RAPID SOURCE PARAMETER DETERMINATIONAND EARTHQUAKE SOURCE PROCESS IN
INDONESIA REGION
Iman Suardi∗
MEE06012

Supervisor:

Yuji YAGI∗∗
Akio KATSUMATA∗∗∗
Osamu KAMIGAICHI∗∗∗∗

ABSTRACT
We proposed a magnitude determination method for the regional network of the Meteorological andGeophysical Agency (MGA), Badan Meteorologi dan Geofisika (BMG). This method was developed
from the empirical formula from Richter’s magnitude by using least square method. We use
accelerogram from regional accelerometer network of BMG for one month range. The magnitude
formula of BMG is as follows:

M BMG = log10 AD + 2.15 log10 R − 1.88
where AD is the maximum displacement amplitude (μm), and R is hypocentral distance (km),respectively. The comparisons in magnitudes among this formula, Tsuboi’s formula (1954), and MW
from Global CMT indicate that this formula could be improved after seismic records are accumulated
in BMG.
Also we determined the moment tensor for the earthquakes by using program written by Kikuchi forcalculating Green’s function and inversion program coded by Yagi. To understand the state of tectonic
stress field of area around epicenters, we investigated the tectonic feature by analyzing the focal
mechanism obtained by moment tensor inversion.

Keywords: Accelerometer, Magnitude formula, Moment tensor inversion.
INTRODUCTION
When the great earthquake of Aceh occurred in December 26, 2004, more than 200,000 lives in total
have been taken as victims, and it is clear that early warning of earthquake and tsunami information isimportant. However, it is too difficult to perform short-term prediction of earthquake, so early warning
information is an important to mitigate tsunami disaster. A new system of tsunami early warning iscarried out as soon as possible. The government of Republic Indonesia through the Meteorological andGeophysical Agency/MGA (BMG) in cooperation with the donor countries has been building the new
system of Tsunami Early Warning System (TEWS) oriented to reduce the loss of lives caused bytsunami attack. Therefore rapid and accurate determination of earthquake source parameters is of anurgent necessity. The purpose of this study is to rapidly determine source parameter and moment
tensor inversion related to tsunami early warning system. The rapid source parameter determination is
focused on determining the earthquake magnitude.
∗

Meteorological and Geophysical Agency (BMG) of Indonesia.
Assoc. Professor, Graduate School of Life and Environmental Sciences, University of Tsukuba, Japan.
∗∗∗
Meteorological Research Institute JMA, Japan.
∗∗∗∗
Japan Meteorological Agency (JMA), Japan.
∗∗

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DATA
In this study, the accelerogram was converted into displacement record with SAC transfer command tomeasure maximum displacement. A third-order Butterworth filter of 0.1Hz cut-off frequency was usedas the high-pass filter. Therefore we used a peak displacement which is used as maximum
displacement amplitude.
Table 1. Earthquake event list from the Global CMT (4 March 2007 – 25
April 2007).
MW Global
Depth
No. Event yyyymmdd
Location
CMT
(km)
1

event120070309-6.34S, 130.23E

5.6

149.3

2

event2

20070313-8.08S, 117.94E

5.6

24.1

3

event320070315-0.73S, 127.60E

5.4

12.0

4

event420070315

4.19N, 127.04E

5.2

18.5

5

event520070317

1.30N, 126.37E

6.2

40.7

6

event620070326

0.98N, 126.05E

5.5

29.0

7

event720070331

1.55N, 122.63E

5.6

21.9

8

event820070407

2.72N, 95.47E

6.1

12.0

We retrieved earthquake
event list from the CMT
global catalog with thesame time range to use MW
as reference magnitude.
We got only 8 events fromthis continuous waveform
data due to many bad
waveforms (Table 1). Also
we retrieved teleseismic
body-wave (P waves) data
recorded at the DataManagement Center of theIncorporated
Research

Institution for Seismology (IRIS-DMC) stations through the internet.

THEORY AND METHODOLOGY
Magnitude Determination of BMG
In this individual study, we propose a magnitude determination method of BMG for the regional
network. The empirical formulas from Richter’s magnitude are the relationships among moment
magnitude, MW, the maximum displacement amplitude, AD (m), and hypocentral distance, R (km),respectively (Richter, 1935). It can be approximately expressed as

α D M W = log10 AD + log10 R + β D R + γ D
α D M W = log10 AD + β D log10 R + γ D

(1)
(2)

where D is an index for displacement, αD is coefficient correction for magnitude, βD is coefficientcorrection for distance, and γD is a constant coefficient, respectively. We denote equation (1) and (2) as
type1 and type2 empirical formulas, respectively. We assume the coefficient for log10AD is 1.0, sinceformer researchers (ex., Utsu, 1982; Katsumata, 1996) indicated that the value of 1.0 is suitable toproduce comparable magnitude to MW on average. We determine the coefficients by using the leastsquare method.
Moment Tensor Inversion
In general, vertical component of observed seismic waveform at the station j due to ordinary
earthquake can be expressed by5

u j (t ) = ∑ M q ∫ G jq (t − τ , x c , y c , z c )T (t )dτ + eo + em
q =1

2

(3)

where M q is moment tensor at centroid of source ( xc , yc , z c ) , T(t) is source time function, and em ismodeling error. The observation equation of (3) can be rewritten in vector form:

d j = G (T (t ), xc , yc , z c ) j m + e j(4)where d and e are N-dimensional data and error vectors, respectively, a is a 5-dimensional model
parameter vector, G is a N x 5 coefficient matrix. The solution of the above matrix equation is
obtained by using least square approach, if the observation waveform (d) and convolution Green’s
function with source time function (G) are known. We determined the depth of hypocenter and theduration and shape of source time function by grid search method since these are needed for moment
tensor inversion.
The teleseismic body waves were windowed for 60 seconds, starting 10 seconds before P arrival time,
and then converted into displacement with a sampling time of 0.25 seconds. To remove effects ofdetailed source process and detailed 3D structure, we apply the low pass filtering in the moment tensor
inversion. Frequency range was selected by a try and error.

RESULTS AND DISCUSSION
Magnitude Determination of BMG
We used 8 earthquake events with data range from 4 March 2007 – 25 April 2007. After selecting andconverting waveforms, we determined the coefficients using the least square method prepared by Dr.
Kamigaichi (2007, personal communication).
For the calculated magnitude of type2, we assumed correction for magnitude αD,, as 1. We obtained
the correction for distance, βD, as 2.15, and a constant coefficient, γD, as -1.88, respectively. Therefore
we can construct the magnitude formula for type2 as follows:

M W = log10 AD + 2.15 log10 R − 1.88

(5)

We compared the both results with the empirical equation from Tsuboi’s formula (1954). The
empirical equation from Tsuboi is as follows

M = log10 A + 1.73 log10 Δ − 0.83

(6)where ∆ is an epicentral distance (km) and A is the maximum displacement amplitude (μm) observed
at each station within 2,000 kilometers from an epicenter. A is given by A =

2
2
ANS
+ AEW
, in which

ANS and AEW are half the maximum peak-to-peak amplitudes of the whole trace of the two horizontal
components. We found that the type2 of magnitude formula is almost similar to Tsuboi’s formula,meanwhile the type1 is not (Figure 1). This is due to the similarity of the equation. The type1 ispolynomial equation; meanwhile type2 and Tsuboi’s formula are the linear equation. The Tsuboi’s
formula is applied to determine magnitude for large earthquakes and for those shallower than 60
kilometers. In this study, we used earthquake events with the depth less than 60 kilometers except
event1 with the depth is 149.3 kilometers.
According to these above reasons, we choose the type2 of empirical formula as a magnitude
determination of BMG. We can express as

M BMG = log10 AD + 2.15 log10 R − 1.88

3(7)

where AD is the maximum displacement amplitude (μm), and R is hypocentral distance (km),respectively.
From Figure 2, we found that the magnitude determination of BMG for all events is systematicallyconsistent with the results from Global CMT.

Figure 1. Example of comparison of maximum
amplitudes for three types of magnitude
calculation plotted against hypocentral distances(km) for each event (event1/20070309).

Figure 2. Comparison between the moment
magnitude from Global CMT and thecalculated magnitude of BMG (type2).

Figure 3 shows the difference between observed
maximum amplitudes and estimated ones plottedagainst hypocentral distances for all the events.
From this graph, we found that the magnitude
determination of BMG is sufficient and reliable
for the hypocentral distance less than 1,000
kilometers. The difference value is in the range
from -0.4 to 0.6. The calculated magnitude
distribution is concentrated less than 50
kilometers in depth with the excluded one isabout 150 kilometers. Since we can expect theshallow earthquakes less than 150 kilometers,
Figure 3. Difference between observed maximum
the magnitude determination of BMG will be
amplitudes and estimated ones plotted against
reliable.
hypocentral (km) distances for all the events.
Moment Tensor Inversion

Figure 4. Example of the results of moment tensor
inversion.

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To understand the detailed source process ofthe earthquakes, we used moment tensor
solution. We only retrieved vertical component
from the IRIS-DMC broadband seismometer
network. Out of 8 earthquake events used todetermine magnitude of BMG, only 5 events
are available to be retrieved from the IRISDMC data server. The program written by
Koketsu and M. Kikuchi for calculating
Green’s function and inversion program coded
by Y. Yagi were used to obtain the moment
tensor. We used the grid search method of
moment tensor inversion to constrain thehypocentral depth. By varying the depth with minimum variance, we obtained a well constrained
depth which is known as the centroid depth.
The results of moment tensor inversion of 5 earthquake events are shown in Figure 4 (for example).
The observed waveforms and theoretical waveforms are systematically almost identical. It means that
we can use these results for further studying the characteristic of seismotectonic of the region.

Figure 6. Comparison between the magnitude
Figure 5. Comparison between the moment
determination of BMG and the moment magnitude
magnitude from Global CMT and the moment
obtained from moment tensor inversion.
magnitude obtained from moment tensor
inversion.
Figure 5, in general, it can be said that results of moment magnitude obtained from moment tensor
inversion are systematically almost consistent with the results from Global CMT.
In this study, the consistency of both results depends on source time duration of moment tensor
inversion. For event4, we found that the source time duration is short and about 3 seconds. The
magnitude determination of BMG of event4 becomes overestimated (see Figure 6). However event6
has the longer source time duration than event4 in which the source time duration is about 12 seconds.
The magnitude determination of BMG of event6 becomes underestimated. Therefore we revealed thatfor the rapid earthquake the magnitude determination of BMG became overestimated while for theslow earthquake the magnitude determination of BMG became underestimated, respectively.

CONCLUSIONS
By using least square method, a small number of event data from a few stations were used to calculate
the coefficients of empirical formula. The obtained formula of magnitude determination of BMG isshown below:

M BMG = log10 AD + 2.15 log10 R − 1.88
where AD is the maximum displacement amplitude (μm), and R is hypocentral distance (km),respectively.
By analyzing the consistency with the other magnitude determination, the formula for magnitude
determination of BMG is still sufficient and reliable for shallow earthquakes less than 150 kilometers
and the hypocentral distance less than 1,000 kilometers.
The seismic moments and moment magnitude estimated by moment tensor inversion are generally
consistent with those of Global CMT solutions. To calculate moment tensor, we used teleseismic bodywaves; meanwhile the Global CMT used long period waves. Therefore there are the differences in thecentroid depths between our moment tensor inversion and the Global CMT solutions.

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The magnitude determination of BMG is systematically consistent with the results obtained by our
moment tensor inversion. For the rapid earthquakes with short source duration time, the magnitude
determined by using the formula for BMG will become overestimated. On the other hand the slow
earthquakes with long source duration time, the magnitude determined by using the formula for BMG
will become underestimated.
RECOMMENDATION
The magnitude determination of BMG cannot estimate magnitude for the hypocentral distance morethan 1,000 kilometers yet. This is due to the limitation of number data used to construct it. Also theestimation of consistency with moment magnitude from moment tensor inversion is slightly not
fixable.
According to above reasons, we recommend the following suggestions:i.
The formula of the magnitude determination of BMG could be improved after seismic records
are accumulated in BMG. Collecting and storing data should be well managed. The long timecollected data is of an urgent necessity in order to make reliable coefficients of this formula.
ii.
The dense distribution of accelerometer station should be realized in order to obtain highquality of data.
iii.
Intensive study of magnitude determination of tsunami earthquakes will give advantage toimprove the reliability of this formula.
AKNOWLEDGEMENT
I would like to express my sincere gratitude to Dr. Omori of MRI and the adviser Dr. Bunichiro
Shibazaki for their continuous support, valuable suggestion and guidance during my study.

REFERENCES
Gutenberg, B., and C.F., Richter, 1954, Princeton University Press, Princeton, N.J..
The Japan Meteorological Agency (JMA), 2006, The Japan Meteorological Agency (JMA), Tokyo.
Katsumata, A., 1996, Bull. Seism. Soc. Am., 86, 832-842.
Kikuchi, M., and H. Kanamori, 1991, Bull. Seism. Soc. Am., 81, 2335-2350.
Richter, C. F., 1935, Bull. Seism. Soc. Am., 25, 1–32.
Utsu, T., 1982, Bull. Earthq. Res. Inst., Univ. Tokyo, 57, 465–497, (in Japanese with English abstract).
Yagi, Y., 2004, Earth Planets Space, 56, 311-316.
Yagi, Y., 2004, Bull. Seism. Soc. Am., 94, 1795-1807.
Yagi, Y., 2006, IISEE Lecture Note 2006-2007, IISEE, BRI.

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