Geophys. J . Int. (1989) 99, 101-108
Two-dimensional coda Q structure beneath Tohoku, NE Japan
Satoshi Matsumoto and Akira Hasegawa
Observation Centre for Prediction of Earthquakes and Volcanic Eruptions, Faculty of Science, Tohoku Universiy, Sendai 980, Japan
Accepted 1989 April 7. Received 1989 April 6; in original form 1989 February 3.
SUMMARY
Based on the single scattering model, coda-Q values (Q,) are estimated for several frequency
bands from the time decay of coda wave amplitude. The Q, value shows a regional variation
and frequency dependency of the form Q, mf”, where n is found to be 0.6-1.2. A method for
estimating the 2-D Q, structure has been developed to investigate the regional variation of
the Q, value beneath Tohoku, the NE part of Honshu, Japan. The Q, value at each grid
point spatially distributed is estimated by averaging the observed Q, values for many
event-station pairs with adequate weighting factors. The weighting factor at each grid point
for an event-station pair is calculated by taking into account the amount of energy
contribution to the coda wave from that grid point. The obtained 2-D Q, structure shows
some relation to the S-wave velocity structure, the Q, structure and the seismic activity in this
area. In general, low Q, regions have a tendency to correspond to the regions with low
S-wave velocity, low Q, value and high seismic activity, while high Q, regions correspond to
those with high S-wave velocity, high Qs value and low seismic activity. In the regions around
active volcanoes and near the coast of the Japan Sea the Q, value is relatively low, whereas it
is relatively high near the coast of the Pacific Ocean.
Key words: coda Q, regionality, Tohoku
1 INTRODUCTION
On short-period seismograms we can see considerable
seismic energy after the direct P- and S-wave arrivals. The
energy in this part, which is called seismic coda, can be
interpreted as scattered energy from randomly distributed
scatterers in an elastic medium. A single scattering model
has been proposed to interpret the origin of the coda wave
(Aki 1969; Aki & Chouet 1975). According to this model,
the coda wave is a superposition of the waves scattered once
to the backward direction due to lateral heterogeneity in the
medium, and Q values can be estimated as a function of
frequency from the time decay of coda wave energy. Sat0
(1977) derived a theoretical formula for the space-time
distribution of the energy density of the coda wave, and
showed that the time decay of coda wave energy is
independent of hypocentral distance and of the ray-path of
direct wave through the medium. The Q value estimated
from the time decay of coda wave amplitude represents the
combined energy loss due to scattering and intrinsic
absorption. We can express the coda Q value (Q,) in terms
of scattering Q value (Q,) and intrinsic Q value (Qi) in the
form (Dainty 1981):
Q,’=
Q;’
+ Q,-’.
In the single scattering model, however, we cannot separate
Q s from Qi.
The Q value estimated from the time decay of coda wave
amplitude reflects an averaged Q structure within a certain
volume of the medium including the source and the
receiver. Recently, several researchers have studied the
regional variation of Q value using coda waves (e.g. Rautian
& Khalturin 1978; Tsujiura 1978; Aki 1980; Roecker et al.
1983; Singh & Herrmann 1983; Del Pezzo et al. 1985; Jin,
Cao & Aki 1985; Sat0 1986; Sat0 et al. 1986). They showed
the coda Q value depends mainly on the region studied. The
coda Q value also shows frequency dependency; the Q value
increases with frequency. This frequency dependency is
expressed approximately by the nth power of frequency,
where exponent n ranges from 0.5 to 1.0.
In the present study, based on the single scattering model,
we try to estimate 2-D spatial distributions of coda Q values
at several frequency bands beneath Tohoku, the NE part of
Honshu, Japan, by using a simple method developed here.
In Tohoku, which is a typical subduction zone, several
studies have been done on the crust and upper mantle
structures. Obara, Hasegawa & Takagi (1986) applied an
inversion technique to the local seismic network data of
Tohoku University, and obtained 3-D P- and S-wave
velocity structures. Their results show the existences of a
high velocity zone corresponding to the descending oceanic
plate and extremely low velocity zones just beneath active
volcanoes. Umino & Hasegawa (1984) estimated the Q,
structure beneath this region by using the spectral ratio
technique of direct P and S waves, in which the ratio of Qp
to Q, is assumed to be independent of frequency. The
present results are compared with the crust and upper
mantle structures obtained by these previous studies.
101
102
2
S.Matsumoto and A. Hasegawa
METHOD
2.1 Q, estimation
First, we try to estimate the coda Q value (Q,) for each
event and station pair at several frequency bands. According
to the single scattering model proposed by Aki & Chouet
(1975), the coda Q value can be estimated from the time
decay of coda wave amplitude by using bandpass filtered
seismograms for an adequate time window. If the medium
through which observed seismic waves propagate is assumed
to be homogeneous and isotropic, the geometrical spreading
factor for the body wave is inversely proportional to the
lapse time (t) measured from the origin time. The energy
density of coda wave E, can be then expressed as:
E,(t) = exp ( - m / Q c ) / t z ,
where o is angular frequency. In the present analysis it is
assumed that coda waves after S-wave arrivals are mainly
composed of backscattered S-waves (Tsujiura 1978). Thus, it
is considered that the Q, value mainly reflects the Q,
structure rather than the Qp structure in the medium. Sat0
(1977) estimated theoretically the single scattering energy
density. He showed that in the case of isotropic scattering
this energy density has the same amount as that in the single
backscattering model proposed by Aki & Chouet (1975) to
within about 10 per cent, if the time decay of coda wave
amplitude is determined by using the portion of the
seismogram later than twice the S-wave travel time.
The time window should be selected carefully because Q,
values obtained may depend on the lapse time from the
origin time. Usually, Q, values estimated from the earlier
part of the coda wave have a tendency to be lower than
those from the later part. This is considered to be due to the
following reasons. One is the contributions of multiplescattering waves to the observed coda waves. The seismic
coda in the later part contains a larger amount of energy of
multiple-scattered waves than in the earlier part (Gao et al.
1983). Moreover, the extent of the region in which scattered
waves propagate is different between the two cases. The
coda wave in the later part of the seismogram is composed
of the waves backscattered by local inhomogeneity in a
larger region than in the earlier part.
Thus, in order to avoid the effect of multiple scattering,
the time window for the analysis should be assigned to the
early part of coda wave data as far as possible. However,
the coda wave amplitude before twice the S-wave travel
time, measured from the origin time, depends on the
radiation pattern (Sato 1977). Therefore it is not
advantageous to use the data before twice the S-wave travel
time for the analysis.
Thus we adopt a start time later than twice the S-wave
travel time (2c)for the time window. The other limit of the
time window (T,,,,,) is determined to be the maximum travel
time of single-scattering waves which propagate within a
previously defined extent of the region. This extent is
defined by the depth limit (Z,,,,,), which is the deepest
location of a scatterer contributing to the generation of coda
wave to be used. For each event-station pair, we calculate
T,,, from the travel time of a ray scattered by a scatterer
located at the depth Z,,,. Using the observed coda wave
data only before T,,,, we can correctly evaluate the Q value
in the medium shallower than Zlrmreven if there is strong
heterogeneity below Zlim. The coda Q value for each
event-station pair is obtained from the observed time decay
of bandpass filtered coda wave data with the time window
from 2T, to Ti,,,.
2.2 Spatial distribution of Q, value
We try to estimate the spatial distribution of the Q, value by
using the apparent Q, values obtained from individual event
and station pairs. Since the formulation for calculating the
coda wave amplitude has strong non-linearity based on the
single scattering model, it is difficult to estimate the spatial
distribution of the Q, value by using ordinary inversion
techniques. In the present study we develop a simple
method for estimating the spatial distribution of the Q,
value.
First, we place many grid points homogeneously in space
in the objective area. The Q, value at each grid point is
estimated as follows. The Q, value is obtained for each
event-station pair. The region contributing to this Q, value
estimation can be determined by 2z, Timand locations of
hypocentre and station. Fig. 1 represents a schematic
illustration of the region in vertical cross-section. The solid
curve (Tim)shows the locations of scatterers at which waves
which arrived at the station at time Ti,,, are backscattered.
In the same way waves arriving at time 2T, are backscattered
by the scatterers along the solid curve ( 2 Q . Since we
analyse coda wave data in the time window between 2T, and
Ti,,,, the region contributing to the Q, estimation is
surrounded by the two curves ( 2 K ) and (Tim).
If a grid point is located within the region surrounded by
the two curves for a certain event-station pair, the Q, value
determined for that pair is assigned with an adequate
weighting factor to that grid point as a datum. The Q, value
for this event-station pair, multiplied by the weighting
factor, is assigned to all the grid points located within this
region. Q, values for all the event-station pairs are assigned
in this way, and the weighted average of Q, values is
calculated at each grid point.
Although the observed time decay of coda wave
amplitude may be affected in some degree by localized
strong scatterers and radiation pattern, we neglect this effect
and only consider the amount of energy contributed to the
coda wave from each grid point and the estimation error of
Q, value for each event-station pair. Thus the weighting
v
surface
Z Lim
Figure 1. Schematic illustration of the region contributing to the
generation of the coda wave in the vertical cross-section. Inverse
triangle and star denote the location of station and hypocentre,
respectively. Grid points distributed homogeneously in space are
shown by solid circles.
2 - 0 coda Q structure
103
40N
+39N
Figure 2. Examples of the regions (enclosed by solid curves) contributing to the estimated Q, value for each event (star) and station (cross)
pair. Solid triangles show the locations of active volcanoes. The estimated Q,value for each event-station pair is assigned with the weighting
factor to the grid points located within its corresponding region
factor for the ith grid point, jth event and kth station pair
and lth frequency band is expressed as
wijkr= (rij + rik)-* * d(Q,<:),
where r, is the distance from the jth event to the ith grid
1 is
. that from the ith grid point to the kth station,
point, rik
and d (Q,;:) is the estimation error of Q,' value for jth
event and kth station pair at lth frequency band.
After analysing many event-station pairs as shown in Fig.
2, the weighted average for ith grid point at lth frequency
band is calculated as:
Qi'
= Ej~c(Qij&*
Wijd/Zidwij/cJ,
The weighted average thus calculated is considered to
represent the coda Q value at each grid point.
The estimation error for the parameter Q,' cannot be
determined, since we d o not know the absolute observation
error of Q,& In our model only the weighting factor is
known, which is considered to correspond to the inverse of
the variance of the relative observation error of Q,Tlp
The
estimation error of parameter Q,;' can be formulated using
this relative observation error and the residual sum of
squares as:
d ( Q i ' ) = {zj/c[(QijAQi')
* Wijkrl/(n- 1)/&k(Wj,kJ}"',
where n is the total number of data. The 2-D spatial
distribution of the coda Q value can be obtained in this way
for each frequency band.
Since accurate evaluation of the depth dependence of the
Q, value is not easy by using shallow earthquakes only
(events with focal depths shallower than 30 km are analysed
in the present study), we averaged the Q, values for the grid
points with the same horizontal coordinates to make the
solution more stable and reliable.
3
DATA
The area selected for the present analysis is the N E part of
Honshu, Japan. We have microearthquake data recorded by
the seismic network of Tohoku University, which covers this
area. The locations of the observation stations used in our
analysis are shown in Fig. 3. About 250 local events that
occurred within the crust with magnitude range from 1.5 to
3.0 are used in the present analysis. The focal depths of
these events are shallower than 30 km, the average depth
being about 8 km. The automatic event detection and
location system of the seismic network of Tohoku l'niversity
routinely processes local events from this area (Hasegawa et
al. 1986). Triggered seismograms for the present 250 events
are A/D converted with sampling frequency of 100Hz and
stored on magnetic tape by the real-time processing system
Fig. 4 shows the vertical cross-section of microearthquakes located by the seismic network of Tohoku
University. From this figure we can see that the descending
Pacific plate exists at depths deeper than 60 km beneath the
land area. The seismic wave velocity and the Q value in the
descending Pacific plate are distinctly higher than those in
104
S. Matsumoto and A . Hasegawa
141.E
+
+ 142. E
A
+
6
40. N
+
39. N
+
+
A
A
9
+
O+
+ +)
PACIFICOCEAN
6
37. N
Figure 3. Map showing the objective area and observation stations
used in the present analysis. The symbols are the same as in Fig. 2.
the surrounding asthenosphere (Hasegawa, Umino &
Takagi 1978). If we choose the depth limit Zlimdeeper than
60km, the existence of the Pacific plate will considerably
affect the estimate for Q, and the assumption of single
scattering may not be always acceptable. Thus, the depth
limit Z,im has been taken as 60 km, which will avoid the
effect of the Pacific plate with high-velocity and high-Q
value. qimcan be determined from hypocentral distance,
focal depth and Zlim. For example, in the case of the
seismograms shown in Fig. 5, Ti,,, is about 30s from the
origin time. For the upper three traces, the epicentral
distance is 28.4 km and the length of the time window is
11S. the epicentral distance is 25.6km and the window
length is 12 s for the lower three traces.
Fig. 6 shows all the event-station pain malysed in the
present study. Most of data used here have hypocentral
distances less than 40 km. Grid points me placed in this area
every 0.2" in both latitude and longitude, and every 10 km in
the vertical direction. The condition for selecting coda wave
data is that coda wave amplitude is greater than the
background noise level and does not saturate during the
time window. The selected seismograms are bandpass
filtered at central frequencies 4, 8, 16 and 24Hz,
respectively. The decay rate of bandpass filter is -24dB
act.-' from each central frequency. Rms amplitude in every
1 s is calculated for coda wave data with the time window
between 2T, and Timand used for the estimation of the Q,
value.
4
RESULTS A N D DISCUSSION
Fig. 7(a)-(d) show the obtained 2-D inverse coda Q
distributions at 4, 8, 16 and 24Hz, respectively. In these
figures, L and H indicate the low.,and high Q, areas,
respectively. The dotted line outlines the region for which
the accuracy of the estimated Q, value is high etiough. In
the area surrounded by the dotted line, the estimated error
of inverse Q, at each grid point is less than a half of the
contour line interval. These figures show the following
features which are common to all the frequency bands:
1. In the region near the coast of the Pacific Ocean, the
coda Q value is higher than those in the inland area and
near the coast of the Japan Sea.
2. The coda Q value is low in the region where active
volcanoes are closely distributed.
The Q, value increases with increasing frequency, as
n
w
n
Figure 4. Vertical cross-section of hypocentres determined by the seismic network of Tohoku University. Hypocentres in the hatched area in
the inserted map are projected on to vertical section. Thick line and inverse triangle show the locations of the land area and the trench axis,
respectively.
2 - 0 coda Q structure
105
HMK
N
S
E
W
I
I
SAW
2 Ts
I
I
Tlim
I
Figure 5. Examples of three-component seismograms at stations HMK (upper three traces) and SAW (lower traces). Bandpass filtered
seismograms between 2T, and Ti,,, are used as data. Epicentral distances are about 30 km for station HMK and 25 km for SAW, respectively.
found in results of previous studies. The frequency
dependency of the coda Q value is characterized by the
following formula:
QJf)m f .
Fig. 8 shows the spatial distribution of n value. Some
regions near the active volcanoes and near the coast of the
Pacific Ocean show a strong frequency dependence for the
Q, value, i.e. n value is larger than 0.9 in those regions.
The spatial distribution of the coda Q value obtained in
the present study has a similar pattern to the S-wave
velocity distribution. Obara et al. (1986) obtained the 3-D
S-wave velocity structure in this region by using inversion
technique. Their results show that the S-wave velocity in the
depth range shallower than 65 km is low around active
volcanoes. On the other hand, the velocity is relatively high
in the region near the coast of the Pacific Ocean. In general,
the low Q, regions correspond to the regions with low
S-wave velocity, and the high Q, regions to those with high
velocity, This suggests that the cause for the low S-wave
velocity is the same as that for the low Q, value, for
example, partial melting. If the medium partially melts, the
average velocity becomes low and the place where the
medium melts acts as a scatterer on elastic wave and absorbs
S-wave energy. Some regions around active volcanoes do
not show low Q, values, although the S-wave velocity is
very low there. This might be due to the low spatial
resolution of the present method for estimating the Q value.
The estimation of Q value by using coda waves cannot have
a high spatial resolution compared with that obtainable
using direct waves. It is not always possible to detect a small
area with an anomalous Q value by the present method.
106
S. Matsumoto and A . Hasegawa
139.E
+
140.E
141.E
+
142.E
+
Figure 6. Map showing event (circle) and station (cross) pairs used
in the present study.
The Q, structure obtained here also shows a similar
pattern to the Q, structure in the same region. Umino &
Hasegawa (1984) estimated the 3-D Q, structure beneath
Tohoku by using spectral ratio of direct P- and S-waves.
In their estimation of Q, value the ratio of Qp and Q, is
assumed to be 2.25. The accuracy of the estimated Q, value
is not so high in the southern part of the area they analysed
because a relatively small number of seismic ray-paths are
used in this area. Therefore we discuss only the northern
part of the area. Although the attenuation models in the two
studies are different from each other, the Q, and Q,
structures have spatially similar patterns. Comparing the
present results to their Q, structure in the depth range
shallower than 56 km, we can see that the low Q, regions
correspond to the low Q, regions, and the high Q, regions
to the high Q, regions.
Fig. 9 shows the seismic activity in Tohoku obtained by
the seismic network of Tohoku University during the period
from 1986 to 1987 in the depth range shallower than 60 km.
Most of the shallow events in the land area are located in
the upper crust (Takagi, Hasegawa & Umino 1977).
Beneath the Pacific Ocean most of the hypocentres are
along the boundary between the descending Pacific plate
and the overriding plate. This seismic activity has some
relationship in spatial pattern with the Q, distribution. The
region with high seismic activity has a tendency to have a
low Q, value and that with low seismic activity has a high Q,
value. Especially in the Kitakami and Abukuma regions
(indicated by A and B In Fig. 9) where the Q, value is
relatively high, the seismic activity is' extremely low. This
may suggest that the relatively low Q, value is caused by the
medium fractured by many small earthquakes.
The spatial distribution of the frequency dependency of
the Q, value (Fig. 8) has a different pattern from the Q,
distribution (Fig. 7). The contours of the n value in Fig. 8
are mostly perpendicular to the trench axis, which does not
relate to any tectonic structures known until now.
139.E
140.E
(b)
141.E +142.E
+ 39. N
+
38. N
37.
38. N
PAC1 FIC OCEAN
OCEAN
+
+
N
+
37. N
[.I 031
Figure 7. The spatial distributions of Q,' at (a) 4, (b) 8, (c) 16, and (d) 24 Hz. In the area surrounded by the dashed line the estimated error
of Q;' is less than a half of the contour-line interval.
2 - 0 coda Q structure
139.E
140.E
141.E t142.E
(4
139.E
140.E
141.E +142.E
107
(d 1
Figure 7. (confd.)
CONCLUSIONS
5
The 2-D spatial distribution of the coda Q (Q,) in Tohoku,
the NE part of Honshu, is obtained by using shallow
microearthquakes with depths shallower than 30 km. The
spatial distributions of Q, values at 4, 8, 16 and 24Hz are
estimated by calculating the weighted average of Q, values
139.E
140.E
for many event-station pairs. The Q, structures obtained
here show the following features:
1. The Q, value increases with frequency, which is
139.E
140.E
141.E +142.E
141.E ~ 1 4 2 . E
4-
40. N
0.8
4-
39. N
4-
38. N
7--
,
I
I
PACIFIC OCEAN
J...
A
4I
I
A
37. N
QEF"
Figure 8. Frequency dependency of the estimated Q, value. The n
value in the formula Qca/n is plotted. Dashed line indicates the
area with the estimated error less than the contour-line interval.
-
O
0°8
M
LI
Figure 9. Epicentre distribution of shallow microearthquakes with
focal depths 0-60Km beneath Tohoku. Events located by the
seismic network of Tohoku University during the period from 1986
to 1987 are plotted. Regions A and B indicate the area of low
seismic activity.
108
S. Matsumoto and A . Hasegawa
consistent with the results of the previous studies. The
frequency dependency of Q, is characterized by Q, f ",
where n value is 0.6-1.2.
2. In the regions near active volcanoes and near the coast
of the Japan Sea, Q, is relatively low. On the contrary, Q, is
relatively high near the coast of the Pacific Ocean. The
distribution of the frequency dependence of Q, has a
different spatial pattern.
3. The Q, structure shows similar spatial features to the
S-wave velocity structure, the Q, structure and the
distribution of the seismic activity. In general the relatively
low Q, regions correspond to the regions with low S-wave
velocity, low Q, value and high seismic activity, while the
high Q, regions correspond to those with high S-wave
velocity, high Q, value and low seismic activity.
These features may suggest that the cause of coda wave
attenuation is closely related to those of the S-wave velocity
variation, S-wave attenuation and the occurrence of small
earthquakes.
ACKNOWLEDGMENT
The authors are much indebted to Professor A. Takagi for
his guidance and encouragement throughout the course of
this study, and to Professor T. Hirasawa for many important
suggestions. We would like to thank the staffs of the
Observation Centre for Prediction of Earthquakes and
Volcanic Eruptions, Kitakami Seismological Observatory,
Akita Geophysical Observatory, Honjo Seismological
Observatory and Sanriku Geophysical Observatory of
Tohoku University for valuable discussions.
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