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

Date Published: January 30, 2019

Publisher: Public Library of Science

Author(s): Mianshui Rong, Hongguang Li, Yan Yu, Hao Sun.


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.

Partial Text

The evaluation of site-effects due to local geology or topography has become a standard requirement in microzonation studies or site evaluation for important facilities [1]. Many empirical methods such as the standard spectral ratio method [2],the linear inversion method [3],the reference event method [4],and the HVSR method [5] are used to identify site characteristics.Among these methods, the HVSR is the spectral ratio technique using records of only one station. So it is an attractive low-cost method.

The increase in the number of borehole instruments provided a significant step forward in directly measuring the effects of surface geology and critical constraints on our methods for interpreting surface observations [15]. Borehole measurements provided direct in situ evidence for the research of the seismic response theory, method and applicability of this geotechnical model. In recent years, many downhole arrays have been built all over the world, and seismic records of two vertical arrays, GVDA and the IWTH25, were incorporated in our dataset.

HVSRs can be obtained through strong motions recorded by the sensors located at different depths for every seismic event. Fig 3 presents an example of observations at different depths for the three components of ground acceleration from IWTH25 site. When the seismic waves propagate from the bedrock through the soil column, the surface to bedrock amplification is significant. The HVSR curves are determined using spectral ratio of S-wave part of horizontal and vertical components. The TF curves are determined using spectral ratio of S-wave part of components at surface over incident upgoing S-wave at borehole site. A more than 10s window beginning 0.5–1 sec before the onset of the S-wave is taken from each records. A 5% Hanning taper was applied to all time windows. All the S-wave Fourier spectra are smoothed by using the logarithmic smoothing function proposed for this correction [25]. Once the spectral ratio for each station and each earthquake was obtained, the logarithmic average and the ±1 standard deviation or the 95% confidence limits of the mean were calculated.

In order to interpret the amplitude discrepancy between the HVSR and the TF for different arrays, the ratio of the average TF to the average HVSR is introduced, as shown in Fig 5. According to the definition of the HVSR and TF, the ratio can be written as (HS/HB)/(HS/VS) = VS/HB. Under the assumption that the HVSR in the firm substrate could be regarded as a constant, the shape of the ratio VS/HB is consistent with the vertical TF, which is denoted by the ratio VS/VB. The TFs of the GVDA and IWTH25 are also shown in Fig 5. As shown in Fig 5, we see the ratios of the average TFs to the average HVSRs are in good agreement with the average vertical TF, indicating that the spectral discrepancy between the TF and HVSR is mainly controlled by the site response of the vertical component.

According to analysis in previous section, based on observation, it is clear that we cannot always assume a borehole sensor located below the soil column in competent granite rock as a suitable reference site, as defined by Steidl et al. [18], with a flat amplitude response in the frequencies of engineering interest. The HVSRs revealed by instruments located on 260m (soft sandstone with Vs 1810m/s) of the IWTH25 site indicates that at this depth, the site may undergo amplification that cannot be ignored. It also appears that one of the principle assumptions that H/V is equal to unity on the bedrock does not necessarily apply in all circumstances.

The observations of ground motion in two vertical arrays presented and analyzed here have provided fundamental data for the comparison of HVSR and TF. The discrepancy between HVSRs and TFs has been explored and interpreted by comparing vertical site response to theoretical and synthetic borehole or outcrop response. In addition, the applicability and conditions of using HVSR as TF have been studied. From what we have discussed above, we can come to the conclusion that the HVSRs from observed earthquakes resemble the TFs for horizontal components, the HVSR method can be used to determine predominant frequency. But discrepancy still exists in absolute amplitudes of HVSRs and TFs. The consistency of them depends on the vertical seismic response of the site, which is also frequency-dependent. The vertical site response can be explained by the P-wave amplification.Commonly, in the low-frequency range within f0, the level of the vertical P-wave amplification is slight, while in high-frequency range near 2 f0 or larger, the P-wave amplification is obvious. Otherwise, the HVSRs and TFs are compared considering the site nonlinearity under severe earthquakes, the results show that in the frequency range in which the P-wave amplification can be ignored, the HVSRs and TFs are in good agreement in amplitude and spectrum.




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