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 Mw 5.6 earthquake. Both of these applications demonstrate a good performance of our SM in a broad frequency range.

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