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Following an earthquake, ground motion time series are needed to carry out site-specific nonlinear response history analysis. However, the number of currently available recording instruments is sparse; thus, the ground motion time series at uninstrumented sites must be estimated. Tamhidi et al. developed a Gaussian process regression (GPR) model to generate ground motion time series given a set of recorded ground motions surrounding the target site. This GPR model interpolates the observed ground motions’ Fourier Transform coefficients to generate the target site’s Fourier spectrum and the corresponding time series. The robustness of the optimized hyperparameter of the model depends on the surrounding observation density. In this study, we carried out sensitivity analysis and tuned the hyperparameter of the GPR model for various observation densities. The 2019 M7.1 Ridgecrest and 2020 M4.5 South El Monte earthquake data sets recorded by the Community Seismic Network and California Integrated Seismic Network in Southern California are used to demonstrate the process. To provide a tool to quantify the uncertainty of the generated motions, a methodology to develop realizations of ground motion time series is also incorporated. The results illustrate that the uncertainty of the generated motions is lower at longer periods. It is shown that the observation density in the proximity of the target site plays a vital role in both error and uncertainty reduction of the generated time series. To demonstrate the concept, the effect of additional observations from combined recording networks is investigated. 

ABSTRACT Ground-motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free-field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground-motion recording instrumentation. In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics-based simulated ground motions of the 1906 Mw 7.9 San Francisco earthquake and Mw 7.0 Hayward fault scenario earthquake in northern California. The method’s performance is further evaluated using the 2019 Mw 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground-motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long-period content of the ground motions as well as directivity pulses.