# Bulletin of the Seismological Society of America

- Copyright © 2006 Bulletin of the Seismological Society of America

## Abstract

The horizontal-to-vertical (h/v) spectral ratio of seismic noise has become a widely used tool in microzonation over the last decade. However, attempts to provide standards for seismic-noise analysis have only recently been made. One point often debated is whether only the stationary part of the recorded signal must be used or also the transients. Until now, no systematic analysis has been carried out to clarify this point. In this study, we compare h/v spectral ratios obtained using stationary noise with those calculated without any *a priori* selection of the signal. Results show that transients have no (or very little) effect on the h/v ratio. Furthermore, we filter the seismograms using a wavelet-packet transform method, to perform h/v spectral-ratio calculations for only the transients. Results show a large variability in the h/v shape that we explain, by means of numerical simulations, as being due to source type and distance from the receiver relative to the thickness of the sedimentary cover.

## Introduction

In 1989 Nakamura revised the horizontal-to-vertical (h/v) spectral ratio of seismic-noise technique, first proposed by Nogoshi and Igarashi (1970, 1971). Since then, in the field of site-effect estimation, a large number of studies using this cheap, fast, and therefore attractive technique have been published (e.g., Field and Jacob, 1993; Lermo and Chavez-Garcia, 1994; Mucciarelli, 1998; Bard, 1999; Parolai *et al.,* 2001). Most of the researchers focused their attention on the comparison of noise h/v spectral ratio and earthquake site response and agreed that the h/v spectral ratio of seismic noise provides a fair estimate of the fundamental resonance frequency of a site. However, attempts to provide standards for the analysis of seismic noise have only recently been carried out (Bard, 1999; sesame, 2004; Picozzi *et al.,* 2005). In this regard, one point that is often debated within the seismological community is whether only the stationary part of the recorded signal should be used, or the transients (e.g., due to human activity, excluding of course very strong and clipped signals) could also be included in the analysis. Most authors exclude nonstationary noise (e.g., Horike *et al.,* 2001) while others (Mucciarelli *et al.,* 2003) showed that the h/v ratio of triggered (nonstationary) noise might even be more similar, especially in amplitude, to the h/v spectral ratio of earthquakes. Apart from the practical aspects—being forced to use only the stationary part of the signal would make the method less attractive, since in urban areas very long periods of measurement or even night measurements may be required—the investigation of the effect of the transient signal on the h/v calculation may provide new insights into the wave-field composition. Since transient noise is expected to be generated mainly by close sources and generally affects the noise spectra at frequencies higher than 1–2 Hz (McNamara *et al.,* 2004), it could have a different effect at sites where the resonance frequency is above or below 1 Hz due to the different composition of the wave field (the ratio between body and surface waves) and the different energy required to penetrate (until the bottom) different sedimentary-cover thicknesses.

In this study, using noise recordings collected at seven stations installed in the Cologne–Bonn area (Germany), we investigate the effect of transient noise on the shape of the h/v spectral ratio, considering stations that show the main peak in the h/v spectral ratio at frequencies lower and higher than 1 Hz. First, we calculate the h/v spectral ratio without making any *a priori* selection of the noise windows. Second, we perform the h/v calculation selecting only stationary- noise windows. Finally, we filter the seismograms using a wavelet-packet transform method (Galiana-Merino *et al.,* 2003) to remove only the stationary part of the signal. h/v spectral ratios are then calculated only for transients. Synthetic simulations are performed to interpret the results.

## h/v Spectra Ratio

In this study, we use noise recordings collected continuously for nearly three months by stations deployed in Cologne (Parolai *et al.,* 2004) and in Bonn for nearly five months (Baliva *et al.,* 2004). The stations were equipped with Mark-L-4C-3D sensors (flat response to velocity between 1 and 40 Hz), with the sampling rate fixed to 100 samples per second. Baliva *et al.* (2004) showed that there exists good agreement between the fundamental resonance frequencies estimated by means of h/v spectral ratio at the Bonn sites (stations b3–b14 in this study) and those obtained by earthquake analysis.

In order to make the test similar to a standard acquisition in the field, noise recordings of 30 min are selected. In one case (station K33 from Cologne) two nonconsecutive windows of 15 min are used to include several transients. Each noise recording is divided into 60-sec windows. Time series are corrected for trends in the data, and tapered with a 5% cosine function at both ends. The fast Fourier transform (fft) is calculated for each component and the spectra smoothed using a Konno and Ohmachi (1998) logarithmic window, with the coefficient *b,* which determines the bandwidth, fixed to 25. The instrumental response correction is performed by considering the poles and zeros of every calibrated station. The horizontal component is obtained as the root-mean-square (rms) average of the north–south and the east–west components, and the h/v spectral ratios are then calculated. Finally, the logarithmic average of the h/v spectral ratio is calculated for each site.

Figure 1 shows examples of the analyzed signals where stationary noise and transients are analyzed together. Transients affect the spectra (Fig. 2) mainly at frequencies higher than 1 Hz.

## h/v Spectral Ratio of Stationary Noise

From each noise recording, stationary-noise windows are selected by adopting a simple algorithm that, similarly to the short-time average/long-time average (sta/lta) algorithm, calculates the rms amplitude over a short moving window (0.5 sec) and compares it to the rms amplitude of the whole noise recording. When, for 60 sec, the ratio is below a certain threshold for all three of the components, the window is selected and used in the analysis. The 60-sec windows are then analyzed in the same way as described above and the h/v spectral ratio calculated. Figure 1 shows stationary windows of noise selected for the h/v spectral- ratio calculation. Although simple, the procedure adopted is able to select windows that are not affected by strong transients. Figure 2 (central panels) shows that the spectra are indeed not affected by amplitude variations due to transients.

## h/v Spectral Ratio of Transients

Galiana-Merino *et al.* (2003) proposed an approach based on wavelet-packet transforms to filter seismograms affected by high-amplitude non-Gaussian noise. The technique was shown to be particularly suitable for also removing noise in the frequency band of the band-limited nonstationary signal. Since we are aiming to infer the effect of transients on h/v spectral ratio, a method that allows the removal of the stationary part of the signal in the frequency band of interest for h/v spectral ratios appears to be appropriate for generating filtered seismograms with only transients. In order to verify the suitability of the method for our analysis, we generated a synthetic signal composed of three sinusoids with frequencies of 2, 5, and 7 Hz and different durations (10, 5, and 7 sec, respectively). The synthetic signal was added to 30 min of noise recorded at one of the stations installed by Parolai *et al.* (2001) in the Cologne area. The amplitude of the stationary noise was scaled so that its maximum value (in the 30-min window) was 0.5 and 1 times the maximum amplitude of the synthetic signal. Figure 3 shows a 60-sec window around the synthetic signal and the synthetic signal added to recorded noise. The 30-min noise recordings have been bandpass-filtered in the frequency band 0.1 to 15.0 Hz. The filtered seismograms (Fig. 3) show the capability of this method to isolate the transient. However, a tendency for the method to also reduce the amplitude of the signal for an increasing level of stationary noise was observed. In order to verify whether this characteristic could limit the use of the method when h/v ratios are calculated using components of the ground motion affected by a different-amplitude stationary noise, we calculated the spectral ratio between the two filtered records. The lower-level amplitude of stationary noise was considered to occur with the horizontal component. The results can be easily extended to the case where the lower level of stationary noise is on the vertical component. Figure 3 shows that the h/v spectral ratio (which should be equal to 1 at the frequencies of 2, 5, and 7 Hz since the used synthetic signals were identical) is negligibly affected by the filtering technique. Artifacts only occur at frequencies where no signal was present in the synthetic transient (e.g., 3 Hz).

Once the suitability of the method has been verified the observed noise recordings are filtered in the same way in the frequency band 0.1–15.0 Hz, within which the main h/v spectral-ratio peak for each station lies. The filtered seismograms are then analyzed using an algorithm similar to that used to select stationary-noise windows. Windows with transients are selected, where the rms amplitude over short windows were greater than a defined threshold. Figure 1 shows examples of selected windows. It is worth noting that stationary-noise windows do not overlap with the windows containing transients. The selected 60-sec windows are analyzed in the same way as described previously and the h/v spectral ratio calculated.

## Results

The h/v spectral ratios calculated using only stationary noise do not significantly differ from those obtained without performing any data selection (Fig. 4), independent of the site resonance frequency and of the frequency content of the transient. On the contrary, the h/v spectral ratios obtained using only transients are generally not consistent with the others, and moreover, show a large variability in the shape, as shown by the large 95% confidence interval in Figure 4. Additional tests that we performed (not included here) showed that the h/v ratios obtained without performing any data selection or using stationary noise do not show such large variability, even when calculated using a smaller number of windows (comparable to those used for h/v spectral ratio of transients). In general, at the same frequency, large amplifications as well as large reductions can occur for h/v spectral ratios obtained using only transients. Smaller variability is always observed for frequencies higher than 1–2 Hz, where the signal energy content is higher (Fig. 2). The large variation at lower frequencies can therefore be explained by the numerical instability of the spectral ratio when calculated over small numbers.

It is worth noting that in general, for the stations showing a main peak at frequencies much lower than 1 Hz (K32, K33), the transient h/v spectral ratio show deamplification (spectral ratio smaller than 1) at frequencies higher than 1– 2 Hz (K33) and 5 Hz (K32). An analysis of the spectra showed that they rapidly decay below those values.

Stations showing a main peak around 1 Hz (b11, b03, b14) displayed a less steep decay in the amplitude spectra for frequencies lower than 2 Hz. The transient h/v ratio indicates mainly deamplification for frequencies higher than 2 Hz at station b03. Station b11 shows deamplification between 1 and 5 Hz and amplifications for frequencies higher than 6 Hz. At station b14, the horizontal spectra are greater than the vertical ones close to the main peak of the h/v spectral ratio (Fig. 2). However, at higher frequencies, spectra of the horizontal and of the vertical components have similar amplitudes, yielding a spectral ratio ≅1.

When the main peak in the h/v spectral ratio is higher than 2 Hz (K06 and b07) we observe different features. At K06, where the transient signal has a small spectral amplitude (spectra are not shown here) and the sedimentary cover is presumably thicker than at b07, considering the lower frequency of the main peak, the h/v spectral ratio shows generally deamplification. The trend in the low-frequency part of the h/v spectral ratios at this station is probably due to the effect of wind on the sensor (Mucciarelli *et al.,* 2005). When the transient has higher spectral amplitudes (much larger than the stationary noise) and the sedimentary cover is thinner (b07), the transient h/v simulates the stationary h/v at frequencies higher than 2 Hz.

## Synthetic Seismograms

In order to explain the observed features, we calculate synthetic seismograms for transients using one source at the time (with only vertical or only horizontal, or both vertical and horizontal forces acting together) located close to the surface at one fixed position. Synthetics are generated for three different propagation models (for three different sedimentary-cover thickness, models 1–3) using a semianalytical method that consists of an improved Thompson– Haskell propagator matrix method that overcomes numerical instabilities by an orthonormalization technique (Wang, 1999). The shallow structures of the models are described in Tables 1, 2, and 3. Synthetic seismograms are calculated for different source-to-receiver distances, and the corresponding h/v calculated. The source spectra are dominated by frequencies higher than 1 Hz, as with the transient ones. When the sedimentary cover is thin (model 1), already at a short distance from the source, a peak in the h/v spectral ratio, at a frequency very close to the resonance frequency of the site, is found (Fig. 5). This happens both when the spectra of all the sources (horizontal and vertical) are considered together (Fig. 5, top left) and separately (Fig. 5). In particular, while the vertical source only generates an amplification peak at the fundamental frequency of the site, horizontal sources yield an overall amplification in the analyzed frequency band with a clear peak at the resonance frequency of the site. The comparison between the results obtained considering the two horizontal components or only the radial one shows the importance of the relative contribution of *SH* multireflected (and Love) and *SV* (and Rayleigh) waves.

For a thicker sedimentary cover (model 2), the results obtained by considering all kinds of sources show a general amplification over the whole analyzed frequency band (Fig. 6, top left). A peak is seen (even if less pronounced) also at distances smaller than 100 m. However, comparing the results obtained for the individual (horizontal or vertical) sources highlights how the vertical source determines the h/v spectral ratio with a peak corresponding to the resonance frequency of the site only at distances larger than 100– 150 m. At shorter distances, h/v spectral ratios mainly indicate deamplification. When horizontal sources are considered (radial and transverse), the h/v always show a large amplification in the whole frequency band, especially (as expected) if the contribution of the transverse component is taken into account. The peak corresponding to the resonance frequency of the site shown in Figure 6 (top left) at distances shorter than 100 m is clearly due to the contribution of horizontal sources.

For a thick sedimentary cover (model 3) the results obtained combining the contribution of all types of sources again show a general amplification over the whole analyzed frequency band (Fig. 7, top left). A peak corresponding to the fundamental resonance frequency of the site is only seen at distances larger than 200 m. No fundamental resonance- frequency peak is found in the h/v spectral ratio when only a vertical source is considered (Fig. 7, top right). The peak that is shown at around 1 Hz may be due to the impedance contrast existing at 80 m depth. When only horizontal sources are considered, the h/v spectral ratio shows a general amplification over the whole analyzed frequency band. A comparison of the two bottom panels in Figure 7 indicates that, while the radial component determines mainly the shape of the h/v spectral ratios (with their peaks), the transverse component yields a general amplification, especially at frequencies higher than 1 Hz.

These results clearly point out the great variability of the h/v spectral-ratio shape that can be expected using only transients. This is consistent with our experimental evidence. The general tendency of deamplification that we observed in our transient h/v spectral ratio may be caused by transients generated by close, mainly vertical, sources. The analysis of synthetics, in fact, points out that increasing the thickness of the sedimentary cover also increase the distances at which the h/v spectral ratio shows a peak corresponding to the fundamental resonance frequency of the site. We attribute this behavior to the fact that over a thicker sedimentary cover, a longer path is required to generate surface (in this case Rayleigh) waves. On the other hand, our synthetic results could provide an explanation for the results of Mucciarelli (1998), who showed that when using active sources, the peak of the fundamental resonance frequency of the site appeared more clearly in the h/v spectral ratio. In fact, this is consistent with considering a vertical source and a thin sedimentary cover, or allowing for some contribution from horizontal sources (the impact is never perfectly vertical and the source is finite and not a point) over thicker sedimentary covers.

## Conclusions

The analysis we performed showed the following:

Transients are dominated by energy at frequencies higher than 1–2 Hz.

There is no (or not always) coherent information in the transient h/v.

Transient h/v depends upon the source type and on the source-to-receiver distance.

Using an active source could lead to h/v spectral ratios showing a clear peak consistent with the fundamental resonance frequency of a site.

Including transients in the h/v spectral-ratio calculation does not worsen the results, even when only 30 min of recordings are available. This is the most important practical application of our study.

Since we are aware that we did not include in our analysis all possible cases, we suggest that similar analyses should be performed on other data sets collected in different areas.

## Acknowledgments

We thank S. M. Richwalski, R. Wang, and D. Bindi for continuous stimulating discussions and comments on the manuscript. K. Fleming kindly improved our English. The comments of the associate editor Diane I. Doser and an anonymous reviewer improved the manuscript. Figures were generated using Generic Mapping Tools (Wessel and Smith, 1991). The Geophysical Instrument Pool Potsdam (GFZ) provided instruments.

- Manuscript received 21 April 2005.