The difference between horizontal-to-vertical spectra ratio and empirical transfer function as revealed by vertical arrays

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 f(0) (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 f(0) or larger, the P-wave amplification is obvious, which maybe explain the discrepancy between the HVSR and the transfer function.