Bulletin of the Seismological Society of America; February 2006; v. 96; no. 1;
p. 228-236; DOI: 10.1785/0120050084
© 2006 Seismological Society of America
Effect of Transient Seismic Noise on Estimates of H/V Spectral Ratios
S. Parolai1 and
J. J. Galiana-Merino2
1 GeoForschungsZentrum
Potsdam
Telegrafenberg
14473 Potsdam,
Germany
parolai{at}gfz-potsdam.de
(S.P.)
2 Departamento de
Física
Ingeniería de Sistemas y Teoria de la
Señal
Escuela Politécnica Superior
Universidad de
Alicante
Ap. Correos 99
03080, Alicante,
Spain
(J.J.G.-M.)
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Abstract
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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.
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Introduction
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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.
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H/V Spectra Ratio
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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.
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Figure 1. Left: time series (black); stationary-noise windows (gray). Right: transient
windows. The 1-min length is indicated in black.
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Figure 2. Left: spectra of the time series (no window selection). Center: spectra of
the stationary-noise windows. Right: spectra of the transient-noise windows
(after removing the stationary part of the signal). Vertical is in black,
north–south is in dark gray, and east–west is in light gray.
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H/V Spectral Ratio of Stationary Noise
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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.
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H/V Spectral Ratio of Transients
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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).
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Figure 3. Left: 60 sec of the synthetic signal (top), 60 sec of the synthetic signal
+ noise (maximum amplitude equal to 0.5 the maximum amplitude of the
signal, middle), 60 sec of synthetic signal + noise (maximum amplitude
equal to 1.0 the maximum amplitude of the signal). Center: the filtered signals.
Right: spectral ratio between the spectra of the signal + 0.5 noise and the
spectra of the signal + 1.0 noise.
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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.
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Results
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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.
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Figure 4. Left: average H/V spectral ratio and 95% confidence interval of
the whole time series (black) and of stationary-noise windows (gray). Right:
average H/V spectral ratio and 95% confidence interval of transient
noise. Vertical bars indicate the position of the main peak in the
H/V spectral ratio obtained using stationary-noise windows. Please
note that the right and left panels have different Y scales.
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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.
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Synthetic Seismograms
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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.
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Figure 5. H/V spectral ratios versus distance for model 1. Top left:
H/V spectral ratio calculated from the contribution of a combined
vertical and horizontal source. Top right: H/V spectral ratio
calculated considering only the contribution of the vertical source. Bottom
left: H/V spectral ratio calculated considering only the contribution
of horizontal sources. Bottom right: H/V spectral ratio calculated
considering only the contribution of the radial component determined by a
horizontal source. The horizontal black line indicates the fundamental resonance
frequency of the model. Gray shows the amplification (values of H/V
greater than 1).
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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.
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Conclusions
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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.
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Appendix
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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 April 21, 2005
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Abstract
Introduction
