correlation into a hybrid deterministic-stochastic broadband ground motion generation module, which successfully generates synthetic time series for seven western US earthquakes with frequency-dependent spatial correlation that closely mimics that of the empirical model. Furthermore, the method also significantly improves the correlation for spectral accelerations, cumulative absolute velocities, and Arias intensities, compared with that derived from the original broadband module.

在相距约50 km的站点上记录的地震动时间序列显示出频率相关的空间相干结构，并且发现相应的地震动强度度量是相关的。由于忽略这种相关性会导致风险分析中地震损失的估计不足，因此量化区域内单个事件期间在不同地点估计的地面运动傅里叶光谱的空间相关性结构至关重要。为了实现这一目标，我们为太平洋地震工程研究中心（PEER）下一代衰减（NGA）West2数据库开发了有效傅里叶振幅谱的事件内残差的经验依赖于频率的空间相关模型。相关模型显示，与较高频率相比，较低频率处的空间相关性随距离的降低较慢，这与基础的地面运动数据一致，并且未观察到对地震震级的显着依赖性。我们使用此经验模型将频率相关的空间相关性纳入混合的确定性-随机宽带地面运动生成模块，该模块成功生成了美国西部七场地震的合成时间序列，其频率相关的空间相关性与经验模型非常相似。此外，与从原始宽带模块获得的频谱加速度，累积绝对速度和Arias强度相比，该方法还显着改善了频谱加速度的相关性。