The horizontal‐to‐vertical spectral ratio (HVSR) method is an efficient tool for determining the resonant frequency of engineering sites. However, there appears to be no consensus on whether HVSR amplitude indicates the absolute amplification at the location of the measurements. Here, we discuss the basic assumption of the HVSR method with respect to its applicability to site amplification via earthquake ground motions. We have also introduced the empirical transfer function (ETF), defined as the ratio of the records at the surface to the records at the borehole site, as a comparison to HVSR, in order to describe the site amplification of vertical borehole arrays. The amplitude discrepancy between the HVSR and the ETF is explored on the basis of the S‐wave recordings from three vertical borehole strong‐motion arrays that have been conducted at three different locations: the Central United States Seismic Observatory in the central United States, the Garner Valley Downhole Array in southern California, and the KiK‐net Ichinoseki‐Nishi Vertical Array in West Ichinoseki, Japan. The results show that the amplitude discrepancy is primarily due to two factors, the vertical site response and the HVSR at the bedrock. The measurements from these strong‐motion arrays demonstrate that the horizontal and vertical components at the firm substrate are not at all equal; however, their ratio is nearly constant and related to the bedrock velocity characteristics. Vertical site amplification occurring at these three sites can be interpreted via the borehole response of the vertical incident P‐wave excitation. As an efficient and economical alternative to the traditional transfer function method, we can extract the S‐wave transfer function from the surface HVSR, under the condition that the P‐wave borehole response and the bedrock HVSR can be accurately evaluated.

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 $TFT$⁠. The mean $TFT$ 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 $HVS$ for estimating the empirical site transfer function. The mean S‐wave $HVS$ curves are similar to the mean $TFT$ spectral ratios for frequencies below approximately the fifth natural frequency at each site; for higher frequencies, vertical‐component amplification from incident SV waves reduces $HVS$ relative to $TFT$⁠. Therefore, $HVS$ curves at these sites reflect the SH‐wave transfer functions for low frequencies. We also observed that $HVS$ curves from ambient noise recordings do not estimate the SH‐wave transfer function at these deep borehole sites for frequencies higher than the fundamental.

This study used 306 accelerograms recorded at 22 strong‐motion stations to investigate the source parameters, quality factor (⁠$Q$⁠), and site effects of S‐wave Fourier acceleration amplitude spectrum (FAS) of the 2019 $MS$ 6.0 Changning earthquake sequence in China with surface‐wave magnitudes (⁠$MS$⁠) of 4.1–6.0. The generalized inversion technique (GIT) was adopted. The inverted stress drop of the mainshock was 1.15 MPa, and those of the aftershocks varied from 0.11 to 1.04 MPa with an average value of 0.43 MPa. The $MS$ of these earthquakes were larger than $Mw$ with an average magnitude difference of 0.22. The inverted $Q$ values increase rapidly with frequencies at 0.5–4.0 Hz from 62 to 2920 and become less dependent at 4.0–25.0 Hz. Such a phenomenon indicates that the propagation path attenuation mechanism transited to intrinsic at high frequencies. A bilinear $Q(f)$ model for which $Q(f)=237.6f1.27$ (⁠$Q<1280$⁠) and $Q=1280$ at higher frequencies was obtained. The high‐frequency attenuation model of the study area was $κ=0.0420+0.0001262R$⁠. The inverted site responses of the 22 stations were compared with those calculated using the horizontal‐to‐vertical spectral ratio (HVSR) method. In general, the amplification curves of most stations obtained with the GIT were similar to those of HVSR, and the amplification levels were relatively higher. Contrarily, obvious discrepancies were observed between the results estimated from the two methods at several stations. Such effects were attributed to the limitation that the majority of the stations were distributed along the boundary of the basin and mountainous areas, and the inverted $Q$ values were representative of the specific area rather than the pure basin and mountainous areas. Finally, a nonlinear soil site effect was observed at 51GXT in earthquakes with peak ground acceleration greater than $300cm/s2$⁠. The nonlinearity obviously aggravated the site amplification at 1.0–5.0 Hz.

The horizontal-to-vertical spectral ratio (HVSR) and empirical transfer function analyses were performed on the S-wave recordings from two vertical borehole strong motion arrays: the Garner Valley Downhole Array in southern California, and the KiK-net Ichinoseki-Nishi Vertical Array in West Ichinoseki, Japan. The results show that the discrepancy between the HVSR and the transfer function is mainly caused by the significant site response of the vertical component, thus, vertical incident P-waves are proposed to play an important role in the vertical amplification. The P-wave amplification is frequency-dependent. In the low-frequency range within f₀ (the fundamental frequency of the site), the effect of the vertical P-wave amplification is slight, this is why HVSR and transfer function match in this frequency range. In the high-frequency range near 2 f₀ or larger, the P-wave amplification is obvious, which maybe explain the discrepancy between the HVSR and the transfer function.