AN INVESTIGATION OF REGIONAL DEPENDENCE
OF THE SLOPE OF THE INITIAL PART OF P-WAVE
ENVELOPE
Lian Chao
MEE12602

Supervisor:

Tatsuhiko HARA 

ABSTRACT
We investigated regional dependence of the slope of the initial part of P-wave envelope, which is used
to determine epicentral distances in the Japan Meteorological Agency and Japan Railway Company
earthquake early warning (EEW) systems. The Tohoku region was chosen as the study region. We
retrieved 19,899 strong motion borehole data for 265 events with magnitudes in the range from 5.0 to
7.6 from KiK-net (Kiban Kyoshin network). Following previous studies, we fitted the function
Bt  exp(  At ) to the initial part of P-wave envelopes to obtain sets of the parameters of A and B andobtained the following relation log B  2.27  log   4.07 by the least squares method. This isconsistent with the previous study which used the data set similar to that of this study within one
standard deviation. Then, we determined intercepts of the above formula for each event keeping theslope to -2.27 to investigate the regional dependence. There appear two tendencies; shallow crust
events have lower values of c, and deeper events in the subducting slab have higher values of c. We
examined the B values obtained for the same set of the stations for the selected three events, and foundthat their differences are significant. These results suggest that the differences of the coefficient c arelikely to be due to earthquake characteristics.
Keywords: EEW, B-∆ method, regional dependence.

1. INTRODUCTION
When large earthquakes occur, Earthquake Early Warning (EEW) can alert areas near the epicenter for
imminent strong ground shaking. There are two kinds of approach in EEW, the onsite approach andthe regional approach. The onsite approach uses the P-wave at the site to estimate ground motion at
the same site. The Pd approach (Wu and Kanamori, 2005) and threshold-based approach (Colombelli
et al., 2012) are examples of this approach. The regional approach estimates magnitude and locationby using data from seismic stations. UrEDAS (Nakamura, 1988), Elarms (Allen and Kanamori, 2003),
Tau_c (Kanamori, 2005), and SAS (Igresias et al., 2007) belong to the regional approaches category.
The Japan Meteorological Agency (JMA) adopted the regional approach, and implemented its
emergency earthquake alarm system. It provided the early warning information as experimental datafor universities and other organizations on 25 February 2004 and has started issuing the earthquake
warning for public from 1 October 2007. The basic methodology is described in Kamagaichi (2004)
and Kamigaichi et al. (2009).
2. B-∆ METHODEarthquake Administration of Hubei Province, CEA.
International Institute of Seismology and Earthquake Engineering, Building Research Institute (IISEE, BRI),
Tsukuba, Japan.
1Odaka et al. (2003) fitted the following function to the initial part of the P-wave envelope:f  Bt  exp(  At )(1)

where A and B are unknown parameters, t is the time from P-wave arrival. They evaluated theparameters A and B for several earthquakes showing that log B is linearly proportional to –log ∆, andthe relation between log B and log ∆ did not significantly depend on earthquake magnitude. Therefore,
they suggested that the epicentral distance could be estimated immediately after the P-wave arrival byusing this relation. Tsukada et al. (2004) obtained this relation between B and ∆ by their further
analyses. This method is called the B-∆ method, and is used as a single station method to determine
epicentral distance in JMA and Japan Railway Company EEW systems. Nakamura et al. (2007)
suggested the possible regional dependence of the coefficient B.

3. DATA RANGE

Figure 1. The study area (the blue
rectangle) and KiK-net stations (the red
triangles) in and around the study area.

We used strong motion data from KiK-net (Kiban
kyoshin network, Aoi et al., 2000) in this study towhich the B-∆ method was applied. KiK-net is a strong
motion network deployed by the National ResearchInstitute for Earth Science and Disaster Prevention(NIED). The format of KiK-net data follows that of theK-NET (Kyoshin network, Kinoshita, 1998). We chose
the Tohoku area as the study region. Figure 1 shows thestudy area and the KiK-net stations in and around it.
265 events were selected in order to obtain 19,899
strong motion data, to which the B-∆ method was
subsequently applied. The magnitude range, period andregion of the events are shown in Table 1. Most of theevents after the 2011 off the Pacific coast of Tohoku
Earthquake occurred in the sea area.

Table 1. The magnitude range, period and region of the events(4 March 2007 – 25 April 2007).
Numbers
Magnitude
PeriodRegionof events
2011.1.1~2013.5.30
6>=7
E139~144, N36~41.5
1997.1.1~2010.12.30
2
2011.1.1~2013.5.30
44
6.0~6.9
E139~144, N36~41.5
1997.1.1~2010.12.30
22
2011.1.1~2013.5.30 E139~144, N36~41.5
173
5.0~5.9
1997.1.1~2010.12.30 E139~142, N36~41.5
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4. DATA ANALYSIS PROCEDURE
In order to decrease the effect of shallow structures on seismic records, vertical component boreholedata (UD1) were used for the application of the B-∆ method to investigate regional dependence. First,
KiK-net data were retrieved in the K-NET ASCII format, and then converted to the SAC binary
format.

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Second, automatic pickings were done as follows. The application of band-pass filter andsquaring of each data point had been done, and then STA (short time average) and LTA (long time
average) rates have been used to determine P-wave arrival. A band-pass filter with corner frequencies
between 5 and 10 Hz was adopted. The STA window was set to 0.05s and LTA window to 1s. The
threshold of the STA/LTA rate was set to 25. If the rate was more than 25 it was considered a P-wave
arrival time. We found that the signals with lower frequency contents often arrived earlier than thetimes determined by the automatic picking. In order to get accurate results, visual confirmation andmanual picking are performed for all of the data.
Third, we applied the B-∆ method to the prepared data. The time window for the analysis
was set to 2 sec. An example of the application of the B-∆ method is shown in Figure 2.
The earthquake occurred on 18 June 2012, with position of N38.87, E142.09. The depth of
this event was 46.8km and the magnitude of
6.1 was determined by the JMA. The solid
black curve in Figure 2 shows the timeseries obtained by taking absolute values of
the waveform data. The red curve in Figure
2 is the envelope. The least squares method
is used to determine the coefficients A and
B of Eq. (1) using logarithmic waveforms ofthis envelope as data following Odaka et al.
(2003). The blue curve in Figure 2 is the
Figure 2. An example of envelope and fitted line.
fitted curve obtained by this procedure.

5. RESULTS AND DISCUSSION
5.1. Relation between B and ∆As Odaka et al. (2003) and Tsukada et al. (2004) have shown, there exists a good correlation between
log B and log ∆. Their relation can be expressed as follows.

log B  a  log   c(2)where a and c are the unknown parameters to be determined by the observed log B and log ∆.
These coefficients were estimated using ourdata set. Figure 3 shows the estimated coefficients B andthe calculated averages of log B for bins with widths of
0.1 for log ∆ with their standard deviations. We foundthat the log B could be fitted as a straight line as afunction of log ∆ approximately in the range from 1.6 to
2.4. This range corresponds to the epicentral distance
range from about 40 to 250 km. Therefore, data in theepicentral distance range from 40 to 250 km werechosen to calculate the coefficients a and c.
Consequently, the following relation between B and ∆was obtained:(3)
log B  2.27  log   4.07
Figure 3. Relation between B-∆, fitted
line with coefficients a and c and errors
in log B average.
The fitted line (the blue line in Figure 3) isclose to the averages of log B in the log ∆ range from 1.6 to 2.4.

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We compared our result toother formulas. Eq. (4) shows thecurrent formula for the relation
between B and ∆ adopted by JMA,
and Eq. (5) is the formula obtained byNakamura using KiK-net data
(http://www.seisvol.kishou.go.jp/eq/E
EW/Meeting_HYOUKA/t03/shiryou2.pdf)

log   0.498  log B  1.965 (4)(5)
log   0.5  log B  1.65
Figure 4. Comparison of relation between B-∆ for 265
events (Eq.(3), blue line), in JMA EEW System (Eq.(4),red line), and produced by Nakamura (Eq.(5), yellow line).

Figure4showsacomparison of the formula obtainedin this study with the two formulas
given above. The log B from Eq. (4) is systematically larger than that from Eq. (5). The log B (and thefitted line) of this study is closer to Eq. (5) in the larger log ∆ ( ~2.4), while they are a little larger inthe smaller log ∆ ( ~1.6), although the differences are within the one standard deviations.
5.2. Regional dependence of coefficient c

Figure 5. Histogram of coefficients c.
with their depth profiles.

In order to study regional dependence of the coefficients of
the B-∆ method, following Nakamura et al. (2007), thevalue of a in Eq.(4) was set to -2.27, and determined thecoefficient c for each event. Figure 5 is a histogram ofestimated coefficients c. The estimated coefficients c
scattered around 4.0, in the range from 3.1 to 5.0.
In order to determine spatial distributions of thecoefficients c, they were classified into three groups in theranges of [3.1, 3.6), [3.6, 4.5) and [4.5, 5.0], respectively.
Figure 6 shows the spatial distributions of these groups

Figure 6. Distribution of coefficients c and depth projections of three groups; coefficient c:[3.0, 3.85), [3.85, 4.25) and [4.25, 5.0] and two respective longitude-depth projection graphs

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The spatial distribution of events with smaller c values (especially in the bottom left panel of
Figure 6) is different from that of events with larger c values (especially in the bottom right panel of
Figure 6). There appears to be the following two tendencies; shallow crust events have lower values ofc, and that deeper events in the subducting slab have higher values of c. The result of this study ispartly consistent with Nakamura et al. (2007), who suggested the differences of the coefficient c
between inland earthquakes and subduction zone earthquakes.
5.3 Examples of events with the different c values
As shown above, it seems that there is aregional difference for the coefficient c.
In order to investigate whether thisdifference is clear in observed B
estimates, three events with different cvalues were selected. The magnitudes of
2 2012-06-28 37.17 141.20 63.2 5.2 4.09 the selected three events were 5.0, 5.1
and 5.2. The difference of the magnitude
3 2005-01-01 36.78 140.98 89.4 5.0 5.04 is small. Figure 7 and Table 2 show thelocations and values of the coefficient c for these three events.
In order to reduce the possible effect of station sites, we selected the B estimates obtained by
28 stations which recorded all three events in the epicentral distance range from 40 to 250km, andused to determine the coefficients c in Eq. (4)Table 2. Earthquake information, c values for selectedearthquakes (the coefficient a is set to -2.27)
Original
Lat
Lon Depthc (a =
No.
M
time(degree) (degree) (km) JMA -2.27)
1 2011-09-23 36.69 140.62 4.2 5.1 3.29

Figure 8. Relation between B-∆ and fittedlines for three events.

Figure 7. Three events are plotted as triangles
with numbers 1, 2 and 3 listed in Table 3.

Figure 8 shows that the B estimates for each event are clearly different from those for otherevents. Event 1 that occurred in shallow crust has smaller B values (and smaller c), which results fromthe gentle slopes of the initial parts of P-wave envelopes, while Event 3 that occurred in subducting
slab has large B values (and larger c), which results from the steep slopes. The differences shown in
Figure 8 (and Figure 6) are likely to be due to earthquake characteristics, because for deeper events inthe subducting slabs the structural effects such as Q (intrinsic attenuation) and scattering to affectslopes of initial P-waves are likely to be larger than or comparable to those for shallow crust events.

6. CONCLUSIONS

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We investigated the relation between B and ∆ and the possibility of regional dependence using
earthquakes that occurred in the Tohoku region. We retrieved strong ground motion from KiK-net for
265 events and obtained 19,899 borehole data (only vertical component data were used). After
automatic P-wave picking and manual confirmation, the dataset for application of the B-∆ method was
prepared.
Using these dataset, we fitted the coefficients A and B for each pair of stations and events.
Then, we calculated averages of log B for bins with widths of 0.1 for log ∆, and then chose the range
corresponds to the epicentral distance range from about 40 to 250 km to calculate the coefficients aand c in the formula log B  a log   c for all data. We obtained -2.27 and 4.07 for the coefficientsa and c, respectively. This fitted line is close to Nakamura’s result, which used a dataset similar to thatof this study, for larger log ∆ (~2.4), while the values of B are a little larger for smaller log ∆ (~1.6),
although the differences are within the one standard deviations.
By setting the slope a to -2.27, the coefficient c was re-determined separately for each
event. There appears to be the following two tendencies; shallow crust events have lower values of c,and that deeper events in the subducting slab have higher values of c. From the comparison of theselected three events, the B estimates for each event are clearly different from those for other events.
The differences are likely to be due to earthquake characteristics.
We are going to investigate the applicability of this method to waveform data in China
following the data processing and analysis procedure in this study to contribute to development of
EEW systems in China.

ACKNOWLEDGEMENTS
In this study, we used strong motion data from KiK-net (Kiban Kyoshin network) operated by the
National Research Institute for Earth Science and Disaster Prevention (NIED). We also usedearthquake information in “The Seismological and Volcanological Bulletin of Japan” issued by theJapan Meteorological Agency (JMA). I am grateful to Dr. Shunroku Yamamoto for his variablelecture and to Dr. Mitsuyuki Hoshiba and Dr. Hayashimoto Naoki for providing me with variable
information on JMA earthquake early warning system and their comments on this work. I am gratefulto Dr. Toshiaki Yokoi and Dr. Nobuo Hurukawa for their valuable advises and comments.

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