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1 Yokohama City University
22-2
Seto, Kanazawa-ku
Yokohama, Japan
236-0027
kkk001{at}yokohama-cu.ac.jp
(S.K.)
2 Mitutoyo Co.
20-1, Sakado 1-chome,
Takatsu-ku
Kawasaki-shi, Japan 213-8533
(M.O.)
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Abstract |
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 Top Abstract IntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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–2
model for P and S waves. An important result is that the
values of corner frequency become nearly constant, 5–6 Hz, in travel times
less than 2.5 sec for SH waves. This suggests that bedrock motions
recorded in the pre-Tertiary basement are becoming incoherent in high
frequencies. Also, the corner frequency of P waves is approximately
twice that for SH waves. Hence, P waves propagate coherently
in high frequencies as compared with SH waves. |
Introduction |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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On the other hand, Fletcher et al. (1990) and Vernon et al. (1991, 1998) were the only studies on the coherency characteristics of body waves along the traveling path using borehole array recordings. This is mainly due to the lack of borehole array recordings. Their studies asserted that site effects control the spatial coherency of body waves so that it decreases rapidly as compared with the coherency of body waves along the traveling path in high frequencies. However, as concluded by Vernon et al. (1998), the estimation of coherency by using array data from shallow boreholes whose depths are shorter than 500 m is difficult in frequencies lower than 10 Hz, because of the contamination of surface-reflected waves into incidence waves. For the engineering applications, the frequency band of 0.1–10 Hz is the most important. In the study on strong motion, in particular, a transition band between deterministic methods and stochastic methods for strong-motion predictions is 0.5–5 Hz (O’Connell, 1999). These facts require the measurement of coherency characteristics of body waves in this frequency band. This is our motivation behind the present study.
In Japan, after the Kobe earthquake of 1995, nationwide networks of strong-motion observation such as a K-NET (Kinoshita, 1998) were constructed, and the data from these networks have been released through the Internet. KiK-net, one of the nationwide networks deployed by NIED (National Research Institute for Earth Science and Disaster Prevention) in Japan has been producing borehole array recordings at over 500 sites, recordings that were recorded simultaneously at the bottom of boreholes and the surface at the same site by using three-component sets of negative feedback accelerometers with a frequency band of 0 to 30 Hz. In this study, we shall use borehole array recordings in the Kanto region, Japan, obtained at six borehole sites with depths of 1200–3510 m.
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Data |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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The investigations of borehole geology, sonic, and density logs were conducted by NIED and reported by Suzuki et al. (1981) and Suzuki and Omura (1999). The determinations of P- and S-wave velocity structures at the IWT, FCH, and SHM sites by using a down-hole method were conducted and reported by Ohta et al. (1980) and Yamamizu et al. (1981). They showed that the velocities of P and S waves propagated vertically in the pre-Tertiary basement are 5.5 km/sec and 2.5 km/sec, respectively, and the average S-wave velocity in the sedimentary layer is approximately 1 km/sec.
The data for investigating the coherency characteristics of direct body waves
that propagate in a sedimentary layer– basement system were obtained from
local events shown in Figure 2a for P waves and
Figure 2b for SH
waves. The data from events shown by open triangles, open circles, open squares,
open reverse triangles, open rhombuses, and solid circles in
Figures 2a and
2b were used for the stations
SHM, FCH, IWT, EDZ, NRT,
and ENZ, respectively. In this study, direct body waves that
propagate coherently in a sedimentary layer–basement system are required
for the estimation of coherence functions. Thus, we used the data from which the
maximum coherence of more than 0.8 in frequencies lower than 5 Hz was estimated.
In addition, the data, in which the influence of the contamination of P
coda to SH waves is insignificant, are also required. The events shown
in Figures 2a and
2b are selected on these
conditions. The hypocenter distances are about 30 km to 150 km. The range of
JMA (Japan Meteorological Agency) magnitude is from 3.2 to 6.1. Two
phases on deep-borehole seismograms, an incident and its surface-reflected
waves, are used for the estimation of the coherence function of a body wave that
propagates in a sedimentary layer–basement system. The surface- reflected
body wave recorded at the bottom of a borehole is contaminated by the direct
body wave when the duration of the direct body wave is longer than the two-way
time at the site. The events in this study must be selected taking account of
this fact. The empirical relations between direct S pulse
(Td) and JMA magnitude
(MJMA) obtained using data recorded at hard rock
and borehole sites are as follows
(Kinoshita and Ohike, 2002):
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Method |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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| (1) |
As an example, Figure 3 exhibits the transverse components of velocity seismograms that were converted from the original acceleration seismograms recorded at site SHM for the earthquake of 16 January 1988. The top and bottom of Figure 3 are recordings at free surface and 2,300 m depth, respectively. It may be easy to identify direct S phases on both borehole and surface recordings and surface-reflected phases on the borehole seismogram, phases that are traveling in a sedimentary layer–basement system. We first determine the start time ti of the direct SH phase, visually, as marked by "A" in Figure 3. By using a time window with length shorter than the two-way travel time estimated according to the S-wave velocity structure at the site (Yamamizu et al., 1981), the cross-correlation function between the direct SH phase and its surface-reflected one is calculated as shown in the top right of Figure 4a. The lag time at which the estimated cross-correlation has its maximum is the separation time td, and it is the two-way travel time of S waves throughout the sedimentary layer–basement system at site SHM. The surface-reflected phase whose start time is given by tj = ti + td, as marked by "B" in Figure 3, is thus determined. By using the two SH phases whose start points are marked by "A" and "B," having the same window length as the one given by the portion whose start and end point are marked by "B" and "BB," respectively, coherence is estimated by applying Welch’s periodogram-averaging method (Proakis and Manolakis, 1996) as shown in the bottom right of Figure 4a. Auto-spectral densities of the direct SH phase and its surface-reflected one are given by the top left and bottom left of Figure 4a, respectively.
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As mentioned previously, two direct incident phases recorded at both the deep borehole and surface are also used to estimate the coherency characteristics of body waves that propagate in a sedimentary layer–basement system. As shown in Figure 3 (top), for example, the onset of the SH phase is marked by "C," also determined by using the cross- correlation method. In this case, the two SH phases used for the estimation of coherence are portions with the start points marked by "A" and "C," having the same window length between "C" and "CC," respectively. The corresponding spectral density, one-way travel time, and coherence are shown in Figure 4b.
The coherence shown in Figure 4a is estimated using the window length of 4.03 sec, which is shorter than the two-way time of 4.63 sec. According to Vernon et al. (1991), the estimation of coherence is robust to window length. They tested two window lengths, 0.5 sec and 2 sec, and found no significant difference on the resultant coherence for body waves from local events. Similarly, Kinoshita (2003) showed that the estimated results of coherence using different windows with length between one-way travel time and two-way travel time did not show significant difference. On the contrary, window lengths that were longer than the two- way time produced significantly different coherence. This may be due to the contamination of surface-reflected waves to incident body waves that appeared on deep-borehole seismograms. Thus, we use data windows with length between the one-way time and two-way time in this study.
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Results |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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–2 model:
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| (2) |
= 0.83
± 0.02 and fc = 9.21 ± 0.36 Hz, where
the error values are the 95% confidence levels of regression coefficients. The
mean value with standard error of two-way time estimated at the SHM
site is 1.73 ± 0.05 sec. Assuming n is a free parameter, we
obtain that n = 2.28 ± 0.22,
= 0.80
± 0.02, and fc = 9.46 ± 0.36 Hz, where
the error values are the 95% confidence levels of regression coefficients. The
corresponding parameters at the FCH site are
= 0.83
± 0.02 and fc = 9.86 ± 0.37 Hz in the
–2 model, and the two-way travel time is 2.00
± 0.05 sec. Assuming that n is a free parameter, the best-
fitted parameters are as follows: n = 2.34 ±
0.22, 
=
0.80 ± 0.02, and fc = 10.13 ± 0.39 Hz,
where the error values are the 95% confidence levels of the regression
coefficients. Data length used for the estimation of coherence is the length of
two-way time – 0.3 sec for each event. In this case, two-way time means
the lag time at which the cross-correlation between the direct phase and its
surface-reflected one is its maximum. –2
model, empirically, as shown by the solid line. The best- fitted parameters are
as follows: 
= 0.86 ± 0.03 and fc = 11.32 ±
0.91 Hz at the SHM site, and the one-way travel time is 0.86 ±
0.03 sec. The result obtained at the FCH site shown in
Figure 6b yields
= 0.91
± 0.03 and fc = 10.07 ± 0.74 Hz in the
–2 model. The one- way travel time is 0.97
± 0.05 sec. Data length used for the estimation of coherence is the
length of twice the one- way time – 0.2 sec for each event. In this case,
one-way time means the lag time at which the estimated cross- correlation
between direct phases recorded at the bottom of a borehole and surface is its
maximum.
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= 0.79
± 0.02 and fc = 3.92 ± 0.17 Hz at the
SHM site, and two-way travel time is 4.81 ± 0.10 sec. Assuming
n is a free parameter, we get the following best-fitted parameters:
n = 2.09 ± 0.17,
= 0.78
± 0.03, and fc = 4.00 ± 0.24 Hz. The
result obtained at the FCH site shown in
Figure 7b yields
= 0.73
± 0.02 and fc = 4.42 ± 0.18 Hz in the
–2 model. The two-way travel time is 4.70
± 0.14 sec. Assuming that n is a free parameter, we get the
following best-fitted parameters: n = 1.80 ± 0.13,
= 0.76
± 0.03, and fc = 4.20 ± 0.26 Hz. Data
length used for the estimation of coherence is the length of two-way time
– 0.6 sec for each event. In this case, two-way travel time means the lag
time at which the cross-correlation between direct phase and its
surface-reflected one is its maximum. 
= 0.94
± 0.05 and fc = 6.00 ± 0.42Hz,
= 0.97
± 0.06 and fc = 5.89 ± 0.55Hz,
= 0.98
± 0.08 and fc = 4.09 ± 0.45 Hz,
= 0.92
± 0.08 and fc = 5.83 ± 0.08 Hz,
= 0.95
± 0.11 and fc = 5.95 ± 1.39 Hz, and
= 0.99
± 0.08 and fc = 5.39 ± 0.51 Hz for
sites SHM, FCH, IWT, NRT,
ENZ, and EDZ, respectively. Also, estimated one-way times
are 2.40 ± 0.04 sec, 2.30 ± 0.08 sec, 3.03 ± 0.13 sec, 1.72
± 0.04 sec, 0.55 ± 0.04 sec, and 1.48 ± 0.04 sec at the
SHM, FCH, IWT, NRT, ENZ,
and EDZ sites, respectively. Data lengths used for the estimation of
coherence are 2.82 sec, 2.82 sec, 2.82 sec, 2.56 sec, 0.95 sec, and 2.56 sec at
the SHM, FCH, IWT, NRT,
ENZ, and EDZ sites, respectively.
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–2 model for the
explanation of coherence characteristics of body waves traveling in a
sedimentary layer–basement system. Thus we use this model hereafter to
explain coherence characteristics. Estimated coherence shown in
Figures 5a,
5b,
7a, and
7b is flat in low frequencies.
This is due to the all-pass characteristics of transfer functions As
demonstrated by
Kinoshita (1999), the transfer
function for a sedimentary layer– basement system, with a direct wave as
input and its surface reflection as output, has maximum-phase characteristics,
and thus all-pass characteristics. However, a transfer function whose input and
output waves are direct phases on deep- borehole and surface seismograms,
respectively, is a minimum-phase system having strong feedback
(Kinoshita, 1999). This means
that the conventional cross-spectrum method cannot apply to the estimation of
coherence (Akaike, 1966), if the
input wave is contaminated by feedback signals that are mainly due to
surface-reflected waves, as in the case of shallow-borehole data. The use of
deep-borehole data can relax this constraint so that a remarkable dip structure
in estimated coherence does not appear in low-frequency bands. |
Discussion |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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–2 model of coherence that is proposed in the
present study. The relationship between travel time and fc/2
for SH waves is shown in
Figures 9a for n
= 2 and 9b for n as free parameter in relation
(2). The corresponding
zero-frequency magnitude of coherence,
versus travel
time, is also shown in
Figures 10a (n
= 2) and 10b (n = free parameter). There is a tendency
that the values of corner frequency become nearly constant (5–6 Hz) for
travel time less than 2.5 sec. Then, the values of corner frequency decrease
with increasing travel time. However, since we have only one data point for
travel time 3–4.5 sec, to find the precise relationship between corner
frequency and travel time in this time range we need more data.
Figures 9a,
9b,
10a, and
10b indicate that the coherence
of SH waves for travel time less than 2.5 sec is well explained by a
characteristic –2 model with a nearly constant
corner frequency and
> 0.9. The
advent of constant corner frequency suggests that the bedrock motion in the
pre-Tertiary basement is incoherent in high frequencies. Assuming the
–2 model of coherence with
1, we get
2 (fc/3) 0.9,
2 (fc/2) 0.8, and
2 (fc) = 0.5. According to
this –2 model, we can evaluate quantitatively
the transition band explained briefly in the introduction. For example, if we
define the transition band by using 2 = 0.8,
then the frequency range of fc/2, 2.5–3 Hz, is the
transition band. Of course, it is more natural to define the transition band by
using the magnitude range of coherence, for example,
2 = 0.8–0.9. Then, the transition band
is approximately from 1.5 to 3 Hz for SH waves.
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Similarly, Figures 5a,
5b,
6a, and
6b indicate that the coherence
of P waves is explained by the –2
model. The ratios of the estimated corner frequencies of the
–2-model obtained for P waves to the
corresponding corner frequencies for SH waves shown in
Figures 7a,
7b,
8a, and
8b are 2.3, 2.2, 1.9, and 1.7,
respectively. Thus, the corner frequency of P waves is approximately
twice that of SH waves Hence, P waves propagate coherently in
high frequencies as compared with SH waves in a sedimentary
layer–basement system.
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Conclusion |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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, where n
is approximately 2. –2 model for SH waves intends to
increase with a decrease in travel time. However, the values of corner frequency
become nearly constant, independent of travel time, for travel time less than
2.5 sec. In the case of SH waves the values of corner frequency are
about 5–6 Hz, and the values of
are larger than
0.9. –2 model for
P waves is approximately twice that for SH waves. Hence,
P waves propagate coherently in high frequencies as compared with
SH waves in a sedimentary layer–basement system. |
Acknowledgments |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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Manuscript received April 20, 2005
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References |
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TopAbstractIntroductionDataMethodResultsDiscussionConclusionAcknowledgmentsReferences |
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| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
and standard error
bars: (a) n = 2 and (b) n is free.
for coherence model
and standard error
bars: (a) n = 2 and (b) n is free.