MAGNITUDE DETERMINATION USINGACCELERATION RECORDS FROM
THE INDONESIAN STRONG MOTION NETWORK
Wijayanto∗
MEE09198

Supervisor: Tatsuhiko Hara∗∗

ABSTRACTWe developed an empirical magnitude formula for Indonesia using absolute value acceleration integral
computed from accelerograms. We used 68 records from the Indonesia strong motion network
operated by the Meteorological Climatological and Geophysical Agency (BMKG) for 13 earthquakesthat occurred in the Indonesia region between November, 2008 and March, 2010 with focal depths lessthan 150 km and Mw  5.9. We followed Wu and Teng (2004) with slight modification to include aterm for focal depth to construct a formula for the new magnitude MewBMKG. We used the leastsquare method under constraints to estimate the coefficients for absolute value acceleration integral,
hypocentral distances, and focal depths.
We compared the estimates of MewBMKG to the moment magnitudes from the Global
CMT catalog. We found a good agreement between them. The RMS of their differences is 0.27 in themagnitude unit. No saturation is observed up to magnitude 7.7. MewBMKG will be able to be obtained
within 3 minutes after earthquakes occurs using data from stations in the epicentral distance less than
300 km. This meets the requirement of the Indonesia Tsunami Early Warning System (InaTEWS). We
also determined a magnitude, MBMG, (Iman 2007), for which the maximum displacements obtained
from accelerograms are used. Differences between MBMG and the moment magnitudes from the Global
CMT catalog are smaller than those between MewBMKG and the moment magnitudes from the Global
CMT catalog. We discussed possible problems in calculation of these magnitude scales for theirimplementation into the InaTEWS.
Keywords: Magnitude, Accelerogram, Tsunami warning, InaTEWS.

1. INTRODUCTION
The Indonesia Tsunami Early Warning System (InaTEWS) was designed first in 2005 after the greattsunami of Aceh on December 26, 2004. From the lesson learned as well as from observations ofhistorical tsunamis in Indonesia, the first tsunami wave will arrive within 20 minutes after anearthquake occurs. The InaTEWS is currently issuing a tsunami warning within 5 minutes based onearthquake parameters such as magnitudes which should be obtained within 3 minutes after
earthquakes occur. However, magnitude determination sometimes underestimated very large events
such as the 2004 Aceh. Therefore, it is imperative for the InaTEWS to determine accurate magnitudes
as quickly as possible. The purpose of this study is to determine magnitudes of strong earthquakes
using acceleration records. For this aim, we determine an empirical magnitude formula base on theabsolute value acceleration integral. The result using this method is then compared with those from the
BMG magnitude, MBMG (Iman 2007) and moment magnitude, Mw, from the Global CMT catalog.

∗

Meteorological Climatological and Geophysical Agency (BMKG), Indonesia.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

∗∗− 115 −

2. DATA
We chose 13 earthquakes (Mw  5.9) whose focal depths are shallower than 150 km that occurred inIndonesia region between November, 2008 and March, 2010 (Table 1). We used the earthquake
parameters (origin time, latitude, longitude, and depth) from USGS and their Mw from the Global
CMT catalog. The accelerogram waveform data from the accelerograph network of the BMKG in their
ASCII format are used. All data were converted to SAC (Seismic Analysis Code) format.
Table 1. List of 13 events used in this study.
No

Event

1
2
3
4
5
6
7
8
9
10
11
12
13

TernateManokwari
Manokwari
Siberut
Tasikmalaya
Padang
Jambi
Saumlaki
Sinabang
Siberut
Tual
SaumlakiPagai

Origin time(yyyy/mm/dd, hh:mm:ss)
2008/11/09, 00:00:00.70
2009/01/03, 19:43:50.65
2009/01/03, 22:33:40.29
2009/08/16, 07:38:21.70
2009/09/02, 07:55:01.05
2009/09/30, 10:16:09.25
2009/10/01, 01:52:27.33
2009/10/24, 14:40:43.72
2009/12/09, 21:29:02.58
2009/12/23, 01:11:58.20
2009/12/26, 08:57:27.48
2010/02/15, 21:51:48.56
2010/03/05, 16:07:01.26

Epicenter(degree)
1.88N, 127.36E
0.41S, 132.88E
0.69S, 133.30E
1.48S, 99.49E
7.78S, 107.30E
0.72S, 99.87E
2.52S, 101.50E
6.13S, 130.38E
2.77N, 95.91E
1.43S, 99.39E
5.53S, 131.21E
7.19S, 128.78E
3.37S, 101.04E

Depth
(km)
96
17
23
20
46
81
9
130
19
19
83
130
26

Mw
(GCMT)
6.6
7.7
7.4
6.7
7.0
7.6
6.6
6.9
5.9
5.9
6.1
6.2
6.7

Mew
BMKG
6.25
7.46
7.11
6.97
7.11
7.71
6.59
6.77
5.99
6.19
6.44
5.84
6.28

MBMG
6.54
7.54
7.21
6.86
7.24
7.49
7.07
7.12
5.81
6.24
6.28
6.29
6.40

3. THEORY AND METHODOLOGY
3.1. Empirical Magnitude Formula using Absolute Value Acceleration Integral, ξEs
To compute the total effective shaking embodied in waveforms of near-field acceleration recordings,
Wu and Teng (2004) defined an absolute value
acceleration integral, ¥Es, as:Te

Es = ³Tp

V 2 + N 2 + E 2 dt ,(1)

where V, N, and E are vertical, north–south, andeast–west components of acceleration signals (ingal) respectively, Tp is the P-wave arrival time, andTe is the end-of-event time of the strong-shaking
duration. Te is defined as the time when theacceleration amplitude drops below 20% of the
maximum amplitude and remains below it for 5
seconds. An example of the acceleration records ofnorth-south component, absolute amplitude ofthree-component data, and absolute value
acceleration integral are shown in the top, middle,
and bottom traces of Figure 1, respectively.

reading

Figure 1. An example of waveform data andprocessed time series for the September 30,
2009 Padang earthquake (Mw 7.5) at PDSI
station.

The following is the formula used in this study:( )M = A + B ⋅ log Es + C ⋅ log( R ) + D ⋅ R + E ⋅ H ,− 116 −

(2)

where ¥Es is absolute value acceleration integral (cm/s), R is hypocentral distance (km), H is focal
depth (km). The coefficients A, B, C, D, and E are the model parameters. There are two differences
between this formula and that of Wu and Teng (2004). First, we included a term of focal depth.
Second, we did not include a term of site corrections considering a limited number of data. We set
initial values to each model parameter based on physical considerations and tendencies of data. Then,we performed inversion under constraints (e.g., Tarantola and Valette 1982) to determine the model
parameters so that the magnitudes from absolute value acceleration integral were consistent with
moment magnitude from the Global CMT catalog.
3.2. Determination of BMG Magnitude, MBMG
To compare the result of magnitudes obtained by absolute value acceleration integral, we obtained
BMG magnitude, MBMG introduced by Iman (2007). This MBMG formula also uses accelerogram data.
We used the same data as we did in magnitude determination using absolute value acceleration integral.
The formula of MBMG is as follows:

M BMG = log10 AD + 2.15 log10 R − 1.88 ,(3)

where AD is the maximum displacement amplitude (ȝm) and R is hypocentral distance (km). The
displacement is obtained by twice integration after a third-order Butterworth low cut filter with thecorner frequency of 0.1 Hz is applied. We manually picked the maximum displacement amplitude
within a reasonable time window corresponding to source time from three component records.

4. RESULTS
4.1. Magnitude Determination using ξEs
We used 68 acceleration records from 13 earthquake events shown in Table 1. After converting
waveforms and calculating the absolute value acceleration integral, we determined the coefficients A,
B, C, D, and E using the least square method under constraints. The estimated coefficients are 0.557,
1.310, 1.389, 0.001, and -0.005, respectively. Thus, the empirical moment magnitude is given by:( )MewBMKG = 0.557 + 1.310 log Es + 1.389 log( R ) + 0.001R − 0.005 H(4)

MewBMKG

Here, we use MewBMKG to reflect that this magnitude is derived empirically through absolute value
acceleration integral computed using acceleration records from the Indonesia strong motion network
operated by BMKG.
9.0
Figure 2 shows the comparison between the Mw
from the Global CMT catalog and the MewBMKG
8.0
magnitudes for 13 events used. The MwBMKG are
calculated from their average for each event. There is agood agreement between them. The RMS of their
7.0
differences is 0.27. MewBMKG does not saturate up tomagnitude 7.7. We plot the difference between
6.0
MewBMKG and Mw from the Global CMT catalog for allof 68 data as a function of hypocentral distance (Figure 3a)
and focal depth (Figure 3b), respectively. The differences
5.0
scatter around zero, which suggest that there is no
5.0
6.0
7.0
8.0
9.0
significant systematic bias with respect to magnitude,
Mw Global CMT
hypocentral distance and focal depth.
Figure 2. Comparison between Mw
GCMT and MewBMKG.

− 117 −

0.8

0.8

MewBMKG - MwGCMT(b) 1.2

MewBMKG - MwGCMT(a) 1.2

0.4
0.0
-0.4
-0.8

0.4
0.0
-0.4
-0.8

-1.2

-1.2

0

200

400

600

800

1000

1200

Hypocentral distance (km)

0

50

100

150

Depth (km).

Figure 3. Difference between the MewBMKG and Mw GCMT for all of 68 data used. (a) As afunction of the hypocentral distance. (b) As a function of the focal depth.

Figure 4 shows the comparisons of attenuation curves of Wu and Teng (2004) and this study
for the Siberut earthquake (Mw 6.7, depth 20 km) and the Saumlaki earthquake (Mw 6.9, depth 130km). The attenuation relations of Wu and Teng (2004) and that of this study are similar to each otherfor shallow events (Figures 4a). For deeper events (Figures 4b), there is a significant difference
between them. The attenuation relation of this study explains the observed ¥Es better. This is mainly
due to including the term for focal depth in this study.
Siberut, M=6.7, H=20 km

(a)

(b)

5.0
Wu&Teng

Wu&Teng

observation

4.0

observation

4.0

this studylog (¥Es) (cm/s)log (¥Es) (cm/s)

Saumlaki, M=6.9, H=130 km

5.0

3.0

2.0

1.0

This study

3.0

2.0

1.0

0.0

0.0

10

100

1000

10

100

Hypocentral Distance (km)1000

Hypocentral Distance (km)Figure 4. Attenuation curves of ¥Es obtained by this study and Wu and Teng (2004).

4.2. Magnitude Determination of BMG Magnitude,
MBMG

8.0

MBMG

The comparison between the Mw from the Global CMT
catalog and BMG magnitude, MBMG, for 13 events usedis shown in Figure 5. MBMG are calculated from theiraverage for each event. There is a good agreement
between them. The RMS of their differences is 0.23.
MBMG does not saturate up to magnitude 7.7.

9.0

7.0

6.0

5.0
5.0

6.0

7.0

8.0

Mw Global CMT

Figure 5. Comparison between Mw
GCMT and MBMG.

− 118 −

9.0

5. DISCUSSIONAs mentioned in sections 4.1 and 4.2, the RMS of the differences between these magnitudes(MewBMKG and MBMG) and Mw from the Global CMT catalog are 0.27 and 0.23, respectively.
Therefore, for the current dataset the estimates of MBMG agree better with Mw from the Global CMT
catalog. However, we would like to point out some possible problems in calculation of MBMG.
Figure 6 shows acceleration
records (stations RGRI and EGSI) for
the Siberut earthquake (Mw 6.7, depth 20km). The corresponding twice integrated
displacement records are also shown foreach acceleration record. Before
integration, a high pass filter with acorner frequency of 0.1 Hz is applied. It
will be desirable to study optimal filter inthis procedure. We observe that thedisplacement records sometimes havelarge amplitudes of long period waves(for example station EGSI). These long
period waves may cause overestimationof magnitude. Also, it will make it
difficult to measure the maximum
displacements automatically within areasonable time window corresponding
to source times.
Figure 6. Examples of the original accelerograms anddisplacement calculated by twice integration.

Figure 7 shows the distribution of the end-of-event times of ¥Es and the times of maximum
displacements. The times of maximum displacement are shorter than the end-of-event times. However,it will be difficult to pick the maximum displacement where there are long period waves. The times ofmaximum displacements picked automatically are longer than the end-of-event times in some stations
in which there are long period waves. Application of the procedure of this study to set an end-of-event
time will be helpful to make calculation of MBMG more stable. When we apply this technique, the timerequired to determine both magnitude scale are the same. The end-of-event times are less than 3minutes after earthquake occurrences at epicentral distances less than 300 km. Therefore, MewBMKG
will be able to obtain within 3 minutes using
end of event time of ¥Es
480
stations distributed at epicentral distances lesstime of maximum displacement (automatic picking)time of maximum displacement (manual picking)P arrival, Refference Depth 10 km
than 300 km. This meets the requirement of the
S arrival, Refference Depth 10 km
420
InaTEWS in which the location and magnitude

High-gain broadband seismograms
recorded at near-field distance may saturate forlarge earthquakes. Accelerogram data could be
utilized as the backup for such a case. Now, the
BMKG have launched a project to install 500
accelerographs spreading around Indonesia region.
Therefore, with this dense accelerograph network,
we can determine a reliable MewBMKG rapidly
for large earthquake from the near-field records
and will be useful for improvement of InaTEWS.

360
300
Time (s)of earthquakes should be determined within 3
minutes and the warning should be issued within
5 minutes after earthquakes occur.

240
180
120

− 119 −

60
0
0

200

400

600

800

1000

Epicentral Distance (km)Figure 7. Distribution of the end-of-event timesof ¥Es and the times of maximum displacement.

6. CONCLUSIONS
We developed an empirical formula to calculate a new magnitude MewBMKG for Indonesia using
absolute value acceleration integral, ¥Es, computed using acceleration records from the Indonesianstrong motion network operated by the Meteorological Climatological and Geophysical Agency(BMKG). We modified the formula given by Wu and Teng (2004) by including a term for focal depth.
Then, we determined the coefficients in the formula so that MewBMKG is consistent with the moment
magnitudes from the Global Centroid Moment Tensors solutions. The RMS of the differences between
MewBMKG and Mw from the Global CMT catalog is 0.27 in the magnitude unit for the current data
set used in this study consisting of the 68 records from 13 earthquakes. The shallow and intermediate
depth events are included in the data set. There is no significant systematic bias with respect tomoment magnitude, hypocentral distance (up to 1,200 km), and focal depth (up to 130 km). Our
results suggest that this magnitude scale does not saturate for large earthquakes up to magnitude 7.7.
The observed absolute value acceleration integral and those computed for this magnitude agree wellwith each other. MewBMKG will be able to be obtained within 3 minutes after earthquakes occurs
using data from stations in the epicentral distance less than 300 km, which meets the demand of
InaTEWS.
We also calculated the BMG magnitude, MBMG, introduced by Iman (2007), and compare
their estimates to Mw from the Global CMT catalog. The RMS of their differences is 0.23. Therefore,
MBMG agrees better with Mw from the Global CMT catalog. However, there might be possible
problems for this magnitude due to long period waves. Therefore, we suppose that MewBMKG will be
useful for rapid and reliable quantification of earthquake sizes, and improvement of InaTEWS.

RECOMMENDATION
The purpose of this study is to determine magnitudes using acceleration records without themagnitude saturation problem for large earthquakes. The BMKG should determine earthquake
locations and magnitudes within 3 minutes after earthquakes occur. MewBMKG will be able to beobtained within 3 minutes using data from stations in the epicentral distances less than 300 km. Thismethod can utilize accelerogram data as the backup of seismogram data when a large earthquake
occurs. The MewBMKG formula could be improved using accumulation of data from large events
and/or from near-field records after the planned 500 accelerograph stations are installed. Also, thereliability of MewBMKG formula should be tested using data from stations in the epicentral distancesless than 300 km. Intensive studies will be necessary to shorten the time required to obtain themagnitude by the method of this study and to treat the possible problem of tsunami earthquakes.

AKNOWLEDGEMENT
I would like to express my sincere gratitude to Dr. S. Ando, Dr. B. Shibazaki and Dr. Y. Fujii for theirvaluable suggestion to improve this manuscript.

REFERENCES
Earthquake Search; USGS, http://earthquake.usgs.gov/earthquakes/eqarchives/epic/
Global CMT Catalog Search, http://www.globalcmt.org/CMTsearch.html
Iman, S., 2007, Individual studies by participant at IISEE/BRI, Japan, 1, 1-28
Tarantola, A. and Valette B., 1982, J. Geophys. Res., 50, 159-170
Wu, Y. M. and Teng, T. L., 2004, Tectonophysics, 390, 205-216− 120 −