RAPID SOURCE PARAMETER DETERMINATION
AND EARTHQUAKE SOURCE PROCESS IN
INDONESIA REGION
Iman Suardi
(For the Course of Seismology, 2006-2007)
ABSTRACT
We proposed a magnitude determination method for the regional network of
the Meteorological and Geophysical Agency (MGA), Badan Meteorologi dan
Geofisika (BMG). This method was developed from the empirical formula
from Richter’s magnitude. We use accelerogram from regional accelerometer
network of BMG for one month range. The accelerograms were converted
into displacement to measure maximum displacement. A third-order
Butterworth filter of 0.1Hz cut-off frequency was used as the high-pass filter.
We use MW from the Global CMT catalog as reference magnitude. To
construct a magnitude formula of BMG, we refer an empirical formula of
Richter’s magnitude. We found that the magnitude formula of BMG is as
follows:
M BMG  log 10 AD  2.15 log 10 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 those earthquake events. To
estimate moment tensor, we used teleseismic body waves retrieved from
IRIS-DMC via internet. The program written by Kikuchi for calculating
Green’s function and inversion program coded by Yagi were used to obtain
the moment tensor. The seismic moments and moment magnitudes obtained
by the moment tensor inversion are generally consistent with those of Global
CMT. Therefore the result of the moment tensor inversion was compared
with the magnitude determination of BMG. We found that the magnitude
determination of BMG is systematically consistent with the results from
moment tensor inversion. However for the rapid earthquakes indicated by
short source duration time, the magnitude determination of BMG will
become overestimated. On the other hand the slow earthquakes indicated by
long source duration time, the magnitude determination of BMG will become
underestimated. At least to understand the state of tectonic stress field of area
around epicenters, we investigated the tectonic feature of the region around
those events by analyzing the focal mechanism obtained by moment tensor
inversion.

The author works for Meteorological and Geophysical Agency (BMG) of Indonesia
CONTENTS
INTRODUCTION.………………………………………………………………………………….
1
Magnitudes……………………………………………………………………………………...
1
Moment Tensor Inversion………………………………………………………………………
1
Purpose of This Study…………………………………………………………………………..
2
Tectonic Setting of Indonesia…………………………………………………………………...
2
DATA……………………………………………………………………………………………….
3
Raw Accelerogram Data from the Accelerometer Network of BMG…………………………..
3
Data Retrieval from IRIS-DMC………………………………………………………………...
6
THEORY AND METHODOLOGY………………………………………………………………...
7
Magnitude……………………………………………………………………………………….
7
Local Magnitude (ML)…………………………………………….………………………...
7
Body-Wave Magnitude (mb)………………………………………………………………..
7
Surface Wave Magnitude (MS)……………………………………………………………..
8
Mantle Magnitude (Mm)…………………………………………………………………….
8
Moment Magnitude (MW)…………………………………………………………………..
8
Broadband P-wave Moment Magnitude (MWP)…………………………………………….
9
Magnitude of JMA (MJMA)………………………………………………………………….
9
Magnitude Determination of BMG…………………………………………..………………… 11
Moment Tensor Inversion……………………………………………………………………… 12
RESULTS AND DISCUSSIONS…………………………………………………………………... 15
Magnitude Determination of BMG……………………………………………..……………… 15
Moment Tensor Inversion……………………………………………………………………… 21
Comparison of Magnitude Determination of BMG with Moment Magnitude from Moment Tensor
Inversion………………………………………………………………………………………... 25
CONCLUSION……………………………………………………………………………………... 26
RECOMMENDATION…………………………………………………………………………….. 27
AKNOWLEDGEMENT……………………………………………………………………………. 27
REFERENCES……………………………………………………………………………………... 28
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 is
important. Loss of lives caused by tsunami attacks is larger than that by earthquake, meanwhile in
Indonesia tsunami attack can reach the coast in about less than 20 minutes. 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 is carried out as soon as possible. The government of
Republic Indonesia through the Meteorological and Geophysical 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 by tsunami attack. Therefore rapid and accurate
determination of earthquake source parameters is of an urgent necessity.
Magnitudes
Rapid and precise evaluation of a potentially tsunamigenic earthquake hypocenter and magnitude is
important for saving lives from tsunami and for mitigating tsunami damage. Current tsunami warning
system uses the hypocentral parameters and magnitude for this purpose. The first seismic magnitude
scale was developed empirically by Richter (1935) for California earthquake, which is determined by
using shorter period amplitudes. Kanamori (1977) proposed the new scale of magnitude, MW, which is
based on seismic moment estimated by using the long period amplitudes at 100 to 300 seconds.
Mostly earthquakes near coast of Indonesia generated tsunami, e.g. the last mega tsunami earthquake
26 December 2004 Aceh. Since the large tsunami attacked the coast in less than 20 minutes after
earthquakes, it is important to estimate the location and magnitude of earthquake as soon as possible,
and release early warning information immediately.
Moment Tensor Inversion
When an earthquake occurs, the seismic waves are propagated from hypocenter which will carry much
information of source mechanism of the earthquake. From seismic waves we can estimate a sudden
rupture taking place along faults. Seismic moment tensor analysis at local, regional and teleseismic
distances has become a routine practice in seismology. The seismic moment tensor contains not only
information of an earthquake size but also information of a state of tectonic stress field and location of
a weak zone (fault zone). Seismological approaches in the source mechanism such as focal mechanism
study are indispensable for studying seismic faults and their rupture processes. The focal mechanism
bears information on the seismic fault and on tectonics around the earthquake source: plate motion and
the tectonic stress which cause the earthquake. Dziewonski et al. (1981) has developed a technique for
determining the moment tensor of earthquakes. The centroid location and time may be interpreted as
the center of the rupture process in space and time. Their solution is called the Centroid Moment
Tensor (CMT). They determined the CMT solution by waveform inversion: waveform fitting of
synthetic seismograms to observed seismograms by a least squares method. Long period seismograms
were used to avoid the effects of lateral heterogeneity of the earth’s structure. They used body waves
with periods longer than 45 seconds and surface waves with periods longer than 135 seconds to
calculate the waveform inversion. Kikuchi and Kanamori (1991) has developed the waveform analysis
method to calculate a moment tensor inversion of teleseismic body waves.
Recently, a lot of researchers have made rapid progress in the study of the rupture process, which is
includes the determination of the time and space slip distribution along fault plane using seismic
waveform. When we construct the rupture process, we can estimate accurate the source area,
displacement of slip, which is important to estimate the accurate tsunami wave and the strong ground
motion using the numerical simulation.
1
Purpose of This Study
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. In generally the grade of tsunami corresponds to the
magnitude, and the grade tsunami became increases with increasing magnitude of earthquake. It is
important for tsunami early warning system to obtain the magnitude quickly and as soon as possible
after the occurrence of large earthquake.
In recent time, BMG Indonesia has established the Earthquake and Tsunami Warning Center (TEWC).
However, earthquake magnitude determination, estimated from amplitudes of body waves (mb), is still
using the conventional methods. In this study, we propose a new rapid method to determine local
magnitude for small and large earthquakes by using accelerogram data from BMG’s accelerometer
regional network. We use the method based on empirical formulas from Richter’s magnitude. The
result of this method is then compared to the moment magnitude, MW, from Global CMT. The new
rapid method will be used by BMG to release a new BMG magnitude correlated to issuance of early
warning. Therefore, to determine moment tensor solution rapidly using global seismic network, we
used moment tensor inversion scheme of tele-seismic P-waveform that was coded by Yagi (2004). By
comparing the synthetic waveform with observed waveform, the centroid depths were obtained by
using grid search procedure. This waveform inversion scheme can be applied for regional broadband
seismograph data set. Although we cannot apply this method to real data that is observed in Indonesia
at present study, this method will be useful to estimate accurate earthquake size promptly. We
determined moment tensor and moment magnitude for each event and then compared them with
Global CMT results. We also compared the moment magnitude MW from Global CMT and from the
moment tensor inversion with the new calculated magnitude of BMG. Finally, for detailing the
mechanism of fault dynamics and also for understanding the seismotectonics of Indonesia region, we
constructed a detailed source process of the earthquakes.
Tectonic Setting of Indonesia
Indonesia is one of the seismically active countries in the world. There are about 170,000 islands
spread out along a belt of volcanic and seismic activity. The general tectonic features of Indonesia are
characterized by deep oceanic trench of the Indian Ocean, volcanic belt, and several marginal basins.
The interaction among the three great tectonic plates, namely Indian-Australia, Eurasia, and Pacific
plates, and other two smaller plates, called Philippines Sea and Caroline plates, makes the tectonic
setting of Indonesia very complex.
According to the plate tectonic theory, the Indonesian Archipelago is located among junction of three
plates, Indian-Australian, Pacific, and Eurasia plates. Indian-Australian belts subducted beneath
Eurasia plate as along as Sumatra basin and Java, and then stretched across western part of Sumatra,
southern part of Java. Such movement of the plate caused the great earthquake and the great tsunami
on 26 December 2004 along the western coast of the island of Sumatra. Also the other great
earthquake occurred on 28 March 2005 near Nias Island off the coast of Sumatra. Subduction of great
tectonic plates continues further south and east/southeast along the great Sunda Trench until eastern
part of Timor and then bends following Banda arch.
The offshore seismic activity along the southern coast of Java has high seismicity and has produced
many destructive earthquakes and several tsunami earthquakes, e.g., which occurred in 17 July 2006.
The subduction of Australian plate slides beneath the sunda plate has average velocity about 60
mm/year in north-northeastward direction. The Java region is tectonically unstable. Further as far as
the east java trench the rate of subduction is about 50 mm/year. Near New Guinea the subduction rate
increases to as much as 107 mm/year. So that, major and great earthquakes occur frequently in this
region.
Pacific belt moved to the west along its border with Australia continent, starting from Papua to
Sulawesi. The junction among three belts is in Maluku region. Oblique subduction of tectonic plates at
high rates along Eastern Indonesia has created a very complex active tectonic zone.
2
In the effect of the movement of each belt form the faults, for instance, Semangko fault at Sumatra,
Palu-Koro fault at Sulawesi, Digul fault and Terera-Aiduna fault at Papua. As a consequence of these
conditions, the most of the hypocenters are located around the boundary of those faults (Figure 1).
Figure 1. Map of Tectonic Setting of Indonesia (Puspito, et.al., 1995).
DATA
Raw Accelerogram Data from the Accelerometer Network of BMG
In order to establish the tsunami early warning system in Indonesia, the Meteorological and
Geophysical Agency (MGA)/Badan Meteorologi dan Geofisika (BMG), Indonesia has been installing
many seismic instruments spreading around Indonesia area. BMG has a plan to install about 160
broadband seismometers, 500 accelerometers, 60 tide gauges, and 15 DART-Buoys, respectively
distributed to the whole of Indonesia region. The target of project will completely finish in 2008. In
recent time, about 42 out of 500 accelerometers have already been installed (Figure 2). Each
accelerometer station is equipped with a three-component Metrozet TSA-100S from Nanometrics Inc.,
which has a wide frequency response of DC to > 225 Hz. Only 25 stations connect to the headquarter
directly in real-time. All data from the accelerometer stations will be stored in database server of BMG
which keeps data of one-month period.
3
Figure 2. Distribution of the new accelerometer network of BMG. Green
triangles denote accelerometer stations. Red stars denote earthquake events
for data range from 4 March 2007 – 25 April 2007.
In this study, we use accelerograms from the raw continuous waveform data with data range from 4
March 2007 – 25 April 2007. We collected a raw continuous waveform data from database server of
BMG. This raw data was converted to Xfiles format (a waveform format from Nanometrics Inc.) by
using Data Playback software prepared by Nanometrics Inc.. Further, we obtained the waveform data
in SAC format through seed format using rdseed software. The accelerogram was converted into
displacement record with SAC transfer command to measure maximum displacement. A third-order
Butterworth filter of 0.1Hz cut-off frequency was used as the high-pass filter (Figure 3). Therefore we
used a peak displacement which is used as maximum displacement amplitude.
4
(a)
(b)
Figure 3. The performance of waveform before converting (a) and after
converting (b) into displacement record for event5 (2007/03/17, M6.2, depth
40.7 km, 1.30N; 126.37E).
5
Also we retrieved earthquake event list from the CMT global catalog with the same time range to use
MW as reference magnitude. We got only 8 events from this continuous waveform data due to many
bad waveforms (Table 1).
Table 1. Earthquake event list from the Global CMT (4 March 2007 – 25
April 2007).
No.
Event
yyyymmdd
Location
MW Global CMT Depth (km)
1
event1
20070309
-6.34S, 130.23E
5.6
149.3
2
event2
20070313
-8.08S, 117.94E
5.6
24.1
3
event3
20070315
-0.73S, 127.60E
5.4
12.0
4
event4
20070315
4.19N, 127.04E
5.2
18.5
5
event5
20070317
1.30N, 126.37E
6.2
40.7
6
event6
20070326
0.98N, 126.05E
5.5
29.0
7
event7
20070331
1.55N, 122.63E
5.6
21.9
8
event8
20070407
2.72N, 95.47E
6.1
12.0
Data Retrieval from IRIS-DMC
We retrieved teleseismic body-wave (P waves) data recorded at the Data Management Center of the
Incorporated Research Institution for Seismology (IRIS-DMC) stations through the internet. We
selected the stations from the viewpoint of good azimuthal coverage with distance range from 300 to
900. The locations of the teleseismic stations are shown in Figure 4.
Figure 4. Teleseismic station map shown as a map view of the configuration
of IRIS stations used for comparing between magnitude determination of
BMG and moment magnitude from moment tensor inversion. Yellow stars
denote the epicenters. Red triangles denote the IRIS stations.
6
THEORY AND METHODOLOGY
Magnitude
The concept of "Earthquake Magnitude" as energy scale relative result of measurement of amplitude
phases was released first time by C. Richter in 1930 (Richter 1935). The energy of earthquake is
expressed with unit magnitude in bases logarithmic scale 10. The logarithmic scale is used due to the
variation of seismic wave amplitudes. The magnitude is obtained as a result of peak-to-peak amplitude
analysis on seismogram with distance correction from epicenter to station. There are many types of
magnitude used occasionally today, but the basic form of all magnitude scales is given by empirical
equation (Lay and Wallace 1995)
M  log( A / T )  f (, h)  Cs  Cr
(1)
where A is the ground displacement of the phase, T is the period of signal, f is a correction as function
of epicentral distance (∆) and focal depth (h), Cs is station site correction, and Cr is a source region
correction, respectively. Some calculations are based on the corrections for the effects of focal depth
or for regional difference in each structure and attenuation. The others are based on the sensitivity of
seismometers at different frequency. The frequency of seismometer has different range, for example,
for short period seismometer Tinstrument~1 second, long period Tinstrument~30 seconds. For short periods,
the largest phases are mostly P or S, and for long periods are surface waves (for shallow earthquakes).
Local Magnitude (ML)
It was introduced by C. Richter in 1930 by using earthquake event catalogue of California earthquakes
which were recorded by a Wood Anderson seismometer. Richter observed that the logarithmic of
maximum ground motion decayed with distance along parallel curves for many earthquakes. The
energy of earthquake can be obtained approximately by measuring epicentral distance and maximum
amplitude of phases. The empirical equation of Local Magnitude is as follows (Lay and Wallace
1995):
M L  log A  2.48  2.76 log 
(2)
where A is the ground displacement of the phase (µm), and ∆ is epicentral distance (km) with   600
km, respectively.
Today ML is rarely used because a Wood Anderson seismometer is not used anymore and the
calculated formula based in California area, so that it is fixable on that area.
Body-Wave Magnitude (mb)
ML is just for local earthquakes in California. To define global seismicity, other kinds of magnitude
were proposed. One magnitude scale is based on the body wave amplitude, which is termed mb (body
wave magnitude). It is defined by the formula
mb  log( A / T )  Q(, h)
(3)
where A is the actual ground motion amplitude (µm) and T is period (sec), Q is a function of epicentral
distance ∆ and focal depth h, empirically determined by Gutenberg and Richter (1956) for eliminating
the path effect from observed amplitude.
The determination of mb is practically based on P or S waves by using short period seismometer with
period nearly about 1 sec, so it is not appropriate for large earthquakes.
7
Surface Wave Magnitude (MS)
The other magnitude scale beside the above body wave magnitude was developed (Gutenberg 1945),
the surface wave magnitude (MS). This magnitude type is obtained by measuring surface waves. For
epicentral distance ∆ more than 2,000 kilometers, the long period seismograms of shallow earthquake
are dominated by surface waves. These waves usually have period of about 20 seconds. The amplitude
of surface waves depends very much on the epicentral distance ∆ and the depth of earthquake source
h. The deep earthquakes do not yield much surface waves, so that in consequence equation of MS does
not need the depth correction. It is defined by the formula (Vanek et al. 1962)
M S  log( A / T )  1.66 log   3.3
(4)
where A is the amplitude of long period waves of the 20 sec period (µm), T is period (sec), and ∆ is
epicentral distance (km), respectively.
MS is very easy to determine because it is based on measuring maximum amplitude of surface waves
without the depth correction, but it is an underestimate for great earthquake. MS does not saturate until
approximately MS = 7.25 but is fully saturated by MS = 8.0.
Gutenberg and Richter (1959) released the equation of relation between mb and MS as follows
mb  0.63M S  2.50
M S  1.59mb  3.97
(5a)
(5b)
They derivate this relation to facilitate the construction of a unified magnitude scale (Geller 1976)
Mantle Magnitude (Mm)
Okal and Talandier (1989) developed “Mantle Magnitude”, Mm, which is determined by measurements
at a variable long period (51 – 273 sec). They had shown that spectral amplitude measurements of
mantle Rayleigh waves can be converted to a magnitude scale, Mm, which is directly related to the
seismic moment Mo of the earthquake (Okal and Talandier 1989). The formula is as follows:
M m  log X ( )  DD  CS  0.90
(6)
where X(ω) is the spectral amplitude at angular frequency ω, CD is the distance correction (geometrical
spreading and Q), and CS is the source correction (depends on period), respectively.
Their method can also be transposed to the time domain, under some simple assumption. By providing
a real time estimate of the seismic moment of distant earthquake, Mm, has considerable potential for
tsunami warning purposes. Also their concept can easily be extended to Love waves and also to
intermediate and deep earthquakes (Okal and Talandier 1989).
Moment Magnitude (MW)
In order to reduce some of the difficulties of magnitude saturation, Kanamori (1977) introduced the
concept of moment magnitude to seismology. The formula of Moment Magnitude is as follows:
M W  (log M o  9.1) / 1.5
(7)
where Mo is a seismic moment.
In the above formula, the seismic moment, Mo, is defined by
M o  D S
(8)
where μ is the rigidity, D is the average offset on the fault, and S is the area of the fault, respectively.
8
The seismic moment is one of the most accurately determined seismic source parameters. For many
great earthquakes, Mo has been determined by using long period body waves, surface waves, free
oscillation, and geodetic data. In this approach, it was tried to extend MS beyond its point of total
saturation and also to provide continuity with large earthquakes. However, the determination of Mo is
much more complicated than magnitude measurement, although modern seismic analyses are routinely
providing Mo for all global events larger than MW=5.0 (Lay and Walace 1995).
Broadband P-wave Moment Magnitude (MWP)
Tsuboi et al. (1995) firstly developed a technique to determine earthquake magnitudes using
broadband seismograms. They obtained the seismic moment, Mo, by the following formula
M o  max (  u z ( xr , t )dt
4 3 r
Fp
(9)
where uz is a vertical displacement of far field P wave in spherically symmetric media at receiver xr, ρ
and α are mean density and P wave velocity along the propagation path, r is epicentral distance, and Fp
is P wave radiation pattern.
They proposed the procedure to calculate broadband moment magnitude, MWP. The P wave portion of
displacement seismograms represents the source time function with a scalar correction for the seismic
moment. The scalar seismic moment at each station from the vertical broadband record can be
obtained by integrating the displacement of the P wave portion of the seismogram. Therefore the
seismic moment, Mo, is obtained from the largest of the first peak (P1) of the P wave portion of
seismogram, or from the difference between P1 and the amplitude (P2) of pP or sP (P1-P2), on the
integrated displacement record of the vertical broadband seismograph record (Tsuboi et al. 1995)
M o  max ( P1 , P1  P 2 )
4 3 r
Fp
(10)
Then the moment magnitude, MW, is calculated by using the equation (7) from Kanamori (1977).
Finally, the broadband p-wave moment magnitude, MWP, is obtained by adding 0.2 as the correction
for the effect of radiation pattern.
M W P  M W  0.2
(11)
Their technique has been proven quite simple and robust, so that it will be effective for the purpose of
rapid determination of tsunami warning applications. In recent time, their method is used not only by
JMA to estimate the first MW for distance earthquake, but also by both U.S tsunami warning centers at
the WC/ATWC and at the PTWC.
Magnitude of JMA (MJMA)
The magnitude, MJMA, estimated by the Japan Meteorological Agency (JMA) is generally referred to in
Japan for the regional seismicity in the area. MJMA is determined from the maximum ground
displacement and velocity amplitudes of the total seismic traces measured at any station within about
2,000 kilometers from the epicenter (Katsumata 1996). There are three kinds of magnitudes of JMA,
those are:
i.
Magnitude MJ at the Local Meteorological Observatories.
For large earthquakes and those shallower than 60 kilometers, MJMA is determined by Tsuboi’s
formula (1954) by using acceleration data of the seismic intensity-meters at the Local
Meteorological Observatories.
M JMA  log AD  1.73 log   0.83
9
(12)
where ∆ is the epicentral distance (km) and AD is the maximum displacement amplitude (µm).
AD is given by AD 
ii.
2
2
, in which ANS and AEW are half the maximum peak-to-peak
ANS
 AEW
amplitudes of the horizontal components.
To obtain the displacement amplitudes, the acceleration data is twice integrated and applied to
the high-pass filter (6 seconds) to stimulate the mechanical strong motion seismogram.
Displacement Magnitude, MD.
For hypocentral distance R more than 30 kilometers and epicentral distance ∆ less than 700
kilometers, magnitude of JMA, MD, is determined by Katsumata’s formula (2004).
M D  log AD   D (, H )  CD
where AD is the maximum displacement amplitude (µm). AD is given by AD 
iii.
(13)
2
2
,
ANS
 AEW
in which ANS and AEW are half the maximum peak-to-peak amplitudes of the horizontal
components. Here  D (, H ) , called the attenuation function, represents a correction term
depending on the epicentral distance ∆ between a given observation point and the earthquake,
and on the focal depth H (Figure 5(a)). CD is a correction due to the deployment of a new
nationwide seismic network and due to the change of filters of seismographs with correction
value = 0.2 used for D93-type seismometer.
If the number of stations involved in the average is less than 3, JMA take into account stations
up to epicentral distance ∆ = 2,000 kilometers. If the number of the stations used to obtain MD
is 2, it is denoted as Md (the Japan Meteorological Agency (JMA) 2006).
Velocity Magnitude, MV.
For hypocentral distance R more than 5 kilometers and epicentral distance less than 1,000
kilometers, magnitude of JMA, MV, is determined by Funasaki et al (2004).
M V  (1 / 0.85) log AZ  V (, H )  CV
(14)
where AZ is the maximum amplitude of the vertical component of velocity (10-5m/s).
Here V (, H ) , called the attenuation function, represents a correction term depending on
epicentral distance ∆ and on the focal depth, H (Figure 5(b)). The constant CV depends on
instrumental conditions of seismographs.
If the number of stations involved in the average is less than 4, JMA take into account stations
up to epicentral distance ∆ = 1,000 kilometers. If the number of the stations used to obtain MV
is 2 or 3, it is denoted as Mv (the Japan Meteorological Agency (JMA) 2006).
10
(a)
(b)
Figure 5. Contour representations of βD (a) and βV (b).(Source: The Japan
Meteorological Agency (JMA), 2006).
Magnitude Determination of BMG
Many formulas have been proposed to express seismic wave amplitude attenuation for determining
earthquake magnitude. Tsuboi (1954) applied a logarithmic function to express attenuation of the
maximum displacement amplitude as
M  log 10 A  1.73 log 10   0.83
(15)
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
, in which
ANS
 AEW
ANS and AEW are half the maximum peak-to-peak amplitudes of the whole trace of the two horizontal
components.
Earthquake magnitude is the mean of magnitudes calculated for stations. Tsuboi’s formula was
constructed to release magnitude, improving with the average magnitude released by Gutenberg and
Richter (1949) for shallow earthquakes. Tsuboi’s formula is applied to earthquakes at depth equal to
60 kilometers or shallower.
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. It can be approximately expressed as
 D M W  log 10 AD  log 10 R   D R   D
 D M W  log 10 AD   D log 10 R   D
(16)
(17)
where D is an index for displacement, αD is coefficient correction for magnitude, βD is coefficient
correction for distance, and γD is a constant coefficient, respectively. We denote equation (16) and (17)
as type1 and type2 empirical formulas, respectively. We assume the coefficient for log10AD is 1.0,
since the expected distribution of a calculated magnitude with the moment magnitude should be
parallel.
11
We determine the coefficients by using the least-square method. The least-square method is
 (log
p
Apq  log 10 R pq   D R pq   D   D M W ) 2
10
Apq   D log 10 R pq   D   D M W ) 2
minimum
(18)
q
 (log
p
10
minimum,
(19)
q
where p is an index for earthquake events, q is that for stations, respectively.
Moment Tensor Inversion
The detailed knowledge of the seismic source process is required to improve the understanding of the
earthquakes and earth structure. The seismic source process represents the dynamic process of the
earth. The observed seismogram is a complex alliance of signature of the source and the effects of
propagation. Knowledge of the propagation effects allows us to constrain the physical process of the
source. Using the limited sampling of seismic waveforms from the sparse broadband seismometers
located on surface enables us to interpret the complex transient phenomena that have taken place in the
deep earth.
Regarding this effort, many procedures have been developed, so that we can compute synthetic
seismograms that are comparable with observed seismograms. The various processes such as the
seismic source process and the propagation process (earth structure response and attenuation) affect
the motion at observation points, and are all combined into synthetic convolution operators. Since
these effects can be treated as liner operators to first order, it becomes simple to test the significance of
changes in the synthetics caused by varying the operators separately.
The Green’s function is generally the marriage of the response function, effect of propagation process,
with unit impulsive slip and/or force (Figure 6). It is important to use accurate Green’s function in
order to obtain suitable solutions, because Green’s function is sensitive to both source mechanisms and
depths in analyzing the rupture source process.
Figure 6. The concept of Green’s function in the seismic source process.
By using moment tensor inversion, the detailed source process of the earthquake can be retrieved from
observed data. The moment tensors for many kinds of earthquakes can be determined in a routine way.
Also trial and error modeling with careful treatment of the data can yield important knowledge about
the source (Yoshida 1995).
Since the seismic moment tensor is always symmetric, the moment tensor can be described as double
couple at any time. Also we can treat source and propagation process as linear operator. So that it is
possible to construct observed waveform by summing the moment tensor weighted displacement for
each moment tensor (convolution function of Green’s function and source time function). For only
12
double–couple, the number of independent components of moment tensor is five. We can choose five
double couple, m1, …, m5, as the basis moment tensors.
In general, vertical component of observed seismic waveform at the station j due to ordinary
earthquake can be expressed by
5
u j (t )    d  G jq (t   , x, y, z ) M q ( , x, y, z )dV  e0
q 1
V
(20)
where V represents the source space, Gjq is the complete Green’s function, Mq is elementary moment
density tensor, and eo is observation error. We represented the seismic source process as point source
model.
5
u j (t )    G jq (t   , xc , yc , zc )M q' ( , xc , yc , zc )d  eo  em
q 1
5
  M q"  G jq (t   , xc , yc , zc )T (t )d  eo  em
(21)
q 1
where M q' and M q" are moment tensor at centroid of source ( xc , yc , z c ) , T(t) is source time function,
and em is modeling error. For simplicity, we assume eo  em to be Gaussian with zero mean and
covariance  2j I .  j is a standard deviation of the far field P wave, which is proportional to the
amplitude of waveform. We assume  j to be proportional to their own maximum amplitude of
observed waveform. The observation equation of (21) can be rewritten in vector form:
d j  G (T (t ), xc , yc , zc ) j m  e j
(22)
Also it can be rewritten in simple vector form as
Gudm1 (t1 ) Gudm2 (t1 )  Gudm5 (t1 ) 
 uud (t1 ) 
m1 
 m1

u (t )
m 
m5
m2
Gud (t 2 ) Gud (t 2 )  Gud (t 2 )
 ud 2 
 2


d    , G 




, m  m3  ,




 
Gnsm1 (t1 ) 
 Gnsm5 (t1 ) 
 u ns (t1 ) 
 m4 


  
m5 

 
 


 

(23)
and 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 the
duration and shape of source time function by grid search method since these are needed for moment
tensor inversion.
If we assume the velocity of P and S waves at near source area, we can determine the depth of
hypocenter using pP and sP pick. The information of fault mechanism is contained in the radiation
pattern. If we simplify explanation of the moment tensor inversion, we can estimate moment tensor
component (or focal mechanism) to fit amplitude of observed waveform and amplitude of radiation
pattern. To obtain the moment tensor solution, we assumed simple triangle source time function, and
varied the duration of source time and the centroid depth.
13
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 the duration and shape of source time function by grid
search method since these are needed for moment tensor inversion.
We converted the source process from the fault plane to the moment tensor by using simple equation.
M xx   M o (sin  cos  sin 2  sin 2 sin  sin 2  )
1
M xy  M yx  M o (sin  cos  sin 2  sin 2 sin  sin 2 )
2
M xz  M zx  M o (cos  cos  cos  cos 2 sin  sin  )
(24)
M yy  M o (sin  cos  sin 2  sin 2 sin  cos  )
2
M yz  M zy   M o (cos  cos  sin   cos 2 sin  cos  )
M zz  M o sin 2 sin 
where  is strike,  is dip,  is slip (x: north, y: east, z: down direction).
To obtain seismic moment and focal mechanism of earthquake form moment tensor components, we
used the method of transformation to convert the moment tensor to the two fault planes. If we have the
eigenvectors (t, b, p) of moment tensor,
 M xx M xy M xz 
0 
Mo 0




 M yx M yy M yz (t b p)  (t b p) 0 0
0 


 0 0 M 
M M M 
o

zx
xy
zz


(25)
We can obtain fault vector (n : unit normal vector to fault plane, d : unit slip vector) from equation
1
1
(t  p), d 
(t  p )
2
2
1
1
Other fault plane model: n 
(t  p), d 
(t  p )
2
2
One fault plane model: n 
(26)
(27)
These equations show that we cannot detect the fault plane by the moment tensor. We could determine
the fault parameters from the fault vectors using the following equations:

n1 

 n2 
  arccos n3 
  arctan  
 d3 

 sin  
  arcsin  
(28)
(29)
(30)
To obtain the moment tensor solution from body waveform (P wave), we assumed simple triangle
source time function and five elementary moment tensor components (Kikuchi and Kanamori 1991),
and varied the duration of source time and the centroid depth. The Green’s function was calculated by
the method of Kikuchi and Kanamori (1991). We used the prem-modify-model to compute the
teleseismic body wave (Figure 7).
14
Figure 7. The structure velocity models of VP and VS (prem-modify-model).
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 of
detailed 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 DISCUSSIONS
Magnitude Determination of BMG
We used 8 earthquake events with data range from 4 March 2007 – 25 April 2007. After selecting and
converting waveforms, we determined the coefficients using the least square method prepared by Dr.
Kamigaichi (JMA).
We assumed a coefficient for magnitude, αD,, as 1, we obtained a coefficient for distance correction,
βD, as 0.0016058, and a constant coefficient, γD, as 0.361785, respectively. So we can construct the
magnitude formula for type1 as follows:
M W  log 10 AD  log 10 R  0.0016058R  0.361785
15
type1
(34)
Table 2. A calculated magnitude for type1:  D M W  log 10 AD  log 10 R   D R   D
No.
Name
yyyymmdd
Depth
1
Event1
20070309
149.3
2
3
4
5
6
7
8
event2
event3
event4
event5
event6
event7
event8
20070313
20070315
20070315
20070317
20070326
20070331
20070407
24.1
12.0
18.5
40.7
29.0
21.9
12.0
Mw
Epicentral
Hypocentral
Amplitudo
GCMT
Distance
Distance
max (mgal)
5.6
395.19
395.37
852.44
5.6
5.4
5.2
6.2
5.5
5.6
6.1
Mcal
Maver
31.00
6.090
5.79
865.42
24.00
6.264
204.14
205.56
216.60
5.523
366.82
367.61
119.80
5.740
333.22
333.44
14.10
4.721
15.01
19.21
16035.00
5.995
539.35
539.48
35.20
5.641
535.71
536.03
9.30
5.101
176.67
177.64
529.50
5.697
586.96
588.37
48.40
5.913
248.24
251.55
516.90
6.065
279.63
282.58
1259.50
6.431
567.91
568.65
8.70
5.127
240.74
242.48
105.00
5.308
304.45
305.83
154.30
5.650
593.03
593.43
10.90
5.336
694.18
694.53
48.00
6.163
399.15
399.75
19.60
5.108
684.70
684.81
30.00
5.920
395.19
395.37
252.60
5.306
5.63
5.45
5.40
6.14
5.36
5.54
6.01
Table 2 shows the result of calculated magnitude of type1. The magnitude is the average of magnitude
of each station. We used the epicentral distance range from 15 kilometers to 900 kilometers as fixed
data. The calculated magnitude is sufficient by indicating the small value of standard deviation that is
about 0.386022.
For the calculated magnitude of type2, we also assumed correction for magnitude αD,, as 1. We
obtained the correction for distance, βD, as 2.15048, and a constant coefficient, γD, as -1.88362,
respectively. Therefore we can construct the magnitude formula for type2 as follows:
M W  log 10 AD  2.15048 log 10 R  1.88362
16
type2
(35)
Table 3 shows the result of calculated magnitude of type2. Also the calculated magnitude of type2 is
sufficient with the small value of standard deviation is about 0.312284.
Table 3. A calculated magnitude for type2:  D M W  log 10 AD   D log 10 R   D
No.
Name
yyyymmdd
Depth
1
Event1
20070309
149.3
2
3
4
5
6
7
8
event2
event3
event4
event5
event6
event7
event8
20070313
20070315
20070315
20070317
20070326
20070331
20070407
24.1
12.0
18.5
40.7
29.0
21.9
12.0
MW
Epicentral
Hypocentral
Amplitudo
GCMT
Distance
Distance
max (mgal)
5.6
395.19
395.37
852.44
5.6
5.4
5.2
6.2
5.5
5.6
6.1
Mcal
Maver
31.00
5.412
5.71
865.42
24.00
6.008
204.14
205.56
216.60
5.608
366.82
367.61
119.80
5.856
333.22
333.44
14.10
4.843
15.01
19.21
16035.00
5.196
539.35
539.48
35.20
5.673
535.71
536.03
9.30
5.135
176.67
177.64
529.50
5.755
586.96
588.37
48.40
5.909
248.24
251.55
516.90
6.177
279.63
282.58
1259.50
6.552
567.91
568.65
8.70
5.138
240.74
242.48
105.00
5.417
304.45
305.83
154.30
5.773
593.03
593.43
10.90
5.328
694.18
694.53
48.00
6.071
399.15
399.75
19.60
5.214
684.70
684.81
30.00
5.837
395.19
395.37
252.60
6.198
17
5.73
5.24
5.45
6.21
5.44
5.54
6.02
Figure 8. Comparison of maximum amplitudes for three types of magnitude
calculation plotted against hypocentral distances for each event.
18
We compared the both results with the empirical equation from Tsuboi’s formula (1954) by plotting
maximum displacement amplitudes against hypocentral distances for each event (Figure 8).
The empirical equation from Tsuboi is as follows
M  log 10 A  1.73 log 10   0.83
(36)
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
, in which
ANS
 AEW
ANS and AEW are half the maximum peak-to-peak amplitudes of the whole trace of the two horizontal
components.
Figure 8 shows the relationship among three types of the calculated magnitude for each earthquake
event. From each graph, we found that the type2 of magnitude formula is almost similar to Tsuboi’s
formula, meanwhile the type1 is not. This is due to the similarity of the equation. The type1 is
polynomial 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  log 10 AD  2.15 log 10 R  1.88
(37)
where AD is the maximum displacement amplitude (μm), and R is hypocentral distance (km),
respectively.
For testing the reliability of this equation, we compare it with the moment magnitude from Global
CMT (Table 4). Figure 9 shows comparison between the moment magnitude from Global CMT and
the magnitude determination of BMG (type2). We found that the magnitude determination of BMG for
all events is systematically consistent with the results from Global CMT.
Figure 9. Comparison between the moment magnitude from Global CMT and
the calculated magnitude of BMG (type2).
19
For further analysis of the consistency, we can determine from the graph the difference between the
calculated magnitude of BMG and the moment magnitude of Global CMT plotted against the moment
magnitude of Global CMT (Figure 10(a)). We observed that the difference is in the tolerance range
from -0.6 to 0.6 in which magnitude distribution of earthquake is concentrated less than 6.5.
Also we can observe the difference between the calculated magnitude of BMG and the moment
magnitude from Global CMT plotted against the depth of earthquakes (Figure 10(b)). We found that
the result is almost similar to the result from Figure 10(a), so that for this case, the difference is still in
the tolerance range from -0.6 to 0.6. The calculated magnitude distribution is concentrated less than 50
kilometers in depth with the excluded one is about 150 kilometers. Since we can expect the shallow
earthquakes less than 150 kilometers, the magnitude determination of BMG will be reliable.
(a)
(b)
Figure 10. (a) Difference between the calculated magnitude of BMG and the
moment magnitude of Global CMT plotted against the moment magnitude of
Global CMT. (b) Difference between the calculated magnitude of BMG and
the moment magnitude from Global CMT plotted against the depth of
earthquakes.
20
Figure 11 shows the difference between observed maximum amplitudes and estimated ones plotted
against 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.
Figure 11. Difference between observed maximum amplitudes and estimated
ones plotted against hypocentral distances for all the events.
Moment Tensor Inversion
To understand the detailed source process of the earthquakes, we used moment tensor solution. We
only retrieved vertical component from the IRIS-DMC broadband seismometer network. The location
of epicenter and station coverage is shown in Figure 4. Out of 8 earthquake events used to determine
magnitude of BMG, only 5 events are available to be retrieved from the IRIS-DMC 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 12. 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.
21
(a)
(b)
Figure 12. The results of moment tensor inversion of 5 earthquake events. (a)
Assumed source time function and focal mechanism. (b) Theoretical
waveforms (red curves) from a point source and observed waveforms (black
curves).
22
From Table 4 and Figure 13, 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.
- Case for event2/20070313
The moment magnitude obtained from moment tensor inversion for this event was about 5.7. This
value is higher than the value obtained from Global CMT that is 5.6. The difference of moment
magnitude for both results is not too significant, is still in tolerance range. Also the depth obtained
from moment tensor inversion is almost similar with the depth from Global CMT, which are 20
kilometers from moment tensor inversion and 24.1 kilometers from Global CMT, respectively. We
revealed that the seismic moment is M o  0.438  1018 Nm , which is in agreement with that of
-
-
the Global CMT: 0.31  1018 Nm . The source duration is 4 seconds, and the minimum variance is
about 0.1404.
Case for event4/20070315
The moment magnitude obtained from moment tensor inversion is 5.3 which is higher than the
value from Global CMT: 5.2. These results are still consistent with each other. Meanwhile the
depth of this study is deeper than Global CMT: 18.5 kilometers. The difference of depth is due to
the inversion calculation procedure. We varied the hypocentral depth from 5 kilometers to 70
kilometers for shallow earthquake to find minimum variance, because the hypocentral depth is not
adequately constrained by the local seismometer network. We found its minimum variance:
0.2280 at 35 kilometers depth. So we obtained the seismic moment for this event from the
calculation, M o  0.1217  1018 Nm , which is significantly bigger than results from Global
CMT: 0.676  1017 Nm . The source duration is 3 seconds.
Case for event5/20070317
For this event, we obtained the same result for all source parameters. The seismic moment for this
event is M o  0.2494  1019 Nm (MW=6.2), which is in agreement with that of the Global CMT:
0.272  1019 Nm (MW=6.2). The centroid depths of both of moment tensor inversion and Global
-
-
CMT are 40 and 40.7 kilometers, respectively. The source duration is 4 seconds, and the minimum
variance is about 0.1893.
Case for event6/20070326
We found that the moment magnitude for both results are same value which is 5.5. Also the
seismic moments for this event are almost similar: M o  0.194  1018 Nm of moment tensor
inversion and M o  0.209  1018 Nm of Global CMT, respectively. The depth from moment
tensor inversion is 50 kilometers with minimum variance of about 0.3506. This value is deeper
than the depth obtained from Global CMT: 29 kilometers. The difference in depth is due to the
calculating of inversion to obtain best depth with minimum variance, and also due to the applied
structure velocity model (prem-modify-model). The source duration is 12 seconds.
Case for event8/20070407
The moment magnitude of moment tensor inversion is 6.0. This value is higher than that obtained
from Global CMT which is 5.9, but it is still consistent. The seismic moment is obtained from the
calculation, M o  0.1273  1019 Nm , which is well consistent with that of the Global CMT:
0.17  1019 Nm . The source duration is 12 seconds. We obtained the depth of 25 kilometers with
minimum variance of about 0.0901. On the other hand, the centroid depth of Global CMT is about
12 kilometers. The deeper depth is caused by the varying of best depth with the minimum variance
in inversion procedure, and also by applying the different velocity structure model of Global
CMT.
23
Table 4. Results of magnitude determination
No.
Name of
event
yyyymmdd
MW GCMT
Depth
GCMT
Mtsuboi
MBMG
MW
Depth
Moment
Moment
Tensor
Tensor
Inversion
Inversion
1
event1
20070309
5.6
149.3
5.6
5.7
no data
no data
2
event2
20070313
5.6
24.1
5.8
5.7
5.7
20.0
3
event3
20070315
5.4
12.0
5.3
5.2
no data
no data
4
event4
20070315
5.2
18.5
5.4
5.4
5.3
35.0
5
event5
20070317
6.2
40.7
6.2
6.2
6.2
40.0
6
event6
20070326
5.5
29.0
5.4
5.4
5.5
50.0
7
event7
20070331
5.6
21.9
5.4
5.5
no data
no data
8
event8
20070407
6.1
12.0
5.9
6.0
6.0
25.0
Figure 13. Comparison between the moment magnitude from Global CMT
and the moment magnitude obtained from moment tensor inversion.
24
The seismic moments of moment tensor inversion are generally almost consistent with those of Global
CMT. However there are differences in the centroid depths of moment tensor inversion with Global
CMT. This is caused by the different velocity structure model that was used for calculating inversion.
It means that the seismic moment is directly independent of velocity structure. However the
earthquake depth gives a slight influence to the seismic moment.
Comparison of Magnitude Determination of BMG with Moment Magnitude from Moment
Tensor Inversion
The comparison between the magnitude determination of BMG and the moment magnitude obtained
from moment tensor inversion is shown in Figure 14. We found that the magnitude determination of
BMG for all the events is systematically consistent with the results from moment tensor inversion.
However we obtained the larger value for event4 and the smaller one for event6, respectively.
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 14). 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 that
for the rapid earthquake the magnitude determination of BMG became overestimated while for the
slow earthquake the magnitude determination of BMG became underestimated, respectively.
Figure 14. Comparison between the magnitude determination of BMG and
the moment magnitude obtained from moment tensor inversion.
To understand the state of tectonic stress field of area around epicenters, we plotted all moment tensor
inversion solutions on the distribution map of the study area (Figure 15). Also we plotted all focal
mechanism solution from Global CMT to compare with those solutions. We found that all focal
mechanism solutions are generally consistent with each other.
In western part of Indonesia region in which event4, event5, and event6 are located in Molucca Sea,
the direction of P-axis of earthquakes indicated that the compression tectonic stress is generally
25
loading with east-west direction, and type of faults is dominantly reverse faults. It agrees with the local
tectonic setting of Molucca Sea. The Molucca Sea is located at the convergence of three major
lithospheric plates: the Eurasian, Philippine Sea and Australian Plates. The three events of earthquakes
are located in this junction. The Philippine Sea plate subducts beneath the Eurasian plate with eastwest direction. Also the complexity of the region due to the presence of micro-plates and fragments
trapped between the converging plates makes event6 slightly different in direction comparing with
both events.
For event2, the direction of P-axis of earthquake is south-north direction with reverse-strike slip fault.
This result appropriates with the tectonic setting of the southern part of Indonesia region which is the
convergence region. The Australian plate relatively subducts beneath the Eurasian plate with southnorth direction.
The tectonic feature of region around event8 is slightly different with other events. The convergence
between the Australian plates and the Eurasian plate is oblique with southwest-northeast direction. We
found that the focal mechanism obtained from moment tensor inversion is agreement not only with the
solution of Global CMT but also with the tectonic setting of this region.
Figure 15. Comparison of focal mechanisms from Global CMT (blue color)
and from moment tensor inversion (red color). Stars denote epicenters; red
triangles denote accelerometer station used for calculating the magnitude of
BMG.
CONCLUSION
In order to improve rapidly and precisely the capability of magnitude determination for tsunami early
warning system of BMG, we constructed a new magnitude determination formula of BMG. 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 is shown
below:
M BMG  log 10 AD  2.15 log 10 R  1.88
26
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 body
waves; meanwhile the Global CMT used long period waves. Therefore there are the differences in the
centroid depths between our moment tensor inversion and the Global CMT solutions.
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 more
than 1,000 kilometers yet. This is due to the limitation of number data used to construct it. Also the
estimation 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 time
collected 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 high
quality of data.
iii.
Intensive study of magnitude determination of tsunami earthquakes will give advantage to
improve the reliability of this formula.
AKNOWLEDGEMENT
My individual study was held in two parts. In first part, it was carried out at Meteorological Research
Institute (MRI) under conducting Dr. Akio Katsumata, and then second part was carried out at
Tsukuba University with supervisor Prof. Yuji Yagi.
In first part, I would like to express my sincere gratitude to my supervisor Dr. Akio Katsumata for
supervising me and giving very useful guidance and suggestions during I studied in MRI, also for his
patience to teach me. I would like to thank to Dr. Omori and all staff of MRI for kindness. I would like
to thank to Dr. Osamu Kamigaichi for preparing least square method program.
In second part, I would like to express my respectful gratitude to my supervisor Prof. Yuji Yagi for his
continuous support valuable suggestion and very useful advices and for his understanding on human
problems of his student. I will never forget for his kindness. Also I wish to thank to Prof. Yujiro
Ogawa and students of Tsukuba University for their good service.
I wish to express my sincerely thanks to my advisor Dr. Bunichiro Shibazaki for his guidance and
suggestion. I also thank Ms. Shibata for her arrangement of our study and life in Japan. I would like to
thank Director of IISEE and staffs for supporting me during I studied in BRI. Finally I wish to thank to
my coursemates for their friendship, and especially the one who is my source of inspiration.
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