Development of a site and motion proxy-based site amplification model for shallow bedrock profiles using machine learning

Accurate prediction of site amplification is crucial for seismic hazard assessment, particularly at shallow bedrock sites where limited data can constrain modeling efforts. Traditional regression-based models often fail to capture complex nonlinear interactions inherent in seismic ground response. This study aims to develop proxy-based linear and nonlinear site amplification models that provide reliable predictions using machine learning (ML) techniques, enabling practical applications in regional ground motion modeling. The outputs of a series of one-dimensional site response analyses were used for training. Three ML algorithms were used: random forest (RF), extreme gradient boosting (XGB), and deep neural network (DNN). The models incorporated four site proxies and two motion proxies to predict site amplification, and their performance was evaluated against both a conventional regression-based model and a rigorous ML model utilizing full shear-wave velocity profiles and input motion spectra. When identical proxies were used, the differences between the regression and ML-based models were not pronounced. However, when the ML model was trained simultaneously with the site and motion proxies for both linear and nonlinear components, the prediction performance was significantly enhanced. This revealed that the traditional two-track approach of the site-proxy-dependent linear component and motion-proxy-conditioned nonlinear component is ineffective. A pairing scheme for site and motion proxies is recommended to achieve the most accurate predictions. Among the three ML methods, the RF algorithm exhibited the weakest performance. The XGB and DNN algorithms’ prediction accuracies were superior to the RF algorithm. The XGB and DNN outperformed each other when predicting the linear and nonlinear components, respectively. The proposed ML models achieved coefficient of determination (R 2 ) values up to 0.97 with root mean square error (RMSE) as low as 0.04 for linear components, and R 2 up to 0.92 with RMSE as low as 0.06 for nonlinear components, demonstrating significant improvements over conventional regression-based models. Compared with a rigorous ML model, the proxy-based models exhibited agreeable predictions with far less information, illustrating the benefit of adopting the ML algorithms for improved adaptability and predictive capability. The constraint imposed on the site type, considering only profiles with a bedrock depth of less than 30 m, may have resulted in the strong performance of the proxy-based model.