MAGNITUDE ESTIMATION FOR EARTHQUAKEEARLY WARNING (EEW) FOR EASTERN CAIROAND THE SOUTH OF SINAI
Ibrahim Zahra
MEE17702

Supervisor:

Bunichiro SHIBAZAKIABSTRACTIn this study, we examined 3 techniques of magnitude estimation for earthquake early warning (EEW):
𝑝corner period 𝜏𝑐 , peak predominant period 𝜏𝑚𝑎𝑥 and initial peak displacement Pd. We established thebest fit relation between each of these parameters and magnitude. We also examined real-timeparameters like the filter cut-off frequency and the time-window of estimation in order to find the values
that give the best fit relation in each technique. We chose eastern Cairo and the South of Sinai becauseof its high importance in Egypt’s economy and future urbanization as well as the moderate to highseismic activity in this region. We used a dataset of 20 earthquakes between 1999 and 2015, from theEgyptian National Seismic Network catalog, in the target region. All of the selected events, except for𝑝one, have local magnitude over 4.0. The results of 𝜏𝑐 and 𝜏𝑚𝑎𝑥 show that the error in magnitude
estimation could reach up to 1.0, in this dataset. The results also indicate that Pd is the best parameter for
magnitude estimation in EEW. Based on results, we made recommendations that could be extended into
the action plan required to achieve an EEW system in Egypt.
𝑝Keywords: Earthquake early warning (EEW), Corner period 𝜏𝑐 , Peak predominant period 𝜏𝑚𝑎𝑥 , Initial
peak displacement Pd

1. INTRODUCTION
Rapid magnitude estimation is a critical task forearthquake early warning (EEW) systems because
EEW utilizes the few seconds between the P-wave anddamaging S-waves or surface waves to minimize thedamage. The magnitude estimation methods in EEW
can be categorized into two categories: methods use
time-domain parameters like initial peak displacement,
and frequency-domain parameters like corner period𝑝𝜏𝑐 or peak predominant period 𝜏𝑚𝑎𝑥 . All theseparameters should be determined in the first few
Figure 1. The selected region, events andseconds from the P-wave onset.
ENSN stations.
The purpose of this study is to determine
which is the best parameter that can be used for magnitude estimation and establish the relationshipbetween the magnitude and each of these parameters, which could be used in the EEW system. Also,
we would determine the best processing parameters that give the best results such as the usage of filters
and the time-window of measurement as well as testing the usability of short-period data after making
a simplified instrumental correction that can be applied in real-time for EEW purpose.


National Research Institute of Astronomy and Geophysics (NRIAG), Egypt.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

12. STUDY AREA AND DATA SELECTION
The target area, in Figure 1, is eastern Cairo and the South of Sinai, which is very important for Egypt’s
economy and in urban development. Many new cities were established in this area in the past 20 years,
which have millions of inhabitants, along the highways connecting Cairo to Suez and Ismailia.
Moreover, a few new cities under establishment like the new capital city in Egypt’s vision for 2030.
The future projects contain high rise buildings and high-speed train in addition to a suspension bridgeconnecting Egypt and Saudi Arabia over the Gulf of Aqaba. The target area also was selected becauseof its seismic activity because of the plate boundary along the Red Sea.
The selected dataset, in Figure 1, contains 20 events from the Egyptian National Seismic
Network (ENSN) of local magnitude over 4.0, except for one M3.7 to enhance regression analysis. The
events occurred between 1999 and 2015. While the largest event recorded in the study was of magnitude
7.2 in 1995 in the Gulf of Aqaba, unfortunately, we do not have local data available because ENSN
was established in 1997. The events were selectedbased on data availability limitations. Someparameter estimation requires using only broadband
data and other parameters require limited epicentral
distance between the station and the events. Also,
all the selected events exist in one or more of theseinternational catalogs: USGS, IRIS, ISC and EMSC
catalogs, because the magnitude determined in the
ENSN catalog was inconsistent with the results ofsome events.

3. THEORY AND METHODOLOGY
3.1. Corner period 𝝉𝒄Figure 2. A simplified flowchart of Dr. Yamada’s
program for calculating 𝜏𝑐 (Yamada and Mori,
We used the program provided by Dr. Yamada 2009).
(Yamada and Mori, 2009) for determining 𝜏𝑐 . The
simplified flow chart of Figure 2 shows explains how it works. First, we input a velocity record, remove
the mean (dcoff), filter the data (butter_filter_data) using Butterworth high pass filter to obtain modified
velocity, integrate (sacint) and differentiate (diff) to obtain modified displacement and modified
acceleration, respectively. Modified velocity andacceleration are used in picking (ppick3) using Allen(1978) STA/LTA method, and then the picking is tuned
for more accuracy (aicpick) using AR-AIC (Takanami
and Kitagawa, 1988). The modified velocity anddisplacement are used to calculate 𝜏𝑐 (centf) according
toKanamori(2005):𝜏𝑐 =𝜏𝜏

2𝜋⁄√∫0 0 𝑢̇ 2 (𝑡)𝑑𝑡⁄∫0 0 𝑢2 (𝑡)𝑑𝑡 , where 𝑢(𝑡) is themodified displacement, 𝑢̇ (𝑡) is the modified velocity
and 𝜏0 is the selected time-window of measurement.
𝒑3.2. Maximum predominant period 𝝉𝒎𝒂𝒙 and initial
peak displacement Pd

2

Figure 3. Modification to the program to𝑝𝑝compute Pd and 𝜏𝑚𝑎𝑥 , where 𝜏𝑚𝑎𝑥 _1 is a a
modified version by Shieh et al. (2008).

𝑝

We modified the previous program to obtain 𝜏𝑚𝑎𝑥 and Pd, as shown in Figure 3 We used the same
modified displacement to calculate Pd, which is the absolute maximum displacement in the selected t0
time window from the P-wave onset. Then, Pd value should be converted into physical units like cm or
m to be used in magnitude estimation.
𝑝𝑝𝑝Both modified velocity and acceleration are used to calculate 𝜏𝑚𝑎𝑥 and 𝜏𝑚𝑎𝑥 _1. 𝜏𝑚𝑎𝑥 is𝑝calculated after Allen and Kanamori (2003). First calculate the predominant period 𝜏𝑖 at each sample:𝑝𝜏𝑖 = 2𝜋√𝑋𝑖 ⁄𝐷𝑖 , where 𝑖 is the sample number, 𝑋𝑖 = 𝛼𝑋𝑖−1 + 𝑥𝑖2 , where 𝑥𝑖 is the modified velocity,
𝐷𝑖 = 𝛼𝐷𝑖−1 +(𝑑𝑥𝑖 ⁄𝑑𝑡)2𝑖 , where (𝑑𝑥𝑖 ⁄𝑑𝑡)𝑖 is the modified acceleration, and 𝛼 = 1 − 𝑑𝑡 is a𝑝𝑝smoothing factor where 𝑑𝑡 is the sampling interval. Then, 𝜏𝑚𝑎𝑥 is the maximum of 𝜏𝑖 in the specific𝑝𝑝𝑝time window. 𝜏𝑚𝑎𝑥 _1 is the same as 𝜏𝑚𝑎𝑥 except for setting the first 0.05 s of 𝜏𝑖 to zero, to stabilize𝑝the values of 𝜏𝑚𝑎𝑥 (Shieh et al., 2008).
3.2. Short-period instrumental correction
We have written a new subroutine to correct the response of short-period seismograms following the 3stage filtering proposed by Yamada et al. (2014). The suggested correction was for enabling the usageof the high-sensitivity network (Hi-Net) short-period stations, to be used in the JMA EEW system. JMA
is currently using their own strong-motion network, which is not as dense as Hi-Net, for EEW system,
to calculate Pd. Figure 4 shows the amplitude response of each stage.

Figure 4. Amplitude response of each stage: a) is a 12 s (0.083 Hz) HPF, b) is a 6 s HPF with integrator(solid-line) and without integrator (dashed-line), and c) is a simplified instrument correction (solid-line)
which is the inverse response of a short-period seismometer with a natural period of 1 s.
The reason behind using 3 stages is that Pd tends to saturate in short-period seismograms
especially for large earthquakes because the long period waves that are radiated by these earthquakes
are heavily damped by short-period seismometers. The first stage is a 12 s high pass filter (HPF) whichshould limit the noise waves longer than 12 s because it would be amplified after the instrument
correction. The second stage, 6 s HPF, is the main filter used by JMA (Katsumata, 2008) except forhaving single integrator to convert velocity to displacement, while JMA EEW system uses double
integration to convert acceleration to displacement. The third stage is a simplified instrumental
correction (Zhu, 2003), which has the opposite response of a short-period seismogram with 1 s natural𝑝period. We shall extend this method to calculate 𝜏𝑐 and 𝜏𝑚𝑎𝑥 using short-period seismograms. In
such case, to obtain corrected velocity, 2nd stage should not include integration.

4. RESULTS AND DISCUSSION
4.1. Corner period 𝝉𝒄3

Using only broadbandb)data, we find the besta)fit
relationshipbetween log( 𝜏𝑐 ) andthe magnitude. We
tested the relation
betweendifferent
combinations of filter
cut-off period (5, 6 or
13 s) and timewindow (2, 3 or 4 s).
For each combination, Figure 6. 𝜏 vs. magnitude: a) From the ENSN local catalog, b) average of𝑐
we determined the International catalogs' magnitudes. Open circles are single station value andlinear relation using closed circle is the average value for one event.
magnitudes from thelocal catalog or using average magnitudes among international catalogs. The results always were betterin case of the average of international catalogs’ magnitudes. That is shown in Figure 5 in terms of thestandard error (SDE) and the scattering. We also tried using short-period data after instrumental
correction but the resulted values of 𝜏𝑐 were almost constant regardless of the magnitude. The best
results were obtainedusing 5 s high passfilter and 4 s time
window, and the best
linear relation was:𝑀 = 0.585 ×𝑙𝑜𝑔(𝜏𝑐 ) + 4.438 (1)4.2. Maximum
predominant period
𝒑
𝝉𝒎𝒂𝒙

𝑝

Figure 5. 𝜏𝑚𝑎𝑥 vs. magnitude: a) broadband data only, b) broadband +Using broadband data corrected short-period. Small constant values around 0.03 s and 0.06 s are
only, in Figure 6 (a), shown in b).
we could not obtain a𝑝linear relationship between 𝜏𝑚𝑎𝑥 and the magnitude. We tried the corrected short-period data and the𝑝results became better, except for some values of 𝜏𝑚𝑎𝑥 that were almost constant at 0.031 or 0.061 s, as
shown in the bottom of in Figure 6 (b). When we limited
the epicentral distance to ≤ 250 km between the event andthe station, these small values disappeared and we obtained
the linear relationship in Figure 7.
As we explained with 𝜏𝑐 , we tested themagnitude from the local catalog and the averagemagnitude of international catalogs. We found the average𝑝magnitude has a better linear relation with 𝜏𝑚𝑎𝑥 , exactly
the same as 𝜏𝑐 . We tested the same combinations of filter
and time-window, and found the best relation using both
broadband and corrected short-period data, filtered by 5 s
HPF and 2 s time-window (which is shown in Figure𝑝7):
𝑀 = 0.593 × 𝑙𝑜𝑔(𝜏𝑚𝑎𝑥 ) + 4.203(2)𝑝
Figure 7. Best results of 𝜏𝑚𝑎𝑥 vs. M
using broadband + corrected short-period
data with 5 s HPF and 2 s time-window.

44.3. Initial peak displacement Pd

Figure 8. Best results of estimated magnitude MPd vs. average magnitude of international catalogs with
5 s HPF. a) broadband + short-period data without correction with 4 s time window, b) after correcting
short-period, and c) the same as b) except for 3 s time-window.
We studied Pd for both broadband and shortperiod seismograms, with or without
correction for the short-period (Figure 8 (a);(b)). There was only a small enhancement but
this enhancement might have been increased
if we had a large earthquake (M6.0 or higher)
which would have caused Pd values tosaturate much in short-period seismograms.
All the used data had a limited epicentral
distance up to 200 km. Using the same
previous procedure of comparing results incase of using local catalog magnitude vs.
using the average of international catalogs’
magnitude. Again, the average international Figure 9. Scaling between Pd (nm) and R (km) for
magnitude was more consistent. The different magnitude ranges with different colors. The
improvement due to using 4 instead of 3 s straight lines represent the obtained best fit relationshiptime-window was insignificant in all cases in Eq. (3) at selected magnitudes M.
(in the order of 0.001 of SDE) as shown in
Figure 8 (b) and (c). The 4 s time window, as expected, gave a slightly better results, because the longer
time window would allow more phases of the P-wave. The best combination was also with 5 s HPF and4 s time-window, and in this case the best linear regression relation (in Figure 8 (b)) is:(3)
𝑀 = 0.9 + 0.571 × 𝑙𝑜𝑔 𝑃𝑑 + 0.571 × 𝑙𝑜𝑔 𝑅
which in this case a multi-variable regression between magnitude and both log(Pd) in nm and log(R) in
km where R is the epicentral distance, as shown in Figure 9. The results suggest that Pd is the bestparameters with the least standard error. The drawback of using Pd is obviously the need of knowing R
which mean that estimated magnitude would be dependent on the estimated epicentral location, i.e.,
wrong location would result in wrong magnitude estimation.

𝑝

Figure 10. The error in estimation vs. magnitude for 𝜏𝑐 , 𝜏𝑚𝑎𝑥 and Pd. MPd has the smallest range oferror in magnitude estimation (−0.4 ≤ 𝐸𝑟𝑟𝑜𝑟 ≤ 0.5).

5Comparing the results of the three parameters, in Figure 10, we can see that the range of error
in estimation is the least using Pd.

5. CONCLUSIONSAs the results suggested, initial peak displacement Pd has the strongest relation with the magnitude,𝑝while 𝜏𝑐 or 𝜏𝑚𝑎𝑥 could still be used for different purpose, like picking or filtering out teleseismic𝑝events. Although magnitude estimation from 𝜏𝑚𝑎𝑥 does not require the knowledge epicentral distance,𝑝limited epicentral distance still needed before calculating 𝜏𝑚𝑎𝑥 .
Results also suggest that simplified Instrumental correction can be used with short-period𝑝seismograms, in case of Pd and 𝜏𝑚𝑎𝑥 , Although the enhancement in results by the correction of shortperiod was small, it could have a higher enhancement in case of a range magnitude earthquake. The
analysis of data indicated that the ENSN catalog of local magnitudes should be reviewed and unified.
The best filter cut-off frequency was 5 s (0.2 Hz) in all the techniques tested, but this also would dependon the range of magnitudes of the analyzed dataset. If the dataset had included a M6.0 earthquake, it
might have needed a filter with a longer cut-off period than 5 s. Also, the difference between 3 and 4 stime-window was insignificant. Therefore, the choice of the time-window between 3 and 4 s depends
on the desired target time of computation (small effect on the estimation accuracy).

6. RECOMMENDATIONS
The limitations of the data available indicate the need for more stations in the target area, especiallyalong the Red Sea shore near to the active faults. New stations should be established with 20 or 30 kmof spacing. Strong-motion sensors can be used, which is a cheaper choice than broadband seismometersand do not require special treatment in station construction as broadband.
This study could be enhanced in case of larger magnitude events, ≥ M6.0, included in the
future. Also, different studies should be conducted in other EEW subjects, such as automatic picking,automatic location and prediction of the seismic intensity. The EEW system software could be
developed using open source platform, such as Earthworm automatic earthquake analysis software thatis currently operated in the Egyptian National Seismic Network.

ACKNOWLEDGEMENTS
I would like to express my gratitude to my supervisors Dr. Bunichiro Shibazaki for his continuous
support and valuable suggestions. Also, a debt of gratitude is owed to Dr. Masumi Yamada for providing
her program and her expert advice.

REFERENCES
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Allen, R.M., and Kanamori, H., 2003, Science, 300, 786-789.
Kanamori, H., 2005, Annu. Rev. Earth Planet. Sci., 33, 195-214.
Katsumata, A., 2008, JMA Quarterly Journal of Seismology, 71, 89-91.
Shieh, J.T., Wu, Y.M., and Allen, R.M., 2008, Geophysical Research Letters, 35.
Takanami, T., and Kitagawa, G., 1988, J. Phys. Earth, 36, 267–290.
Yamada, M., and Mori, J., 2009, Journal of Geophysical Research: Solid Earth, 114.
Yamada, M., Tamaribuchi, K., and Wu, S., 2014, J. Jpn. Assoc. Earthq. Eng, 14, 21-34.
Zhu, L., 2003, Geophysical Research Letters, 30.

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