Stochastic Model to Characterize High-Frequency Ground Motion at Depth Validated by KiK-Net Vertical Array Data

The design of important structures for earthquake resistance requires an assessment of the local seismic hazard. One of its essential components is a site response that evaluates the amplification and attenuation of ground motion on a local scale. The shaking on the ground surface (in which it is generally measured) differs from the one at a depth; therefore, there is a need to characterize the ground motion at depth for important underground structures and buildings with deep foundations. In this study, we introduce a method to characterize the high-frequency (> 1 Hz) ground motion at depth. The method makes use of a novel stochastic model (SM) that relates the ground motion at depth and on the surface in the Fourier domain. The SM is physics-based, its spectral amplification resembles an empirical 1D site response, and it allows reliable full-waveform ground-motion predictions. The method is validated through the comparison with empirical surface-to-borehole amplification curves observed in 144 selected KiK-net vertical arrays in Japan. Using a frequency range of 0.1-50 Hz, we identified 36 and 83 sites with a good and partially good mutual fit of theoretical and empirical amplification curves, respectively. Finally, we demonstrate the performance of the method in two diverse applications. First, we design a Bayesian inversion of the empirical surface-to-borehole amplification to retrieve the S-wave velocity model and an effective value of t* (the path-integrated effect of the quality factor). This inversion is applied to all selected KiK-net sites. Second, we perform a full-waveform prediction of the ground motion at depth from surface recordings of the 2018 northern Osaka M-w 5.6 earthquake. Both of these applications demonstrate a good performance of our SM in a broad frequency range.