Citation: Widiarso, A., A. Katsumata (2022), Rapid magnitude estimation using local earthquake waveform
data and the application to earthquakes in Indonesia including the 2010 Mentawai tsunami earthquake,
Synopsis of IISEE-GRIPS Master’s Thesis.

RAPID MAGNITUDE ESTIMATION USING LOCAL
EARTHQUAKE WAVEFORM DATA AND THE
APPLICATION TO EARTHQUAKES IN INDONESIAINCLUDING THE 2010 MENTAWAI TSUNAMI
EARTHQUAKE
Aziz Widiarso1
MEE21717

Supervisor: Akio KATSUMATA2ABSTRACTThis study aims to estimate earthquake magnitude quickly using vertical component data from
Broadband seismographs for improvement of tsunami warnings. We formulate using displacement andintegrated displacement data with a cut-off of more than 100 seconds. Empirical relationships wereobtained for displacement and integrated displacement with moment magnitude. Data selection ofseismic records was done before estimating the relationships of amplitudes by observing the amount ofdata to unselect records with gaps and the maximum amplitude to eliminate spike data. We compared
the magnitudes of the formulas for displacement (MD) and integrated displacement (MID). We found thatMID yielded better estimates than MD. MID also produced appropriate estimates for earthquakes withstrike-slip focal mechanisms. On the other hand, for deep earthquakes, MD yielded a better estimate. In
the case of the 2010 Mentawai tsunami earthquake, MID produced an underestimated whereas theestimate was obtained no more than 3 minutes after the earthquake origin time.
Keywords: Magnitude estimation, MID, MD, tsunami earthquake.
1. INTRODUCTION
Magnitude is one of the principal parameters of an earthquake; it represents the released energy andpotential impact on the area near the earthquake's epicenter. In contrast to the earthquake's intensity witha different value for a particular area, an earthquake has one value of magnitude. By using earthquake
magnitude information, a government can determine the appropriate response regarding the evacuationof affected areas and warnings for potential disasters such as tsunamis. There are two methods toestimate the magnitude of an earthquake: empirical method and theoretical method. The empiricalmethod uses evidence-based on gathered experience or observation data without any or a small amountof theoretical evidence. On the other hand, the theoretical method works with logical assumptions andtheory based on research.
Badan Meteorologi Klimatologi Geofisika (BMKG) uses Seiscomp3 for processing theearthquake waveform. Seiscomp3 is a seismological software for data acquisition, processing,
distribution, and interactive analysis developed by GEOFON, Germany. Seiscomp3 offers various typesof magnitude estimation inside the program. Including empirical methods such as MLv, mb, mB, and MJMA
1
2

Agency for Meteorology, Climatology, and Geophysics, Indonesia.
Professor, Toyama Univ.

1and theoretical methods MWP and MW by the waveform inversion methods. BMKG uses summary
magnitude (MSUM) in the first information release and updates the magnitude using MW afterwards. MSUM
is a weighted average of the individual magnitudes over by Seiscomp3. MSUM gives attempts to be thebest possible compromise between all magnitudes. Since MSUM depends on the calculation of othermagnitudes, the accuracy and speed of the calculation are related to other magnitudes. For the local
station, MSUM considers MLv and MJMA. However, local magnitude (MLv) is saturated for earthquakes
bigger than 6.5 (Sitaram & Borah, 2007), and MJMA indicated saturation during the 2011 Great East
Japan earthquake (Hirose et al., 2011). It became necessary to formulate a new magnitude estimationthat can estimate the proper magnitude in 5 minutes to give better earthquake information and tsunami
warning.
2. DATAWe used data from vertical component broadband seismographs because it is more sensitive to longperiod waves, which can overcome the problem of magnitude saturation (Aki, 1967). Broadband
seismograph records long-period seismic waves well, but instrument correction is still necessary tonormalize the more extended period waves. We used 135 earthquakes of more than magnitude 6 in 10
years period from 2012 to 2021. We eliminated 14 deep earthquakes (>400 km) from our calculation.
The distribution of earthquakes can be seen in Fig. 1, where the open circle represents the earthquake,and the triangle symbolizes the broadband seismograph.

Figure 1. Distribution of the 2012-2021 earthquakes and broadband seismometers.
3. METHODOLOGY
We formulated the empirical earthquake magnitude formula by observing the relation between
magnitude to the maximum amplitude of long period wave and hypocentral distance of the stations.
Several steps of data processing are required for the process of calculating the formula.
3.1 Data preparation
Instrumental response correction was conducted in the time domain to normalize the damped long period
waves during the recording process. In time domain process is necessary for rapid real-time processing.
We used the recursive filter for instrument response correction proposed by Katsumata et al. (2021).

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The recursive filter was obtained by calculating the z-transform of the inverse response in the Laplacetransform expression. The recursive formula utilized the two lower poles of station to calculate theconstants used in the formula. We transform the velocity data into displacement and integrated
displacement by applying the numerical integrations. Then, low-cut Bessel filters with cut-off 100
seconds were applied to suppress the baseline shifting due to multiple integration prosses. The cut-offof 100 seconds was chosen refers to Katsumata et al. (2013).
3.2 Maximum amplitude data selection
Most magnitude estimation formulas require a specific time window to determine the maximum
amplitude to be selected. The time window serves to specify what part or phase of the seismic wave will
be used in the calculation. For example, MWP uses the P wave phase of an earthquake wave. A wide time
window will produce a magnitude with a small error but require more time in the calculation. On theother hand, a narrow time window results in a fast calculation with a high error value (Leyton et al.,2018). We calculated magnitude formula using any earthquake wave phase adopted from Katsumata etal. (2013). When any phase can be used for calculations, a specific time window for finding the
maximum amplitude is not required. This makes the calculation process simple and robust.
3.3 Data selection
Our earthquake seismic wave database contains bad quality data such as gaps, spikes, and high noise
data. We want to eliminate the bad quality data from the formulation. The gaps data were selected byobserving the number of data recorded in one stream, and spikes data were removed observing thedeviation with the logarithmic regression for each earthquake event. We calculated logarithmic
regression of maximum amplitude to hypocentral distance for each earthquake, then calculated thestandard deviation of maximum amplitude to model. We got 0.59 as standard deviation from our dataset.
The data limit is determined to be twice the standard deviation, and stations that exceed this limit are
assumed to be the bad quality data.
3.4 Formulation
The empirical method uses evidence based on observational data that has been collected. We looked forthe correlation between the maximum amplitude and station distance by determining the values of theconstants a, b, and c in Eq. 1.
𝑀 = 𝑎 log10 𝐴 + 𝑏 log10 𝑅 + 𝑐 ,(1)
where A and R are the maximum amplitude and hypocentral distance, respectively. Determination of
constants a, b, and c is done by minimizing the difference between M in Eq. 1 and MW from Global CMT.
Constant a was determined first, then b and c were calculated using the weighted least square method.
When the values of constants a, b, and c are determined simultaneously, the great earthquake will diverge
further from MW (Katsumata et al., 2013). The weight factor was used because of the least frequent
occurrence of large earthquakes.
4. RESULT AND DISCUSSION
The a, b, and c constants derived from the weighted least square method are shown in Table 1. MD has
a higher a constant rather than MID. This relationship has been seen in previous research for velocity anddisplacement data (Katsumata, 2001; Katsumata et al., 2013, 2021). The magnitude quality was thenassessed by comparing the MID and MD to the MW from Global CMT.
MD has differences ranging from -0.38 to 0.35 with a standard deviation of 0.1453, while
MID differences range from -0.4 to 0.32 with a standard deviation of 0.1269. MID gives a better magnitude
estimation than MD by the smaller standard deviation. Figure 2 shows the distribution of magnitudedifferences of MD and MID to MW. MD has more dispersed data than MID, which is denser around the zero3

line. Large earthquakes are estimated well with a difference of ±0.1 magnitude compared to small
earthquakes with ±0.3 magnitude, even though small earthquakes have a more significant number ofoccurrences in this data set.
Table 1. Constants for MD and MID.
a
b
c
MD

0.898

1.308

5.835

MID

0.789

1.167

5.359

A

For comparison with thecurrent system at BMKG, the difference
between MSUM and MW is shown in Fig. 2.
MSUM has differences ranging from -0.67 to
0.26 with a standard deviation of 0.1556.
MSUM tends to give underestimatedmagnitude since most magnitudes are
below the zero line. Small earthquakes arereasonably well estimated, but large
earthquakes are remarkably underestimated.
This shortcoming is terrible for a tsunami
warning considering that large earthquakes
have the potential to generate a tsunami.
Indonesia has a high potential
for strike-slip earthquakes. Intraplate faults
are found in most areas, such as the Great
Sumatran and Palu-Koro faults. In the dataset, all earthquakes with a magnitude
more than 7.5 were strike-slip. The
strike-slip earthquake is shown as a red
circle in Fig. 3. The magnitude estimation
gives appropriate results even for strikeB
slip, even though the data used for the
calculation was the vertical component
seismogram that is sensitive to a typical
dip-slip earthquake.
As we mentioned, the 14 deep
earthquakes were eliminated from thecalculation. The inhomogeneous anelastic
attenuation (QS) properties at the crust,shallow and deeper parts of the upper
mantle, could impact the recorded
amplitude by seismograph at the surface(Katsumata, 2001). The properties
difference differ from amplitude scaling forCshallow and deep earthquakes. In addition,
as deep earthquakes do not have enoughenergy to move the surface, there is no
Figure 2. Difference of moment magnitude (MW) to potential for a tsunami. We compared themagnitude from displacement (A), integrated magnitude estimation of MD, MID, and MSUM
displacement (B), and summary magnitude (C).
for 14 earthquakes deeper than 400 km. In
contrast to the results for shallow

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earthquakes, MD gives a better estimation
than MID for deep earthquakes, while MSUM
has the most underestimated value (Fig. 4).
For the estimation of time requiredin the calculation, we calculated the MID forthe 2010 Mentawai tsunami earthquake
over time using 22 nearest seismographs
and then compared it to MSUM. Figure 5
shows MID, MSUM, MBA, and MW as the solid
black line, solid grey line, blue dash line,
and red dash line, respectively. MBA ismagnitude formula proposed by Katsumata,
et. al. (2021) for tsunami earthquakes. The
Figure 3. Magnitude estimation for strike-slip earthquake. MBA formula can estimate the magnitude
and source duration of an earthquake bycomparing the observation data andsynthetic data with various source duration.
The MBA precisely estimated the 2010
Mentawai earthquake by 7.84. The MSUM
fluctuated in the first 2 minutes and reached
the final magnitude of 7.1 after 2.5 minutes.
On the other hand, MID raised stably andreached 7.4 after 3 minutes. The differencein characteristics is due to the direct link
between MID and the earthquake waveform,
whereas MSUM is calculated from theaverage of other magnitudes. Threeminutes is a good time for tsunami warning
dissemination considering the tsunami
Figure 4. Magnitude estimation for deep earthquakes.
golden time at the Sunda Strait segment
varies from 5 to 40 minutes (Ponangsera et al., 2021). However, the estimation was underestimated by
0.4 from the moment magnitude as expected.

Figure 3. The 2010 Mentawai tsunami earthquake magnitude estimation.

55. CONCLUSION
We calculated an empirical formula for rapid earthquake magnitude estimation using Broadband
seismograph data. The formula was formulated by observing the relationship between the maximum
logarithmic amplitude of earthquake waveform with a cut-off of more than 100 seconds and thelogarithmic hypocentral distance of each station with the moment magnitude (MW) of the Global CMT.
Two formulas were proposed in this research, ie., magnitude displacement (MD) and magnitude
integrated displacement (MID).
MID produced a better magnitude estimate than MD with smaller standard deviation values,
0.1269 and 0.1453, respectively. The MSUM formula used by BMKG for information on the firstearthquake and tsunami tended to underestimate the magnitude of a large earthquake. MID provided areasonable estimate of earthquakes with a strike-slip mechanism even though it only used verticalcomponent data in its calculations. MD and MID gave an underestimated magnitude for deep earthquakes,
but overall, MD was better for deep earthquakes.
Tsunami earthquakes tend to give underestimated magnitude estimates. We calculated MID
and MBA for the 2010 Mentawai tsunami earthquake. As expected, MID produced an underestimatedmagnitude of 7.4 with a difference of 0.4 from MW, while MBA yielded a better estimate of 7.84. The MID
estimation speed was quite good, producing a final magnitude 3 minutes after the earthquake's origin
time.
ACKNOWLEDGMENT
I would like to express my deepest appreciation to my supervisor Dr. Akio Katsumata-sensei and myadvisor Dr. Bunichiro Shibazaki-sensei for the knowledge and guidance that enabled me to finish myresearch. Second, I want to thank BMKG for providing the data, all my courses mate, and my fiance forsupporting me through all these courses.
REFERENCES
Aki, K. (1967). Scaling law of seismic spectrum. Journal of Geophysical Research, 72(4), 1217–1231.
https://doi.org/10.1029/JZ072i004p01217
Hirose, F., Miyaoka, K., Hayashimoto, N., Yamazaki, T., & Nakamura, M. (2011). Earth, Planets andSpace, 63(7), 513–518. https://doi.org/10.5047/eps.2011.05.019
Katsumata, A. (2001). Magnitude determination of deep-focus earthquakes in and around Japan with
regional velocity-amplitude data. Earth, Planets and Space, 53(5), 333–346.
https://doi.org/10.1186/BF03352390
Katsumata, A., Tanaka, M., & Nishimiya, T. (2021). Rapid estimation of tsunami earthquake
magnitudes at local distance. Earth, Planets and Space, 73(1), 72. https://doi.org/10.1186/s40623021-01391-7
Katsumata, A., Ueno, H., Aoki, S., Yoshida, Y., & Barrientos, S. (2013). Rapid magnitude determinationfrom peak amplitudes at local stations. Earth, Planets and Space, 65(8), 843–853.
https://doi.org/10.5047/eps.2013.03.006
Leyton, F., Ruiz, S., Baez, J. C., Meneses, G., & Madariaga, R. (2018). How Fast Can We Reliably
Estimate the Magnitude of Subduction Earthquakes? Geophysical Research Letters, 45(18), 9633–
9641. https://doi.org/10.1029/2018GL078991
Ponangsera, I. S., Kurniadi, A., Ayu Puspitosari, D., & Hartono, D. (2021). Determination of tsunami
run-up and golden time in the megathrust subduction zone of the sunda strait segment. E3S Web
of Conferences, 331, 07007. https://doi.org/10.1051/e3sconf/202133107007
Sitaram, M. V. D., & Borah, P. K. (2007). Signal duration and local Richter magnitudes in northeast
India: An empirical approach. Journal of the Geological Society of India, 70(2), 323–338.

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