JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Using τc to Estimate Magnitude for Earthquake Early Warningand Effects of Near-field Terms
Masumi Yamada
Pioneering Research Unit for Next Generation, Kyoto University, Uji, Gokasho, 611-0011, Japan

Jim Mori
Disaster Prevention Research Institute, Kyoto University, Uji, Gokasho, 611-0011, Japan

Abstract. This paper analyzes strong-motion records of 24 large earthquakes to investigate the relationship between τc (the period parameter of the first motion) and moment magnitude. The records of some of the large-magnitude events very close to thesource include large near-field terms. Therefore, if we include the data with large nearfield terms, we may overestimate the final size of the magnitude. We indentified records
with large near-field terms, and did not include these data in processing the records tocompute τc for each event. Our analysis shows that the value of τc is between the earthquake corner period and the period determined by the record duration τ0 . If the magnitude is less than 6, τc closely approximates the corner period, whereas τc for larger earthquakes depends on the rupture process and location of asperity. τc for large earthquakes
provides a lower bound on the event magnitude, and approaches the corner period if alonger record is used.
We also propose a method to classify the records with and without large near-fieldterms. If the peak displacement amplitude for the first 3 seconds (P d3) exceeds 1 cm
and τc exceeds 2 s, the record is more likely to include large near-field terms.
For the purpose of quick onsite warnings, stations observing large near-field terms provide valuable information. Large near-field terms can be observed only if the magnitudeis large and the epicentral distance is small. Therefore, if the displacement exceeds a threshold (e.g. P d = 0.5 cm), the ground motion at the site would likely become very large.
This criterion will help to issue warnings to the blind zone, which is the region where
there is insufficient time to issue a warning before the strong shaking arrives.
A current problem of the early warning system is its reliability in quick magnitude determination. The magnitude
estimation of JMA is based on a magnitude-displacement
relationship. Therefore, the initial magnitude estimate isusually an underestimate at the beginning, and grows as
the fault rupture propagates. As long as the amplitude of
the ground motion is used for magnitude estimation, theproblem of initial underestimation is inevitable.
In order to improve the magnitude underestimation, thispaper analyzes the τc method, which is another algorithm todetermine the earthquake size. One of the merits of the τcmethod is that it uses the frequency content of the groundmotion to estimate the size of the magnitude. The frequency
component is usually more sensitive to the magnitude thanground motion amplitude in the initial few seconds of the
P-wave, but the linear relationship with the magnitude forlarge earthquakes is still debated [Zoll et al., 2006, @; Rydelek et al., 2007, @; Wu and Kanamori, 2008b, @]. Olson
and Allen, 2005 [@] proposed that the final magnitude of anearthquake is partially controlled by the initiation process
within the first few seconds of the rupture, so the predominant frequency of the initial process scales with the final
magnitude. Wu and Kanamori, 2005a [@] also shows thatthe τc scales with magnitude even for Mw > 7, without any
obvious sign of saturation. On the other hand, recently,
Rydelek et al., 2007 [@] processed a high-quality Japaneseseismic network (Hi-net) dataset and showed that no trend
between predominant frequency and magnitude is evident if
Mw > 6. Also, Yamada and Ide, 2008 [@] came to similar
conclusions considering models of earthquakes with complex
ruptures.
In this paper we analyze strong-motion records of 24 large
earthquakes. We investigate the effects of the near-field term

1. Introduction
In October 2007, the Japan Meteorological Agency(JMA) launched a publicly available earthquake early warning system. It is one of the most extensively implemented
systems in the world since it provides early warning to the
public via TV and radio for the whole country.
Since the public release, JMA has issued warnings several
times. The first one was for the Miyakojima-oki earthquake(Mj 5.2), which occurred near the islands 1000 km southeast of Honshu on May 12, 2008. The warning was issued 17
s after the origin time, but it overestimated the magnitude
since the epicenter was actually closer to the closest station
than the estimated location (with 50 km error). The station
density was very sparse in those islands, so the quick andaccurate determination of the epicenter was difficult.
The second event for which a warning was issued was the
Ibaraki-oki earthquake (Mj 6.9), May 8, 2008. This is a
subduction-zone earthquake, located 100 km east offshoreof the Ibaraki prefecture, which should be optimal to issue
an early warning. The determination of the epicenter was
accurate within a 20 km error at 27 s after the origin time,
but the magnitude was underestimated by 0.9. The estimated maximum seismic intensity was under the thresholdto issue a warning until 80 s after the origin time had elapsed
when the strong motions arrived across most of the severely
shaken area.

Copyright 2017 by the American Geophysical Union.
0148-0227/17/$9.00

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YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

and the record duration used to compute τc , and provide a
relationship between τc and magnitude that takes into account the possible presence of large near-field terms.

2. Strong-Motion Data

where u(t) is the vertical displacement high-pass filtered at
0.075 Hz, and τ0 is the duration from the P-wave onset foreach record (generally τ0 = 3 seconds). In this paper, various values of τ0 are tested to check the effect of τ0 .
τc of each record is computed from the vertical acceleration component. For each event, the median of the closest 10
stations is selected to determine the value of τc . The valueof τc depends on the site condition, radiation pattern, andother effects at each station. The effects of these factors on
the determination of τc are not clear, and will be analyzed in
more detail in future work. Here, we use the median of the
10 stations to remove this variance. Note that the 2002 Denali earthquake and 2008 Wenchuan earthquake have only a
few near-source records. Therefore, τc of the Denali earthquake is the median of the closest 6 stations and τc of the
Wenchuan earthquake is the value from only one station.
Also, the Wenchuan record saturates in 5 s after the P-wave
arrival, so values of τc for τ0 equal to 10 and 20 s are notavailable.

We used strong-motion datasets from 24 earthquakes withmagnitudes greater than 6.0 and focal depths less than 100
km. The list of events is shown in Table 1. All inland
events include at least one record within 50 km epicentral
distance, and all events in subduction zones include at least
one record within 150 km epicentral distance. Moment magnitudes from the Harvard CMT catalog are used.
The strong-motion dataset for the 1994 Northridge, 1999
Chichi, 1999 Izmit, 2002 Denali, and 2004 Parkfield events
are the same as the dataset used by Yamada et al., 2007[@]. The strong-motion dataset for the 1999 Hector Mine
earthquake is provided by the U.S. Geological Survey seismic network and the Southern California Earthquake Center (SCEC) Data Center. The records of the aftershocksof the Chichi earthquake were provided by the Taiwan 4. Results and discussion
Central Weather Bureau Seismic Network. Strong-motion 4.1. τ with τ 3 secondsc0
records of the 2008 Wenchuan earthquake were recorded
Figure 1 shows the relationship of the τc calculated withby the China Earthquake Administration network. The
records are available at the website of the China Earth- τ0 equal to 3 s, as a function of moment magnitude for all 24
quake Data Center (http://data.earthquake.cn). The Japan events. The median values of τc for the closest 10 stations
Agency for Marine-Earth Science and Technology (JAM- are shown on the plot. This figure uses the same method as
STEC) recorded the strong motions of the 2003 Tokachi- the results shown in Figure 2 of Wu and Kanamori, 2008b
oki earthquake with seafloor accelerometers located above [@], but data which include large near-field terms have been
the shallow portion of the seismogenic zone. We used removed.
In the Figure 2 of Wu and Kanamori, 2008b [@], τc seems
seismograms from three stations (KSL1, KSL2 and KSL3)
for the mainshock, and one station (KSL1) for the af- to be strongly dependent on the magnitude, but the magnitershock in the offshore Kushiro-Tokachi network system tude dependence of τc seems to be weaker in this figure. In(http://www.jamstec.go.jp/scdc/top e.html). Data from our figure, there are some events with small τc and relatively
the seafloor accelerometers may include both direct waves large Mw (e.g. 1999 Hector Mine, 2000 Western Tottori,
from the seismic source and reflections from the water or 2001 Geiyo, and 2002 Denali). The order of the Butterfree surface, so we use the records of less than 3 s from the worth filter slightly changes the frequency content and may
affect the relationship [Shieh et al., 2008, @], so we used the
P-arrival.
The rest of the events which occurred in Japan were same filter as Wu and Kanamori, 2008b [@].
The dashed line shows the theoretical relations between
recorded by K-net and KiK-net operated by the National Research Institute for Earth Science and Dis- the corner period and moment magnitude [Brune, 1970, @].
aster Prevention in Japan and the JMA strong mo- Assuming a circular fault of radius r, the corner period tc
tion network. The K-net and KiK-net data are avail- (which is 1/fc , where fc is the corner frequency) is given byable at their websites (http://www.k-net.bosai.go.jp/ and Madariaga, 1976 [@];
http://www.kik.bosai.go.jp/). JMA records are also availr
able online. (http://www.seisvol.kishou.go.jp/eq/kyoshin/jishin/index.html)
.
(2)
tc =
0.21VsSince we are interested in near-source earthquakes, therecords with epicentral distances greater than 150 km are
Since the r scales with moment M0 and stress drop ∆σ by
not used.
7M0 1/3
r = ( 16∆σ
) , the corner period is;

3. Method
We processed the accelerograms obtained from 24 earthquakes according to the following procedure. The offset ofthe accelerograms is corrected by subtracting the mean of
the pre-event portion of data. The records are integrated
once in the time domain and high-pass filtered using asecond-order one-way Butterworth filter with a corner frequency of 0.075 Hz. Note that this one-way Butterworth
filter is recursive, so we can carry out this filtering in realtime. The filtered velocity records are integrated once morein the time domain to obtain the displacement records.
The period parameter, τc , for a given duration of the beginning of the record is computed by the following equation[Kanamori, 2005, @; Wu and Kanamori, 2005a, @]:τc = 2π

sR τ

0

R0τ0
0

u2 (t)dtu̇2 (t)dt

,

(1)

tc =

1
0.21Vs



7M0
16∆σ

1/3

.

(3)

Here, we assume Vs = 4 km/s and ∆σ = 10 MPa. Since
M0 = 103/2(Mw +10.73) , log10 tc scales with 1/2Mw . The
dashed line in Figure 1 has the same slope with the corner
period relation (Equation 3) and the intercept is determined
to fit the data estimates of τc using τ0 20 s, which should be
an adequately long time window to accurately measure theactual corner period for all but the very largest events.
In our observations, the values of τc are in the shaded
triangle area in Figure 1 and do not seem to follow a linear relationship. This can be explained as follows. The
ruptures of small to moderate earthquakes (Mw < 6.0) aremostly contained within 3 s, so the estimation of τc gives
values equivalent to the corner period and the data generally follow a relation close to the slope of the dashed line
[e.g. Olson and Allen, 2005, @]. If the magnitude is greater

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS
than about 6.0, the whole rupture is not contained in thefirst 3 s while the estimate of τc depends only on the beginning portion of the earthquake The earthquake may initiatewith either large or small moment accumulation, dependingon the locations of the areas of large slip. Earthquakes withsmall initial ruptures have smaller values of τc , such as forthe 2002 Denali earthquake. If areas of large slip are close
to the epicenter, τc becomes closer to the corner period (seeFigure 2). Therefore, if τc is large, it indicates a large event,but a small τc may represent a lower limit value and then we
will not know exactly the eventual size of the earthquake.
4.2. Effect of the value of τ0
The purpose of the τc measurements is to quickly estimate
the size of the earthquake, so there is trade-off between the
speed of the estimate and using a longer time window, τ0 ,for more reliable information. In order to characterize theeffect of the value of τ0 , we determine τc using various values of the time window τ0 . The determination of τc using
τ0 equal to 10 s is shown in Figure 3. The rupture process
of most earthquakes with magnitude less than 7 terminates
within 10 s, so the value of τc approaches the corner period.
τc of earthquakes with magnitude greater than 7 may also
be close to the corner period, but depend on the rupture
process. This relationship is shown by the shaded region in
Figure 3. For earthquakes with magnitude less than 7, there
is a general linear relation between magnitude and the logof τc . For earthquakes with magnitudes greater than 7, thevalue of τc can have any value greater than 2 s (this number corresponds to the lower bound of τc for earthquakes
with magnitude greater than 7). For example, the 2003
Tokachi-oki earthquake is very large (Mw 8.3), and the rupture duration is much longer than 10 s. Therefore, the valueof τc even using τ0 equal to 10 s is still small compared tothe total size of the magnitude. Although for this event,the S-wave has arrived at some of the near-source stations
by 10 s after the origin time, so this estimate of τc is also
contaminated by the effect of the S-wave.
Figure 4 shows the values of τc with τ0 equal to 20 s.
τc of most of the events with magnitude less than 7.5 approaches the corner period. Similar to Figure 3, the shaded
area shows the region of expected values. Also, for comparison, the values of τc with τ0 equal to 1 s are shown in
Figure 5. There is a clear saturation of magnitude, and therange of τc spans only 1 to 3 s. The correlation between
τc and magnitude is very weak in this figure. There is alimitation of the τc values for characterizing the initiationof the waveform and the exact physical meaning of τc is difficult to interpret [Simons et al., 2006, @; Wolfe, C., 2006,@]. However, we use this parameter as a simple estimate of
the initial pulse duration.
From these observations, τc using τ0 equal to 3 s represents the size of the magnitude if the event is smaller thanmagnitude 6. For larger earthquakes, τc would be less thanthe corner period and greater than the lower bound definedby τ0 . Using τc equal to 3 s seems to provide a reasonable
threshold to identify large earthquakes that can cause shaking damage. In practice, a realtime system will likely havean initial estimate at 3 s, and frequent updates at intervalsof one to several seconds.
4.3. Effect of the near-field term
The strong motions of large earthquakes very close to thefault include long-period components and static displacements. These are the near-field terms, that begin to arriveat the same time as the P-wave. Figure 6(a) shows typical records with large near-field term components, and 6(b)shows records with little near-field contributions. It is clearthat the near-field term is long period (often monotonicallyincreasing) between P- and S-wave arrivals.
The effect of the near-field term has not been considered
for the magnitude estimation so far [Allen and Kanamori,

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2003, @; Wu and Kanamori, 2008a, @]. However, recent
studies show the near-field term may contaminate magnitude estimation significantly [Wu and Kanamori, 2008b, @].
McGuire et al., 2008 [@] pointed out the importance of thenear-field term on earthquake early warning applications using a wavelet analysis, although their study did not provide
a comprehensive evaluation. To examine the influence of thenear-field term, we distinguished the data that contain large
near-field terms by identifying the records with clear ramps
between the P- and S-waves in the displacement records.
Figure 7 shows the relationship between τc and magnitude for the records with and without large near-field terms.
Values of τc for the records with large near-field terms arelarger than those without near-field terms, so they tend tooverestimate the magnitude.
Some of the 1999 Chichi earthquake records include large
near-field terms, so if these records are included, the valueof τc becomes longer than if only the direct P waves wereused. This overestimated τc places the Chichi earthquake on
the linear trend in Wu and Kanamori, 2005a [@]. The slip
at the beginning of the Chichi earthquake is relatively small[Ji et al., 2003, @], which should have resulted in a value ofτc which is relatively small compared to its final magnitude.
τc of the 2004 Niigata-ken Chuetsu earthquake would also
be overestimated if we had included the records with large
near-field term.
From Figure 7, if τc exceeds 3 s, it is either due to a large
near-field term or a very large earthquake. However, it isdifficult to distinguish between these two cases. Figure 8
shows the range of epicentral distance and magnitude forwhich the near-field term is dominant in the records. The
amplitude of the near-field term depends on the magnitude,
radiation pattern, initial rupture, and epicentral distance.
This figure shows the near-field term tends to be large if themagnitude is large, and the epicentral distance is small.
In order to classify the records with and without large
near-field terms, the combination of τc and peak displacement of the first 3 s (P d3) is effective. Figure 9 shows therelationship between τc and P d3. If P d3 exceeds 1 cm and τcexceeds 2 s, the record is more likely to include a large nearfield term. Therefore, to accurately estimate the earthquake
size from τc , the records with large near-field terms should
not be used. At the same time, for the purpose of quick
on-site warnings, stations observing large near-field terms
provide valuable information. Note that we do not haveenough records with large near-field terms for earthquakes
with magnitude greater than 7.6 (see Figure 8). Therefore,
we are not sure if this classification criterion can be applied
for the very large earthquakes. Wavelet analysis is one of thealternative procedures to characterize large near-field terms[McGuire et al., 2008, @].
Wu and Kanamori, 2005b [@] proposed an on-site warning criterion for a threshold P-wave displacement of P d =0.5 cm. If the displacement exceeds this value, the groundmotion at the site would likely become very large. Figure 10
shows the peak ground velocity (PGV) of the vertical component and the time after the P-wave arrival for the verticaldisplacement to exceed P d = 0.5 cm. Most of the records
with large near-field terms exceed 0.5 cm within 2 s, andsome exceed the threshold in less than one second. There
are a few misclassified records that exceed this threshold but
produce small PGV less than 10cm/s, such as 2004 Kushiro
earthquakes, which occurred in the offshore subduction zone
with no data within 50km from the hypocenter. However,
the overall success rate for issuing warnings is satisfactory.
This criterion will help to issue warnings to the blind zonethat is close to the source and for which it is difficult toX-4

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

obtain an event location and magnitude before the S wave
arrives.
The advantage of this threshold warning using near-fieldterms is that it can be quick and does not require the information from other stations (i.e. a single station warning).
The current earthquake early warning system provided by
JMA is a network-based approach, and multiple records areprocessed simultaneously to determine the magnitude andlocation. On the other hand, this on-site approach uses
available data at a given site to predict the local groundmotion. This method is suitable for the region close to
the epicenter, since it can provide a warning to the area
faster than the network-based approach. If we incorporate
this algorithm into the real-time strong motion stations, theon-site approach can issue a very quick warning, and the
network-based approach can later issue more location andmagnitude based information. For practical applications,
we may have to solve some technical problems, but we hopethat this approach will provide quicker warning for the region close to the source.

5. Conclusions
This paper analyzes strong motion records of 24 large
earthquakes to investigate the relationship between τc (theperiod parameter of the first motion) and moment magnitude. We investigate the effects of the near-field term andthe record duration used to compute τc , and provide a relationship between τc and magnitude for data that do notcontain large near-field terms.
We analyzed the records which do not have large nearfield waveforms, and computed τc for each event. The valueof τc for the first 3 s of the P-wave gives a lower bound of themagnitude. If the magnitude is less than 6, τc is close to thecorner period, whereas τc for larger earthquakes depends on
the rupture process and locations of areas of large slip. In
practice, if the value of τc is large, the earthquake must belarge with large slip near the epicenter. If the value of τcis small, the event may be a small earthquake, or may be alarge earthquake that grows later. τc for large earthquakes
approaches the corner period, if a sufficiently long record
duration is used.
Fortunately, the near-field term for large earthquakes becomes very clear in the 3 s after the origin time, so theclassification of the record with and without large near-fieldterms is possible. One of the ways to do this is to measureboth the peak displacement and τc . We propose a method
where records with Pd3 exceeding 1 cm and τc exceeding 2s, are more likely to include a large near-field term.
For the purpose of quick on-site warnings, stations observing large near-field terms provide valuable information.
Large near-field terms can be observed only if the magnitudeis large and the epicentral distance is small. Therefore, if thedisplacement exceeds a threshold (e.g. P d = 0.5 cm), theground motion at the site would likely become very large.
This criterion will help to issue warnings to the blind zonethat is close to the source.
Acknowledgments. We are deeply appreciative of comments provided by the associate editor, reviewers, and Dr. Hiroo Kanamori whose detailed comments greatly improved thismanuscript. We thank all the institutions providing strong motion data, especially the COSMOS data center, SCEC data center, NIED and JMA. This research was supported by the Program for Improvement of Research Environment for Young Researchers from Special Coordination Funds for Promoting Scienceand Technology (SCF) commissioned by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

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M. Yamada, Kyoto University, Uji, Gokasho, 611-0011, Japan(masumi@eqh.dpri.kyoto-u.ac.jp)

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

Earthquake
Date
Latitude Longitude Depth(km) Mw
Northridge
1994/01/17
34.21-118.5418.0
6.6
1995/01/17
34.59
135.04
17.9
6.9
Kobe
Izmit
1999/08/17
40.75
29.86
17.0
7.6
Chichi-1
1999/09/20
23.81
120.85
8.2
7.6
1999/09/20
23.81
120.868.2
6.4
Chichi-2(aftershock)
Chichi-3(aftershock)1999/09/20
23.61
120.81
1.1
6.4
Chichi-4(aftershock)1999/09/22
23.83
121.0515.6
6.4
Chichi-5(aftershock)1999/09/25
23.85
121.00
12.1
6.5
1999/10/16
34.59-116.27
0.0
7.1
Hector Mine
Western Tottori
2000/10/06
35.27
133.35
9.0
6.7
Geiyo
2001/03/24
34.13
132.6946.5
6.8
Denali
2002/11/03
63.52-147.44
4.9
7.8
2003/05/26
38.82
141.6572.0
7.0
Northern Miyagi
Tokachi-oki-1
2003/09/26
41.78
144.0827.0
8.3
Tokachi-oki-2(aftershock) 2003/09/26
41.71
143.69
21.4
7.3
Kii-1
2004/09/05
33.03
136.8037.6
7.2
2004/09/05
33.14
137.14
43.5
7.4
Kii-2
Parkfield
2004/09/28
35.81-120.38
5.5
6.0
Mid Niigata-1
2004/10/23
37.29
138.87
13.1
6.6
37.31
138.93
14.2
6.3
Mid Niigata-2(aftershock) 2004/10/23
Kushiro2004/11/29
42.95
145.2848.2
7.0West off Fukuoka
2005/03/20
33.74
130.189.2
6.6
Off Miyagi
2005/08/16
38.15
142.2842.0
7.2
Noto Hanto
2007/03/25
37.22
136.6910.7
6.7
2007/07/16
37.56
138.61
16.8
6.6
Niigata-ken Chuetsu-oki
Off Ibaraki
2008/05/08
36.17
141.72
88.3
6.8
Wenchuan
2008/05/12
30.99
103.3619.0
7.9
Iwate-Miyagi Nairiku
2008/06/14
39.03
140.88
11.9
6.9
Table 1. List of the earthquakes used for the analysis. Moment magnitude (Mw ) is cited from the Harvard Centroid Moment Tensor solution.

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X-6

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

Figure 1. Relation between moment magnitude (Mw )and period parameter (τc ) using τ0 equal to 3 s. The
shaded area shows the possible values of τc . The dashedline shows the theoretical relation between magnitudeand corner period.

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

M

X-7

M

3 sec

3 sec
Figure 2. Schematic diagrams of the slip distribution
and moment-rate function. Earthquakes with small initial ruptures (left figure) have smaller values of τc . Ifareas of large slip are close to the epicenter (right figure),τc becomes closer to the corner period. Stars in the slip
distribution indicate the epicenter.

Figure 3. Relation between moment magnitude and τc using τ0 equal to 10 s. The symbols are the same as in Figure 1.

X-8

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

Figure 4. Relation between moment magnitude and τc using τ0 equal to 20 s. The symbols are the same as in Figure 1.

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

X-9

Figure 5. Relation between moment magnitude and τc using τ0 equal to 1 s. The symbols are the same as in Figure 1.

X - 10

10Izmit:YPTTokachi−oki:KSL1
Chuetsu:041
Noto:ISK006
Chuetsu−oki:CB5(a) with NF term

0
−10
0
10

1

2

3
Hyogoken:kob
Parkfield:EFU
Chuetsu:NIG019
Noto:ISK005
Chuetsu−oki:KRW(b) w/o NF term

0
−10
0

1

2

3 time (s)cFigure 6. The first 3 s of the displacement records(a)with large near-field term and (b) without large nearfield term. The zero of the X-axis is the initial P arrival.

Tau

disp (cm)disp (cm)YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

010with NF term
w/o NF term
6

6.5

7
7.5
Magnitude

8

Figure 7. Magnitude and τc using τ0 equal to 3 s foreach record in this study. The circle and cross symbols
indicate data with and without large near-field terms,
respectively.

8.5

YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

X - 11

2

Epicentral distance (km)

10

1

10

with NF term
w/o NF term
6

6.5

7
7.5
Magnitude

8

8.5

Figure 8. Magnitude and epicentral distance of stations
that recorded data used in this study. The symbols are
the same as in Figure 7.

1

Tauc

10

0

10

with NF term
w/o NF term
−1

10

−2

0

10

10

2

10

Pd3
Figure 9. P d3 and τc using τ0 equal to 3 s for each record in this study. The symbols are the same as in Figure 7.

X - 12YAMADA AND MORI: EEW AND EFFECTS OF NEAR-FIELD TERMS

2Time to exceed 0.5cm (s)10with NF term
w/o NF term
1

10

0

10

0

10

1

10
PGV (cm/s)
Figure 10. PGV and the time after the P arrival forthe vertical displacement to exceed P d = 0.5cm. The
symbols are the same as in Figure 7.

210