S-Wave Inversion Explains Seismic Site Response Discrepancies

Researchers have demonstrated that a significant portion of the discrepancies between observed and theoretical seismic site responses in Japan can be explained by optimizing one-dimensional S-wave velocity structures. The study, published in Earth, Planets and Space, quantitatively evaluates the extent to which misfits between empirical and theoretical transfer functions can be resolved within a strictly one-dimensional framework. By applying advanced inversion techniques to 51 specific monitoring stations, the team showed that adjusting velocity models significantly improves the agreement between predicted and recorded ground motion amplification. This finding suggests that previous assumptions attributing these mismatches solely to complex two- or three-dimensional geological effects may be incomplete.

The research focuses on a specific category of seismic monitoring sites known as low-variability and poor-misfit, or LP, stations. These sites were previously identified in a classification system by Thompson et al. (2012) among the KiK-net network in Japan. LP sites are characterized by stable inter-event site responses, meaning the spectral ratios between surface and borehole recordings show relatively small variability across different earthquakes. However, despite this stability, conventional one-dimensional modeling based on available borehole velocity data fails to adequately reproduce the observed amplification characteristics. This persistent mismatch has long posed a challenge for seismic hazard assessment and engineering ground-motion simulations.

One-dimensional wave-propagation models are widely adopted in seismology due to their clear physical interpretation and computational efficiency. They have been the standard approach for site-specific response estimation for decades, with their performance repeatedly examined in blind prediction exercises. Nevertheless, non-negligible discrepancies between empirical transfer functions and theoretical transfer functions have been reported at various sites globally, including in Mexico City, Garner Valley, and Japan. These mismatches are often attributed to multidimensional wavefield effects associated with soil heterogeneity or basin geometry, which introduce additional amplification that one-dimensional models cannot capture. Alternatively, uncertainties in in situ S-wave velocity profiles and limitations in geologically derived structures may lead to the observed differences.

To address this, the study utilized horizontal site amplification factors, or HSAF, derived from the generalized spectral inversion technique as the primary target for inversion. HSAF is defined as the ratio of the Fourier amplitude spectrum on the earth’s surface to that on the seismological bedrock for the horizontal component. Theoretical HSAFs were calculated using a classical one-dimensional wave-propagation model for horizontally layered media. The observed HSAFs were extracted from strong-motion records obtained from the KiK-net, K-NET, and other networks, covering a period from January 1995 to June 2019. The data selection included earthquakes with specific magnitude, depth, and distance criteria to ensure a robust dataset for analysis.

The core of the methodology involved a Monte Carlo-initialized particle swarm optimization algorithm to search for optimal velocity models. This algorithm was designed to minimize the discrepancy between theoretical and observed HSAFs. A goodness-of-fit index was defined as the ratio of the Pearson product-moment correlation coefficient to the mean absolute error, ensuring that the inversion favored solutions with both high spectral shape similarity and low amplitude error. The algorithm treated S-wave velocity and layer thickness as individual variables, initializing the search with a Monte Carlo simulation based on initial reference models constructed from KiK-net borehole data and nationwide geological models.

For a representative example, the study examined station IBRH18 in Ibaraki Prefecture, which has a borehole sensor installed at a depth of 504 meters. The inversion results for this site clearly improved the HSAF fitting, reducing the mean absolute error and increasing the correlation coefficient. The initial model had substantially underestimated amplification below 15 Hz and showed an opposite spectral trend to the target above 8 Hz. The optimized model resolved these discrepancies, producing a smoother spectral representation that more closely matched the observed data. The velocity structure of the best-inverted model showed lower S-wave velocities in the near-surface layers and higher velocities at intermediate depths, indicating a redistribution of the subsurface structure rather than a uniform shift.

Statistical evaluation across all 51 LP sites confirmed that the improvements observed at IBRH18 were systematic. The median mean absolute error for HSAF decreased from 0.281 to 0.111, while the median Pearson’s R increased from 0.692 to 0.902. All 51 sites showed improved mean absolute error and goodness-of-fit index values, and 50 of the 51 sites showed improved correlation coefficients. These improvements were statistically significant, as indicated by Wilcoxon signed-rank tests yielding p-values below 0.001. The results demonstrate that a considerable part of the original discrepancy can be explained by optimizing the one-dimensional velocity structure within the prescribed search space.

Surface-to-borehole spectral ratios, or SBSR, were also evaluated to provide independent validation of the inverted velocity structures. Although SBSR was not directly used as an inversion constraint, it showed moderate but evident improvements. The median mean absolute error for SBSR decreased from 0.182 to 0.133, and the median Pearson’s R increased from 0.774 to 0.888. More than 75% of the stations showed improved SBSR metrics, supporting the physical consistency of the effective velocity structures obtained through the HSAF-based inversion. This simultaneous improvement in a related but non-targeted metric reinforces the validity of the optimized models.

The study highlights that the initial poor agreement at LP sites should not be interpreted solely as evidence of inherently unexplainable two- or three-dimensional site effects. Instead, uncertainties or limitations in the initial one-dimensional velocity profiles can account for a considerable part of the mismatch. The inverted profiles are best interpreted as effective structures that reproduce the target spectral responses under assumed one-dimensional conditions, rather than as unique representations of the true subsurface structure. This distinction is crucial for understanding the maximum attainable one-dimensional explainability of site responses.

However, some stations still show relatively large misfits even after optimization. These remaining discrepancies suggest that lateral heterogeneity, borehole-related effects, damping-parameter uncertainty, and other issues may contribute to the unexplained component of the site response. The effective one-dimensional structures do not fully explain all observed responses, and the residuals may be associated with complex geological features that cannot be captured by a strictly one-dimensional model. This finding provides a quantitative framework for distinguishing the one-dimensionally explainable component from the remaining unexplained component.

The implications of this research extend to seismic hazard assessment and engineering ground-motion simulations. By providing a method to quantify the one-dimensional explainability of site responses, the study offers a tool for interpreting differences between empirical and theoretical site responses. The effective velocity structures obtained can serve as reference models for subsequent one-dimensional and higher-dimensional site response analyses. This approach helps in refining the understanding of how geological conditions control earthquake ground motions, ultimately contributing to more accurate seismic hazard evaluations.

The study underscores the importance of velocity-structure inversion procedures in seismology. By optimizing S-wave velocity models, researchers can better reproduce observed site responses and identify the limits of one-dimensional modeling. The systematic improvements observed in this study provide a robust foundation for future research into the complexities of site response.

Subject of Research: Quantification of one-dimensional explainability of seismic site responses via S-wave velocity inversion

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

Article References: Wang, Z., Kawase, H., Lai, Y., Nakano, K., & Sun, J. (2026). Quantifying the 1D explainability of low-variability and poor-misfit site responses via S-wave velocity inversion for site amplification factors. Earth, Planets and Space, 78(1), Article 219. https://doi.org/10.1186/s40623-026-02553-1

Image Credits: AI Generated

DOI: 10.1186/s40623-026-02553-1

Keywords: seismic hazard assessment, site response analysis, S-wave velocity inversion, particle swarm optimization, KiK-net, ground motion simulation, empirical transfer functions, one-dimensional modeling, Quantifying, explainability, low-variability, poor-misfit