Quantifying the 1D explainability of low-variability and poor-misfit site responses via S-wave velocity inversion for site amplification factors

One-dimensional site response analysis is widely used in seismic hazard assessment, but its explanatory capability is often considered to be limited when we have sites where existing velocity structures cannot reproduce the observed amplification characteristics. This study quantitatively evaluates the extent to which such misfits between theory and observation can be explained within a one-dimensional framework by optimizing the S-wave velocity structures at the selected sites with low variability but poor misfit in Japan. We focus on 51 stations that were previously classified as having stable inter-event site responses but poor agreement between empirical and theoretical transfer functions. Horizontal site amplification factors derived from the generalized spectral inversion technique are used as the targets, and a Monte Carlo-initialized particle swarm optimization algorithm is applied to search for optimal velocity models that can improve the consistency between observed and theoretical site amplification characteristics. The optimized models are then evaluated in terms of the fitting improvements on both horizontal site amplification factors and surface-to-borehole spectral ratios. The optimized velocity structures improve the reproduction on horizontal site amplification factors at all stations and the surface-to-borehole spectral ratios at more than 75% of the stations, with statistically significant overall improvements. These improvements indicate that a considerable part of the original discrepancy can be explained by optimizing the one-dimensional velocity structure. However, some stations still show relatively large misfits even after optimization, suggesting that lateral heterogeneity, borehole-related effects, damping-parameter uncertainty, and other issues may contribute to the remaining misfit. These findings provide a quantitative framework for distinguishing the one-dimensionally explainable component of site-response discrepancy from the remaining unexplained component, and highlight the importance of the velocity-structure inversion procedure in interpreting the differences between empirical and theoretical site responses.