A data-driven ground-motion model for Fourier amplitude spectra of shallow crustal earthquakes using the NGA-West3 database

Abstract

Effective Amplitude Spectra (EAS) provide a physically interpretable representation of ground motion that reflects source, path, and site effects and can be used within random vibration theory to estimate response spectra. In this study, we develop a data-driven ground-motion model (GMM) for EAS using the NGA-West3 database, focusing on shallow crustal earthquakes in the western United States. The model is formulated as a multi-output artificial neural network (ANN) that simultaneously predicts EAS across a broad frequency range, allowing cross-frequency correlations to be learned directly from the data. Six explanatory variables are used as inputs: moment magnitude, rupture distance, fault dip, depth to the top of rupture, time-averaged shear-wave velocity in the upper 30 m, and basin depth to the 2.5 km/s shear-wave velocity horizon. The model predicts the natural logarithm of EAS at 22 discrete frequencies between 0.05 and 33 Hz. Frequency-dependent data availability is handled using a masked loss function that allows partially observed spectra to contribute to training without imposing listwise deletion. To avoid information leakage from correlated recordings of the same earthquake, model development and evaluation are performed using event-level partitioning. Hyperparameters are selected using 10-fold event-grouped cross-validation, and predictive performance is subsequently assessed using an independent event-level holdout dataset excluded from model development. Following model selection and independent evaluation, the final ANN is retrained using the complete retained NGA-West3 dataset. The resulting model produces smooth, physically plausible spectra across magnitude, distance, and frequency, with spectral trends qualitatively consistent with expected magnitude scaling, distance attenuation, ω-square-type source behavior, magnitude-dependent corner-frequency effects, and high-frequency decay. Aleatory variability was quantified using a sequential mixed-effects residual decomposition into between-event, site-to-site, and event-site-corrected components. The estimated standard deviations exhibit clear frequency dependence and are consistent with trends reported in existing empirical EAS models. Overall, the proposed ANN-based EAS GMM provides a data-driven framework for representing source, path, site, and cross-frequency behavior without prescribing a fixed analytical functional form.