Abstract

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.

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