|
|
||||||||
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.)
| Abstract |
|---|
|
|
|---|
2
model for P and S waves. An important result is that the
values of corner frequency become nearly constant, 56 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 |
|---|
|
|
|---|
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 0.110 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 0.55 Hz (OConnell, 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 12003510 m.
| Data |
|---|
|
|
|---|
|
|
|
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 layerbasement 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 layerbasement 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):
|
|
|
|
| Method |
|---|
|
|
|---|
|
| (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 layerbasement 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 layerbasement 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 Welchs 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.
|
|
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 layerbasement 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.
| Results |
|---|
|
|
|---|
2 model:
|
| (2) |
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,
2
model, empirically, as shown by the solid line. The best- fitted parameters are
as follows:
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.
|
|
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,
|
|
2 model for the
explanation of coherence characteristics of body waves traveling in a
sedimentary layerbasement 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 |
|---|
|
|
|---|
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,
2 model with a nearly constant
corner frequency and
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, 2.53 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 = 0.80.9. 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
layerbasement system.
| Conclusion |
|---|
|
|
|---|
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 56 Hz, and the values of
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 layerbasement system. | Acknowledgments |
|---|
|
|
|---|
Manuscript received April 20, 2005
| References |
|---|
|
|
|---|
Akaike, H. (1966). Some problems in the application of the cross-spectral methods, in Advanced Seminar on Spectral Analysis of Time Series, B. Harris (Editor), John Wiley & Sons, New York,81 107.
Der, Z. A., M. E. Marshall, A. ODonnell, and T. W. McElfresh
(1984). Spatial coherence structure and attenuation of the
Lg phase, site effects, and the interpretation of the Lg coda,
Bull. Seism. Soc. Am.74
,1125
1147.
Fletcher, J. B., T. Fumal, H. Liu, and L. C. Carroll
(1990). Near-surface velocities and attenuation at two boreholes
near Anza, California, from logging data, Bull. Seism. Soc.
Am. 80,807
831.
Harichandran, R. S., and E. H. Vanmarcke (1986). Stochastic variation of earthquake ground motion in space and time, J. Eng. Mech. Div. ASCE112 ,154 174.
Hindy, A., and M. Novak (1980). Pipeline response to random ground motion, J. Eng. Mech. Div. ASCE106 ,339 360.
Kinoshita, S. (1994). Frequency-dependent attenuation of
shear waves in the crust of the Kanto area, Japan, Bull. Seism. Soc.
Am. 84,1387
1396.
Kinoshita, S. (1998). Kyoshin-net (K-NET), Seism. Res. Lett.69 ,309 332.
Kinoshita, S. (1999). A stochastic method for
investigating site effects by means of a borehole arraySH and Love waves,
Bull. Seism. Soc. Am.89
,484
500.
Kinoshita, S. (2003). Local event seismograms, Technical Note of the National Research Institute for Earth Science and Disaster Prevention 240,1 190 (in Japanese).
Kinoshita, S., and M. Ohike (2002). Scaling relations of
earthquakes that occurred in the upper part of the Philippine Sea plate beneath
the Kanto region, Japan, estimated by means of borehole recordings,
Bull. Seism. Soc. Am.92
,611
624.
Loh, C. (1985). Analysis of the spatial variation of seismic waves and ground movements from SMART-1 array data, Earthquake Eng. Struct. Dyn.13 ,561 581.[CrossRef]
Luco, J. E., and H. L. Wong (1986). Response of a rigid foundation to a spatially random ground motion, Earthquake Eng. Struct. Dyn. 14,891 908.[CrossRef]
McLaughlin, K. L., L. R. Johnson, and T. V. McEvilly
(1983). Two-dimensional array measurements of near-source ground
accelerations, Bull. Seism. Soc. Am.73
,349
375.
Menke, W., A. L. Lerner-Lam, B. Dubendorff, and J. Pacheco
(1990). Polarization and coherence of 5 to 30Ha seismic wave fields
at a hard- rock site and their relevance to velocity heterogeneities in the
crust, Bull. Seism. Soc. Am.80
,430
449.
OConnell, D. R. H. (1999). Replication of
apparent nonlinear seismic response with linear wave propagation models,
Science 283,2045
2050.
Ohta, Y., N. Goto, F. Yamamizu, and H. Takahashi (1980).
S-wave velocity measurement in deep soil deposit and bedrock by means of an
elaborated down-hole method, Bull. Seism. Soc. Am.70
,363
377.
Proakis, J. G., and D. G. Manolakis (1996). Digital Signal Processing, Prentice Hall, Upper Saddle River, New Jersey, 911913.
Suzuki, H., and K. Omura (1999). Geological and logging data of the deep observation wells in the Kanto region, Japan, Technical Note of the National Research Institute for Earth Science and Disaster Prevention 191,1 80 (in Japanese).
Suzuki, H., R. Ikeda, T. Mikoshiba, S. Kinoshita, H. Sato, and H. Takahashi (1981). Deep well logs in the Kanto-Tokai area, Review of Research for Disaster Prevention, National Research Center for Disaster Prevention 65,1 162 (in Japanese).
Takahashi, H., and K. Hamada (1975). Deep borehole observation of the earth activities around Tokyo, Pageoph 113,311 320.[CrossRef]
Toksoz, M. N., A. M. Dainty, and E. Charrette (1991). Coherency of ground motion at regional distances and scattering, Phys. Earth Planet. Interiors67 ,162 179.[CrossRef]
Vernon, F. L., J. Fletcher, L. Carroll, A. Chave, and E. Sembera (1991). Coherence of seismic body waves from local events as measured by a small-aperture array, J. Geophys. Res.96 ,11,981 11,996.
Vernon, F. L., G. L. Pavlis, T. J. Owens, D. E. McNamara, and P. N. Anderson
(1998). Near-surface scattering effects observed with a
high-frequency phased array at Pinyon flats, California, Bull. Seism.
Soc. Am. 88,1548
1560.
Yamamizu, F., H. Takahashi, N. Goto, and Y. Ohta (1981). Shear waves velocities in deep soil deposits, Zisin34 , 465479 (in Japanese).
This article has been cited by other articles:
![]() |
K. Sawazaki, H. Sato, H. Nakahara, and T. Nishimura Time-Lapse Changes of Seismic Velocity in the Shallow Ground Caused by Strong Ground Motion Shock of the 2000 Western-Tottori Earthquake, Japan, as Revealed from Coda Deconvolution Analysis Bulletin of the Seismological Society of America, February 1, 2009; 99(1): 352 - 366. [Abstract] [Full Text] [PDF] |
||||
![]() |
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; 98(1): 463 - 468. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |