Bulletin of the Seismological Society of America; February 2006; v. 96; no. 1;
p. 165-175; DOI: 10.1785/0120050082
© 2006 Seismological Society of America
Coherency Characteristics of Body Waves Traveling in a Sedimentary Layer–Basement System in the Kanto Region, Japan
Shigeo Kinoshita1 and
Miho Ohike2
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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By means of borehole array recordings obtained at six stations from local
events, we estimated coherency characteristics of body waves that propagate in a
sedimentary layer–basement system in the Kanto region, Japan. The
estimated coherence is characterized by an 
–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.
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Introduction
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The coherency characteristics of ground motion are affected by the scattering
and attenuation in the propagating processes. Many studies on the seismic
scattering were carried out to survey the statistical characteristics of solid
media of the Earth by using array recordings. Among them, the coherency
characteristics of seismic waves have been investigated mainly by using surface
array recordings for local and regional events
(McLaughlin et al., 1983;
Fletcher et al., 1990;
Vernon et al., 1991,
1998) or direct surface waves
such as Lg waves
(Der et al., 1984;
Toksoz et al., 1991).
For engineering purposes, the coherency characteristics of ground motion are
applied to make design indexes for pipeline systems and to construct stochastic
methods for strong- motion predictions. The main purpose of these studies is to
investigate so-called spatial coherency, and they found that the dependence of
the spatial coherency on event (or approach azimuth of seismic waves) is not
significant and the magnitude of spatial coherency decreases with increases in
frequency and separation distance between observation points. The results on
spatial coherency of body waves have been explained using empirical relations,
in particular single- exponential coherency functions
(Hindy and Novak, 1980; Loh, 1985;
Luco and Wong, 1986;
Menke et al., 1990) or
double-exponential coherency functions (Harichandran and Vanmarcke, 1986), which
were empirically constructed.
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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We used the array data recorded at six borehole stations, IWT,
FCH, SHM, NRT, EDZ, and
ENZ, deployed in the Kanto region, central Japan. The geological
structures in these boreholes are illustrated in
Figure 1, where the bottoms of
the boreholes are 500–800 meters below the top of the pre- Tertiary
basement covered by the sediment layer. We call such a geological structure the
"sedimentary layer–basement system." The locations of these
six sites are given in Table 1
and shown in Figures 2a and
2b as well as the locations of
the local earthquakes used for this study. The slant angle of each borehole from
a vertical line is within 3°. The array recordings used in this study were
obtained from the two three-component sets of negative-feedback accelerometers
with a natural frequency of 450 Hz and a damping factor of 0.6–0.7, which
were installed at the bottom of a borehole and at the surface at stations
IWT, FCH, and SHM, or at the 10 m depth at
stations NRT, EDZ, and ENZ. The overall
response of the recording system is flat in the frequency band between 0 and 30
Hz (–3-dB point) and the sampling rate is 100 Hz or 200 Hz. The dynamic
ranges of the recording system are 12 bits/sample at the IWT,
FCH, and SHM sites (for details, see
Takahashi and Hamada, 1975;
Kinoshita, 1994) and 16
bits/sample at the NRT, EDZ, and EDZ sites,
respectively. In this study, we used P and SH waves. The
orientation of the borehole-bottom seismometers is coincident with that of the
borehole-surface seismometers installed at the NRT, ENZ,
and EDZ sites, that is, the north–south, east–west, and
up–down directions. However, the orientation of the borehole-bottom
seismometers installed at the SHM, FCH, and IWT
sites is not coincident with that of the surface seismometers. Thus, we first
compensated for the difference in the orientation of the borehole-bottom
seismometers at these three sites according to the results measured by using an
electric azimuth meter. After that, two horizontal components were rotated to
obtain the SH component parallel to the directions of the maximum
principal axis of the trajectory ellipse of the direct S phase
(Kinoshita, 1994;
Kinoshita and Ohike, 2002).
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Figure 1. The six borehole stations, ENZ, FCH, IWT,
SHM, NRT, and EDZ, that are arranged from west
to east across the central Kanto region, on a sedimentary layer–basement
system.
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Figure 2. (a) Locations of two deep-borehole sites, SHM and FCH.
The borehole array recordings from these sites are used for investigating the
coherency characteristics of P waves. The data from events whose
locations are shown by open triangles and open circles are used for stations
SHM and FCH, respectively. (b) Locations of six borehole
sites, SHM, FCH, IWT, EDZ,
NRT, and ENZ. The borehole array recordings from these
sites are used for investigating the coherency characteristics of SH
waves. The data from events whose locations are shown by open triangles, open
circles, open squares, open reverse triangles, open rhombuses, and solid circles
are used for stations SHM, FCH, IWT,
EDZ, NRT, and ENZ, respectively.
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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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and
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The
average values of Td for MJMA
6.1 are 4.2 sec and 4.4 sec for interplate and intraplate events,
respectively. The estimated average values of two-way time between the surface
and the bottom of borehole levels at the SHM and FCH sites
are 4.8 sec and 4.6 sec, respectively, as will be shown later. Thus, we used
data from events with a range of MJMA 3.2– 6.1.
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Method
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The lagged coherence is defined as
| (1) |
where Pij(td, f) is the
cross-spectrum of body waves x(di, t) and
x(dj, t), where di and
dj indicate the depths of the recording sites i and
j; the separation time td =
|ti – tj|; and
ti, tj are the corresponding onset times of the
interested phase. Pii(f) and
Pjj(f) are the auto-spectra of the two seismograms
recorded at depths of di and dj,
respectively. Two wave sets are used for the estimation of coherence in this
study. One is to make a comparison between incidence phase and its
surface-reflected one recorded at the same deep borehole. The other is to
compare the direct body-wave phases recorded at the deep borehole and the
surface.
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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Figure 4. (a) Coherence estimated by using a direct SH phase and its surface
reflection recorded at deep borehole. (b) Coherence estimated by using two
direct SH waves recorded at deep borehole and surface (solid circles).
Dotted lines indicate 95% confidence level of regression analysis.
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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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Coherence of P Waves
To study the coherence of P waves, we used vertical component
seismograms only.
- Coherence characteristics estimated from the comparison between the direct
P phase and its surface-reflected one on borehole seismograms:
Figures 5a and
5b are results obtained by
using the data from events shown in
Figure 2a at stations
SHM and FCH for 11 and 18 events, respectively. Solid
circles are mean coherence and dotted lines are the 95% confidence levels of
regression coefficients. Applying a nonlinear least-squares fitting method, the
solid line in Figures 5a and
5b can be best fitted by the
following –2 model:
| (2) |
The model parameters for station SHM are
= 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.
- Coherence characteristics estimated from the comparison between direct phases
recorded at the bottom of a deep borehole and surface:
Figures 6a and
6b are results obtained by
using the data from events shown in
Figure 2a at the SHM
and FCH sites, respectively. Solid circles are mean coherence and
dotted lines are the 95% confidence levels of the regression coefficients. Total
numbers of events used for the estimation of coherence are 21 and 22 for
stations SHM and FCH, respectively. Again, the estimated
coherence can be best interpreted by an –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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Figure 5. Coherences estimated from events recorded at stations (a) SHM and
(b) FCH for P waves (solid circles). Dotted lines indicate
95% confidence level of regression analysis.
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Figure 6. Coherences estimated from events recorded at stations (a) SHM and
(b) FCH for P waves (solid circles). Dotted lines indicate
95% confidence level of regression analysis.
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Coherence of S Waves
For S waves, we used the SH component only. The station and
event locations are shown in
Figure 2b.
- Coherence characteristics estimated from the comparison between the direct
S phase and its surface reflection recorded at the deep borehole:
Figures 7a and
7b are results obtained at the
SHM and FCH sites, respectively. Solid circles are mean
coherence and dotted lines show the error ranges of the 95% confidence levels of
the regression coefficients. Total numbers of events used for the estimation of
coherence are 30 and 26 for stations SHM and FCH,
respectively. The solid line is the nonlinear fitting to relation
(2). The best-fitted parameters
are
= 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.
- Coherence characteristics estimated from the comparison between direct phases
recorded at the bottom of a deep borehole and surface:
Figures 8a,
8b, and
8c are the coherence
characteristics estimated for stations SHM, FCH, and
IWT, respectively. The coherence characteristics estimated at the
NRT, ENZ, and EDZ sites are also shown in
Figures 8d,
8e and
8f, respectively. Solid circles
are the mean values of coherence and dotted lines are the 95% confidence error
levels of regression coefficients. The total numbers of events used for the
estimation of coherence are 22, 16, 15, 25, 10, and 13 for stations
SHM, FCH, IWT, NRT, ENZ,
and EDZ, respectively. The best-fitted parameters to relation
(2) are as follows:
= 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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Figure 7. Coherences estimated from events recorded at stations (a) SHM and
(b) FCH for SH waves (solid circles). Dotted lines indicate
95% confidence level of regression analysis.
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Figure 8. Coherences estimated from events recorded at stations (a) SHM, (b)
FCH, (c) IWT, (d) NRT, (e) ENZ, and
(f) EDZ for SH waves (solid circles). Dotted lines indicate
95% confidence level of regression analysis.
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All estimates of coherence obtained for the vertical component of P
waves and SH component of S waves show that it is empirically
reasonable to use the –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.
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Discussion
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The main point is the characteristics of the empirical
–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.
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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A fundamental issue in strong-motion seismology and earthquake engineering is
to determine the frequency band in which body waves propagate coherently in a
sedimentary layer–basement system. To respond to this issue, we
investigated down-hole array recordings including deep-borehole seismograms
obtained in the Kanto region, Japan, and obtained the following results:
- Coherence characteristics of body waves from local events and traveling in a
sedimentary layer–basement system are empirically modeled by
, where n
is approximately 2.
- The corner frequency fc in the
–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.
- The corner frequency in the –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.
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Acknowledgments
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The authors deeply appreciate Dr. Anshu Jin for her constructive suggestions
and critical review of this manuscript. This study was supported in part by
grant-in-aid for scientific research No. 15560408 in Japan and by the
JNES (Japan Nuclear Energy Safety Organization) open application
project for enhancing the basis of nuclear safety.
Manuscript received April 20, 2005
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This article has been cited by other articles:
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S. Kinoshita
Deep-Borehole-Measured QP and QS Attenuation for Two Kanto Sediment Layer Sites
Bulletin of the Seismological Society of America,
February 1, 2008;
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Abstract
Introduction
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.