MOMENT TENSOR AND SOURCE PROCESS OF
EARTHQUAKES IN FIJI REGION OBTAINED BY
WAVEFORM INVERSION
Seru Sefanaia*
MEE07167

Supervisor:

Yuji YAGI**

ABSTRACTWe evaluated the quality of the local seismic waveform recorded at Yasawa station established by theMineral Resources Department (MRD, Fiji), and tried to estimate moment tensor solution by using
this waveform data. We also estimated moment tensor solution and seismic source process by using
teleseismic body wave so as to investigate the faulting system in Fiji region. As for the evaluation of
the quality of the waveform recorded at the Yasawa station, we found that EW and NS components
were down frequently, and moment tensor solution obtained by 3 components of the Yasawa station is
totally opposite to the Harvard CMT solution. This result may suggest that the polarity of the local
seismometer components was in a reverse direction and magnification of the seismometer response
information is not correct at this stage. We obtained a consistant result when we divided by -10 toobserved waveform. Moment tensor inversion analysis was also carried out for 30 events by using
teleseismic body-wave downloaded from the IRIS-DMC. Final results are well consistent to Harvard
CMT solution. Rupture source process analysis was conducted for the two deep intraslab events that
occurred respectively along the Tonga Kermedec subduction zone and two shallow depth events
which occurred respectively along the transform fault zones. The rupture processes for the two deep
earthquakes are characterized by the rupture propagating mainly along the strike of the fault plane.
The two shallow events occurred along the transition zone also characterized by the rupture
propagating along the strike of the Fiji Fracture Zone but are controlled by the geometry of the fault.
Keywords: Moment tensor inversion, Rupture process inversion, teleseismic data, near-source data.
INTRODUCTION
Earthquake focal mechanisms are basic and important information in seismology and have beenutilized for understanding regional tectonic stress fields, source mechanisms of large earthquakes,
simulation of strong motion, faulting systems, tsunami generation and so on. It is important toestimate focal mechanisms of earthquakes routinely as well as to make a homogenous catalogue of
moment tensors (or focal mechanisms) from small to large earthquakes for future references.
Moment tensor and rupture process inversion analysis has not so far being carried out in Fiji.
Therefore in this study, we evaluated the quality of the local seismic waveform data obtained from theYasawa broadband station established by Mineral Resources Department (MRD, Fiji), then we tried
to estimate moment tensor solution by using this waveform data and as well as to estimate moment
tensor solution and seismic source process using teleseismic body wave so as to investigate thefaulting system in the Fiji region.
____________________________*Mineral Resources Department (Seismology Section) of Fiji.
**Ass. Professor, Institute of Physical Sciences, University of Tsukuba, Japan.
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DATA
We used both near-source data recorded at Yasawa broadband station established by Mineral
Resources Department, Fiji with range from March 2003 to December 2005 as well as teleseismic
body-wave (P-wave) data recorded at FDSN and GSN network stations collected by the DataManagement Center of the Incorporated Research Institution for Seismology (IRIS-DMC).
Table 1: Shows the quality of Yasawa station components
The raw continuous Yasawa
waveform data was converted fromnanometrics to seed format bymakeseed software provided by
Nanometrics Inc. Further, we
obtained the waveform data in SAC
format by using rdseed software
which was available from the IRISDMC homepage. The broadband
data were converted and numericallyintegrated from volts into the ground
velocity cm/s and then band-passed
between 0.01 and 0.1 Hz to reduce
the effect of fine 3D structure anddetailed source process. Table 1

o – Waveforms well recorded.
x – Component broken.

shows the quality of waveforms recorded at the Yasawa station in each period. For teleseismic bodywaves we retrieved and selected the IRIS-DMC stations from the viewpoint of good azimuthal
coverage with the distance range from 30° to 90°. We referred to earthquake event list from theHarvard CMT catalogue from year 1990 to present. Thirty events with Mw > 6.5 occurred within Fijiregion were analyzed for moment tensor inversion and 4 of these events were analyzed for theirsource rupture processes.
THEORY AND METHODOLOGY
Moment Tensor Inversion
To obtain moment tensor components of overall earthquake, we represented the seismic source
process as point source model.
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u j (t ) = ∑ G jq (t , ξ c ) * M q' (t , ξ c ) + eo + em
q =1

= ∑ M q′′ (G jq (t , ξ c ) * T (t ) ) + eo + em
5

(1)

q =1

where M q' and M q" are moment tensor at centroid of source ξ c , T(t) is source time function, and em ismodeling error. For simplicity, the observation equation of (1) can be rewritten in vector form:(2)d j = H (T (t ), ξ c ) j a + e j2

where d and e are N-dimensional data and error vectors, respectively, a is a 5-dimensional model
parameter vector, H is a N x 5 coefficient matrix. The solution of the above matrix equation is
obtained by using least square approach, if we assumed source time function and the centroid location.
We determined the depth of centroid and the duration and shape of source time function by gridsearch method since these are needed for moment tensor inversion for the analysis of teleseismic bodywave. For analyses of near-source data, we applied low pass filter to mitigate source time function
effect and then estimated the depth of centroid by grid search method.
Rupture Process Inversion
To estimate rupture process, we basically followed the formulation by Yagi and Fukahata (2008). A
vertical component of P-wave at a station j due to a shear dislocation source on a fault plane S is givenby2

u j (t ) = ∑ ∫∫ G jq (t , ξ ) * D& q' (t , ξ )dS + eo ,

(3)

q =1

where G jq is a Green’s function, D& q' is a spatio-temporal slip-rate distribution, and * denotes the
convolution operator in time domain. To formulate the inverse problem, we represent the spatiotemporal slip-rate distribution D& q' by linear combination of a finite number of basis functions:KL

D& q' (t , ξ c ) = ∑∑ aklq X k (ξ )T (t ) + δD& q' (t , ξ ) ,(4)

k =1 l =1

where aklq are model parameters to be determined from observed data. X k (ξ ) and Tl (t ) are thebasis functions for space and time, respectively. We can rewrite in vector form:

d j = H j a + e mj ,(5)where dj and emj are Nj-dimensional data and error vectors, respectively, a is a M-dimensional model
parameter vector, and Hj is a N j × M coefficient matrix.

RESULTS AND DISCUSSIONS
The results of this study are divided into three (3) main parts:
Part I: Moment Tensor Inversion using near source data obtained by Local Seismic Station
The local data set obtained for this study was from the period of its establishment in March, 2003 to
December, 2005. We estimated the centroid moment tensor solution by using local seismic data whichcontains three components waveform. Green’s function for near-field was calculated using programby Kohketsu (1985), and performed waveform inversion using program by Yagi (2006). To obtain thelocation of centroid, we applied the grid search method.

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b)
a)

c)

We found the inconsistencies between this study solution(Figure 1a) and the Harvard CMT solution even if
waveform fitting is good (Figure 1b). The result for thisstudy is totally opposite to the Harvard CMT solution. Oneof the possibilities for this difference may be the polarity setup (EW and NS) components is in a reverse direction. If we
divide by -1 to the waveform in our SAC program, the focal
mechanism is well consistent with the result of Harvard
CMT (Figure 1c). We should point out that our result(Figure 1c) is ten times larger in seismic moment than the
Harvard result. This result implies that the magnification of
the Yasawa seismometer information is not correct at thispresent time.

Figure 1. Moment tensor solutions. a) Result obtained by this study using local seismic
data recorded at Yasawa station. b) Harvard CMT solution. c) Result for the reverse
polarity waveform. The red curve is the theoretical waveform and the black curve is theobserved waveform.
Part II: Moment Tensor Inversion by using Teleseismic Body Waveforms.
In Part II of this study, 30 events (Mw >6.5) that occurred within the Fiji region were analyzed byusing teleseismic body waveforms downloaded from the Data Management Center of theIncorporated Research Institutions for Seismology (IRIS-DMC). We performed moment tensor
inversion analysis for these local events by using moment tensor inversion programming coded by
Yagi (2008). The depth of hypocenter, the seismic moment (Mo) and the final focal mechanism‘beachball’ solutions of this study was computed with that of Harvard GMT solutions.

Figure 2. Graph of Depths (Harvard Solution)-km
vs. Depths (this_study) in km.

Figure 3. Graph of LogMo (Harvard Solution)
vs. LogMo (this_study)

Our results reveal the consistencies with the depths of hypocenters (Figure 2) and logMo (Figure 3)
in the two solutions. Such a difference observed is due to that the Harvard University routinely carried4

out the overall waveform picking in their moment tensor analysis, whereas in this study utilizes only
the P-wave for such analysis of moment tensor.
Figure 4 exhibits the final moment tensor solution of
this_study plot as “beachballs” on the Fiji region map.
Shallow depth events with strike-slip faulting typeoccurred mainly along the two Fracture zones, the Fiji
Fracture Zone and the Hunter Fracture Zone. The rest
are intermediate to deep intraslab earthquakes along thetwo subduction zones with mostly reverse and normal
faulting type.

Figure 4. Focal mechanism plot of this study.
Part III: Analysis of rupture source process
Four earthquakes were analyzed for their rupture source processes during their occurrences. Two deep
intraslab events which occurred along the Tonga subduction zone and two events were of shallow
depths occurred along the Fiji Fracture Zone. We applied inversion code originally given by Yagi andFukahata (2008) so that the constraints of smoothness and positivity were imposed on the solution
used in this analysis. To detect actual fault plane, we found the fault plane and average slip direction
which show best fitting using grid search method.
In general, for deep earthquakes rupture
propagates mainly along the strike direction due
to the thinness of the seismogenic zones at deeper
depths as proved by our results shown on Figure
6. As for shallow earthquakes along the Fiji
Fracture Zone, the rupture propagates along the
strike (NE and SW) direction and breaks somepart of the fault, however the propagation of the
rupture seems to be controlled by the geometry of
the fault as proved by this study solution shown
on Figure 7.
Figure 5. Indicates the location of the two events
plotted as “beachballs” on Fiji map

Figure 7. Shows the final results of inversion for one of
Figure 6. Shows the final results of inversion
for one deep event 19940309. The star indicates the shallow depth earthquake 19980112. The star
5 indicates the location of the initial break.
the location of the initial break.

CONCLUSION
In this study, we first investigate the quality of waveforms recorded at Yasawa station which isoperated by the Mineral Resources Department of Fiji. Using three components waveform recorded at
Yasawa, we tried to estimate the centroid moment tensor solution so as to compare it with the result ofHarvard CMT. We found that the solution by this study is not consistent with the Harvard CMT. If we
divided by -10 to the observed waveform, we can obtain a consistent result as the Harvard CMT. On
the other hand, moment tensor inversion analysis was carried out by using teleseismic bodywaveforms for 30 past local earthquakes (Mw>6.5) retrieved from IRIS-DMC. We found that middle
earthquake with shallow depth located along the two major fracture zones, the Fiji Fracture Zone
(FFZ) and the Hunter Fracture Zone (HFZ) and intermediate and deep earthquakes located within thetwo subducting slab, the Tonga Kermedec subduction zone and the Vanuatu Trench. The focal
mechanisms are well consistent with tectonic setting. In the final part of this study, source process
inversion was performed for four events. As for deep earthquake, since thickness of seismogenic
zones within the slab decreases with depths, the direction of rupture propagation during a large
earthquake should be mainly along the strike of the slab. For shallow earthquake occurred within the
Fiji Fracture Zone, rupture propagated along strike direction, NE and SW direction or parallel to thedirection of the Fiji Fracture Zone. In general, for shallow earthquakes during such rupture, it breaks apart of the fault and the rupture propagation direction seems to be controlled by the orientation or thegeometry of the fracture zone. Our results agree well to the theory.
RECOMMENDATION
Based upon the purpose of this study, the following recommendations are put forward.
1. To investigate and check the polarity of Yasawa broadband station as well as themagnification of the seismometer information and efforts should be made for our Mineral
Resources Department (MRD) to monitor and maintain this station.
2. Also to check and maintain our CTBTO broadband station.
3. Moment tensor analysis to be carried out routinely for all medium-large size earthquakes thatwill occur within the Fiji region by using both near source data and teleseismic body-wave.
4. Database for this analysis should be compiled and accessed as references for future purposes.
ACKNOWLEDGEMENT
I would like to take this great opportunity to express my heartfelt thanks to my advisor Dr Hiroshi
Inoue for the important advice given all the time especially regarding our seismic network in Fiji.
REFERENCES
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Kohketsu, K., 1985, J. Phys. Earth, 33, 121-131.
Rognvaldsson, S. T. and Slunga, R., 1993, Bull Seis. Soc. Am. Vol. 83, 4, 1232-1247.
Tibi, R., Estabrook, C. H. and Bock G., 1999, Geophys. J. Int. (1999), 138, 625-642.
Yagi, Y., Kikuchi, M., 2000, Geophys. Res. Lett., Vol. 27, 13, 1969-1972.
Yagi, Y., Mikumo, T., Pacheco, J. and Reyes, G., 2004, Bull Seis. Soc. Am. Vol. 94, 5, 1795-1807.
Yagi, Y., 2007-2008, IISEE/BRI.

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