Citation: Ratri, A., H. Miyake, S. Kita (2022), Source modeling of the 2018 Lombok earthquake sequence
estimated from the empirical Green’s function method, Synopsis of IISEE-GRIPS Master’s Thesis.

SOURCE MODELING OF THE 2018 LOMBOKEARTHQUAKE SEQUENCE ESTIMATED FROM THE
EMPIRICAL GREEN’S FUNCTION METHOD
Aldilla Damayanti Purnama Ratri1
MEE21701

Supervisor: Hiroe MIYAKE2, Saeko KITA3ABSTRACTIn 2018, a series of earthquakes in Lombok, Indonesia, occurred close together, causing a lot ofcasualties and property damage. To quantify the effect of the earthquake, we need to study source
characteristics and conduct source modeling for these earthquakes. Therefore, we simulated the target
event with strong motion data of the smaller event in the surrounding area, which have the closest
hypocenter and similarity of focal mechanism to the target event using the empirical Green’s function
method. Then, we determined the parameters of source modeling, including source dimension ratio (N)and stress drop ratio (C) to conduct broadband ground motion simulation. After that, did a grid searchcalculation to get the best fit values for the strong motion generation area (SMGA). From the grid search,
we obtain the best-fit SMGA size and the rupture starting point that can be used to capture the rupture
propagation and aftershock directions for seismic hazard assessment. The SMGA size indicated that thewestern part of Lombok (the region of Mw 6.4 and 7.0) showed lower stress drop than the eastern part(the region of Mw 6.9) and all were still lower stress drops than the empirical relationship of the SMGA
size to the seismic moment for crustal earthquakes. Furthermore, the relative SMGA locations indicate
a relationship among the foreshock, the mainshock, and the largest aftershock that may trigger eachother and have similar source characteristics with rupture directions.
Keywords: Earthquake, empirical Green’s function, grid search, strong motion generation area
1. INTRODUCTION
The 2018 Lombok earthquake sequence started with Mw 6.4 at a shallow depth on 28 July 2018. In thesame area, a more significant earthquake with Mw 7.0 occurred on 5 August 2018 and caused somecasualties and damaging buildings. Another series of substantial earthquakes occurred on 19 August
2018 with Mw 6.9 striking the eastern part of Mw 7.0. Hereafter, we call the Mw 6.4 as the foreshock,
the Mw 7.0 as the mainshock, and the Mw 6.9 as the largest aftershock. These earthquake sequences arecategorized as crustal earthquakes that have shallow source faults. These earthquake sequences arelocated parallel to the Flores back-arc thrust. The Flores back-arc thrust is one of the major active faults
in Lombok that extend westward from Flores Island (Hamilton, 1977, 1979; Silver et al., 1983). The
detail of the tectonic setting of Lombok are shown in Figure 1. Lombok is one of the regions in Indonesia
with a unique geotectonic position since the active tectonic plates surround the area in the four cornersof the wind. Regarding this, we try to know the characteristics of the earthquake in Lombok. Therefore,
we simulated the target event with strong motion data of the smaller event in the surrounding area using
the empirical Green’s function method (EGFM). Then, we estimate strong motion generation areas
Indonesia’s Agency for Meteorology, Climatology, and Geophysics (BMKG), Jakarta, Indonesia.
Associate Professor, Earthquake Research Institute (ERI), University of Tokyo.
3
International Institute of Seismology and Earthquake Engineering, Building Research Institute.
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(SMGAs) to construct source modeling for the Lombok earthquake sequence and to know the stressdrop.

Figure 1. Tectonic setting of Lombok with earthquake sequences in 2018 withtarget events and strong motion stations.
2. DATATo conduct broadband (0.1-10 Hz) ground motion simulation, we used the smaller event (foreshock oraftershock) that satisfy as an EGF event from the hypocenter and focal mechanism category. Therefore,
we used earthquake data summarized in Table 1.

No.

1.
2.
3.
4.
5.
6.

Table 1. Parameters of the target and EGF events used in this study
Date
Hypocenter location
Mw
Focal Mechanism
Lat
Long DepthFault Strike
DipRake
(km)
Plane
(°)
(°)
(°)
(°)
(°)
28/07/2018 -8.28 116.51 14.6
6.4
FP 1902196
FP 2
264
698829/07/2018 -8.32 116.44 10.0
5.1
FP 1631880
FP 225472
9305/08/2018
116.47 17.6
7FP 19621103-8.29
FP 2262708528/07/2018
116.51 14.6
6.4
FP 1
90
2196-8.28
FP 2
264
6988
19/08/2018
116.7
23.5
6.9
FP 1
943496-8.37
FP 2
266
57
86
19/08/2018
116.59 11.2
6.2
FP 1
107
26100-8.44
FP 2276
65
85

Note

Target
event
EGF
event
Target
event
EGF
event
Target
event
EGF
event

We also used the horizontal components of the strong motion data obtained from thestations of the Indonesia National Agency for Meteorology, Climatology, and Geophysics (BMKG).
These stations have various accelerometers and digitizers with a sampling rate of 100 Hz. The detailedsensor locations and target earthquakes for this research are shown in Figure 1.
3. METHODOLOGY
3.1. Empirical Green’s Function Method (EGFM)

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Source modeling of these earthquakes is performed by the empirical Green’s function method (EGFM).
The EGFM is a method for modeling earthquakes using strong ground motion, which uses foreshock oraftershock related to a large earthquake as an empirical Green’s function event (Irikura and Kamae,
1994). The main principle of the EGFM is using the smaller event that is close to the target (larger)
event with a similar focal mechanism because the smaller event has already contained the information
about the path propagation and local site effects that cover the velocity structure.
Then, to conduct source modeling, we need to do a waveform simulation by determining
parameters for source modeling, including source dimension ratio (N) and stress drop ratio (C), which
can be written as Eqs. (1-2):
𝑁 = 𝑓𝑐𝑒 ⁄𝑓𝑐𝑡
𝐶= ((1)

𝑀0 𝑓𝑐𝑡 3)( )𝑚0 𝑓𝑐𝑒(2)

Where N and C are the ratios of source dimensions and stress drops between large and small
events, respectively. While, 𝑓𝑐𝑡 and 𝑓𝑐𝑒 is the corner frequency of the target and EGF events,respectively.
3.2. Grid search calculation
To construct the simulation using the EGFM, the dimension of length and width, the initial rupture
position (subfault (i,j)) relative to the SMGA, the rise time, and the rupture velocity inside SMGA wereset as search parameters. First, we determined the initial value of the element event size given as Eq. (3):𝑆𝑖𝑧𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑒𝑣𝑒𝑛𝑡 = 1⁄𝑓𝑐𝑒 ∗ 𝑉𝑟(3)Where 𝑓𝑐𝑒 is the corner frequency of the EGF event in Hz and 𝑉𝑟 is rupture velocity. In
this research, the range of 𝑉𝑟 is ( 0.6 – 0.9 ) of the shear velocity. Shear velocity depends on the depthof the target event. Then, we did a grid search calculation to get the best value for the SMGA parameters,
including the size of the element event for the SMGA (length and width), the best position for the initial
rupture (i,j) based on the selected strike and dip for each event, the rise time, and the rupture velocity
inside the SMGA. To search the best solution for this, we need to consider the maximum correlation andminimum residual values between the observed and synthetic displacement waveforms.
4. RESULTS AND DISCUSSION
4.1. Estimation source parameters by EGFM
According to the calculation for source modeling parameter, waveforms for the target event are
simulated using the EGFM, then comparing the observation and synthetic waveforms for horizontal
components in acceleration, velocity, and displacement. The scaling parameters for source modelingand the best fit value for the SMGA parameters using grid search calculation are summarized in Table2.
Table 2. Scaling parameter for source modeling and best fit values for SMGA.
Parameter

Source dimension ratio (N)Stress drops ratio (C)Foreshock(Mw 6.4 paired toMw 5.1)
41.3

3Mainshock(Mw 7.0 paired toMw 6.4)2
2.35

Largest aftershock(Mw 6.9 paired toMw 6.2)20.88

Size of the element event
for SMGA (km)Rupture starting point (i,j)
Rise time (s)Rupture velocity (km/s)

Length: 4.6
Width: 3.8
(2,1)
0.21
2.5

Length: 16
Width:15
(1,1)
0.84
3.0

Length: 11.2
Width: 8.2(1,1)
0.6
2.8

The foreshock modeling indicated that the area of the SMGA was the smallest. On the otherhand, the largest SMGA was obtained for the mainshock event. Regarding the SMGA size for theseevents, the western part of Lombok (the area of Mw 6.4 and Mw 7.0) had a lower stress drop than theeastern part of Lombok (the area of Mw 6.9). We can see this in Figure 2, in which green and purple
lines show the SMGA for the 2018 Lombok earthquake sequence. The green line represents the SMGAfor Mw 7.0, 6.4, and 5.1, while the purple line represents the SMGAs for Mw 6.9 and 6.2.

Figure 2. Scaling relationship between strong motion generation area andseismic moment (left) and between rise time and seismic moment (right).
(Update from Miyake et al.,2003).
To validate the stress drop estimation based on the relationship of the SMGA and seismicmoment, we calculated the stress drop for the 2018 Lombok earthquake sequence shown in Figure 2.
We obtained that the stress drop for the mainshock was 1.84 MPa, but for the largest aftershock was3.85 MPa. All of the stress drops were still lower stress drop than the empirical relationship of the SMGA
size to the seismic moment for crustal earthquakes. This suggests the local stress drop variation in theLombok region as well as the regional stress drop variation due to the tectonic setting. In addition, from
Figure 2, we also see that the rise time for the 2018 Lombok earthquake sequence (black squares) is
located in line with the black line. It means that the rise time for the 2018 Lombok earthquake sequenceis similar to the rise time for the crustal event in the United States and Japan (Miyake et al., 2003).
4.2. Source modeling of the 2018 Lombok earthquake sequence
We conducted a source modeling (Figures 3 and 4) on the map based on the best fit value of the SMGA
parameters obtained in Section 4.1 and selected strike and dip projected on the horizontal plane basedon the dip direction. Figure 3 shows the sample modeling for the foreshock event (left) and thecomparison of the observed and synthetic waveforms of acceleration, velocity, and displacement
recorded at the TWSI station at subfault (2,1) (right).
Based on Figure 3 (left), the initial rupture starts at the red star, at the top left-hand of theSMGA, and extends radially toward the bottom right-hand direction (southeast direction) with 2.5 km/s

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of the rupture velocity. The waves are well detected at the TWSI station because they are proportional
to the direction of the rupture propagation. Therefore, the waveform at TWSI in Figure 3 (right) has alarger amplitude and narrower duration than other stations. It is possibly due to the directivity effect.

Figure 3. The foreshock source modeling (left) and the comparison of theobserved and synthetic waveforms of acceleration, velocity, anddisplacement recorded at the TWSI station (right).
As seen in Figure 3, we also conducted source modeling for the mainshock and the largest
aftershock. We obtained that the rupture location for these targets started at a similar position and had
the same rupture propagation direction (Figure 4). The position dominated at the shallow northwestern
corner of the SMGA and extended radially toward the southeast downdip direction.
Based on the evaluation of the rupture propagation and the SMGA size for each event, weobtained a relationship between the foreshock, the mainshock, and the largest aftershock. The foreshock
event may trigger the mainshock, and the mainshock event may trigger the largest aftershock. Therefore,
these Lombok sequences shared similar source characteristics.

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Figure 4. Combination of three source modeling for the target earthquakes in
the 2018 Lombok earthquake sequence. The star and the rectangle
respectively represent the hypocenter and the SMGA for the foreshock (blue),the mainshock (red), and the largest aftershock (black).
5. CONCLUSIONSThe series of the Lombok earthquakes that occurred from July to August 2018 have uniquecharacteristics due to the source heterogeneity in different tectonic settings over the world. To
understand the source characteristics of these earthquakes, we conducted the simulation and modelingusing EGFs for the foreshock with Mw 6.4, the mainshock with Mw 7.0, and the largest aftershock withMw 6.9. We selected one earthquake to be an EGF event that satisfies the requirements, including thefocal mechanism and hypocenter very close to the target event.
The foreshock modeling indicated the smallest SMGA. On the other hand, the largest
SMGA was obtained for the mainshock event. Regarding the SMGA size and rise time for these events,
the western part of Lombok (the region of Mw 6.4 and Mw 7.0) had a lower stress drop than the easternpart of Lombok (the region of Mw 6.9). All were still lower stress drops than the empirical relationshipof the SMGA size and rise time to the seismic moment for crustal earthquakes. This suggests the local
stress drop variation in the Lombok region as well as the regional stress drop variation due to the typicaltectonic setting of the target region.
The rupture for these targets started at a similar position and had the same rupture
propagation direction. The position dominated at the shallow northwestern corner of the SMGA andextended radially toward the southeast downdip direction. Finally, from examining the rupture
propagation and SMGA size for each event, we obtained a relationship among the foreshock, themainshock, and the largest aftershock. The foreshock event may trigger the mainshock, and themainshock event may trigger the largest aftershock. Therefore, these Lombok sequences shared similarsource characteristics.
ACKNOWLEDGEMENTS
This research was conducted during the individual study period of the training course “Seismology,Earthquake Engineering and Tsunami Disaster Mitigation” by the Building Research Institute, JICA,and GRIPS. I would like to express my sincere gratitude to my supervisor Dr. Hiroe Miyake for her
valuable support and experience which helped me to complete my research successfully, and to Dr.
Saeko Kita for her guidance and advice during my individual study. I would also like to acknowledge
Dr. Takumi Hayashida and Dr. Tatsuhiko Hara for their permanent support from the beginning to theend of the program. I would also like to express thankfulness to Ariska Rudyanto, S.Si, Dipl. Tsu, M.Scand Angga Wijaya, S.Tr for their data support and processing during my individual study.
REFERENCES
Hamilton, W, 1977, Subduction in the Indonesion region. In island arcs, Deep sea trenches and backarc basins (eds M.Talwani and W.C.Pitman), http://doi.org/10.1029/ME001p0015.
Hamilton, W, 1979, Tectonic of the Indonesia region, Geol. Soc. Malays. Bull. 6, 3-10.
Irikura, K., & Kamae K., 1994, Estimation of strong ground motion in broad-frequency band based ona seismic source scaling model and an empirical Green’s function technique, Ann. Geofis, 37, 17211743.
Miyake, H., Iwata, T., & Irikura, K., 2003, Source characterization for broadband ground-motion
simulation: Kinematic heterogeneous source model and strong motion generation area, Bull. Seismol.
Soc. Am, 93, 2531-2545.
Silver, E.A., Reed,D., & McCaffrey, R., 1983, Back-arc thrusting in the Eastern Sunda Arc, Indonesia:
A consequence of arc-continent collision, J. Geophys. Res. 88, 7429.

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