Recordings of weak‐motion S waves at two deep vertical seismic arrays in the northern Mississippi embayment (i.e., vertical seismic array Paducah [VSAP] and the Central United States Seismic Observatory [CUSSO]) were used to estimate empirical site responses using ratios of surface‐to‐bedrock transverse‐component amplitude spectra . The mean curves were also compared with theoretical transfer functions derived from Thomson–Haskell propagator matrices. The results were comparable, indicating that mean spectral ratios, calculated from few (10) events at local and regional distances, represent empirical linear S‐wave transfer functions for weak‐motion SH waves at these sites. At both sites, the largest amplifications implied by the theoretical responses and the observed S‐wave spectral ratios occur at frequencies higher than the sites’ fundamental frequencies.
These spectral ratios were used to evaluate the suitability of surface S‐wave horizontal‐to‐vertical spectral ratios for estimating the empirical site transfer function. The mean S‐wave curves are similar to the mean spectral ratios for frequencies below approximately the fifth natural frequency at each site; for higher frequencies, vertical‐component amplification from incident SV waves reduces relative to . Therefore, curves at these sites reflect the SH‐wave transfer functions for low frequencies. We also observed that curves from ambient noise recordings do not estimate the SH‐wave transfer function at these deep borehole sites for frequencies higher than the fundamental.