FOCAL MECHANISM DETERMINATION USINGWAVEFORM DATA FROM A BROADBAND STATION
IN THE PHILIPPINES
Vilma Castillejos Hernandez
MEE10508

Supervisor:

Tatsuhiko Hara

ABSTRACT
We performed time domain moment tensor inversion using broadband waveform data recorded at a
broadband seismic station in the Philippines to investigate its applicability. We used a time domain
moment tensor inversion code (TDMT_INVc) in this study. The Green’s functions are computed byfrequency wavenumber integration program. We utilized broadband waveform data recorded at aseismic station at Davao; the station code is DAV. The waveform data were retrieved from theIncorporated Research Institutions for Seismology-Data Management Center (IRIS-DMC). We
analyzed two earthquakes that occurred near station DAV. They are the events that occurred on
September 18, 2009 (Mw 5.7) and May 31, 2010 (Mw 5.9). We used three one-dimensional cruststructure models to compute Green’s functions. They were model iasp91 and the two other models(J1 and S1) from CRUST 2.0. The obtained solutions of the focal mechanisms were compared to theGlobal CMT. In terms of focal mechanisms and variance reductions, we obtained better solutions
when we used model J1 as a crust structure. We performed inversions over a range of source depth.
The variations of variance reductions as a function of depths show the clear peaks, which suggeststhat it is possible to determine a good focal depth. It is difficult to have a tight constraint for focal
depth using the variance of residuals divided by the percent double-couple in our analyses. Since
another seismic station in the study area has been upgraded to a broadband station recently, it will bepossible to improve the accuracy of focal mechanism determination by the procedure used in thisstudy.

Keywords: Focal mechanism, moment tensor, broadband waveform, velocity structure.

1. INTRODUCTION
Focal mechanisms provide important information for seismotectonic and hazard studies to regions
such as the Philippines, where about twenty earthquakes occur everyday. Each earthquake radiates
seismic waves that travel through the earth and are recorded by the seismic stations on the surface.
Seismic waves are practically the only signal that can penetrate into the depth of the earth and bringback information about the interior of the earth.
Moment tensor/Focal mechanism analysis involves fitting theoretical waveforms withobserved broadband waveforms to determine moment-tensor elements. A broadband seismic
waveform carries the characteristics of earthquake source and structure along the propagation path.
Given a set of seismograms and an appropriate structure model one can correct for propagation effects
and obtain information on the source. Also, investigation using broadband waveform of local
earthquakes can estimate seismic velocity structure (e.g., Dreger et al. 1990).
Philippine Institute of Volcanology and Seismology–Department of Science and Technology, Philippines.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

1Since the broadband seismic stations in the country are continuously increasing in number,various seismological data analyses will be able to perform such as determination of focal mechanism
solutions and an investigation of the crustal structure beneath these broadband recording stations. In
the present study, we investigated the applicability of time domain moment tensor inversion by
performing inversions using broadband data from an existing broadband station in the Philippines. We
used three crust models to investigate which is more appropriate for the study region.
2. DATA
2.1 DAV Station
The station DAVAO (DAV) is located in the city of Davao on the island of Mindanao, southeastern
Philippines. It is located in an area of intense seismicity and complex tectonics. Digital broadband
seismic data from DAV station has been available since 1994 and can be accessed from theIncorporated Research Institutions for Seismology-Data Management Center (IRIS-DMC).
2.2 Event Selection
The focal depth is less than 40 km. The epicentral distance is less than 200 km. The short epicentral
distances help to reduce possible errors introduced by the differences between the velocity model andthe true ground structure such as scattering effects and phase shifts.
The seismograms used in this study are from two moderate crustal earthquakes. The 1 st event
is an Mw 5.7 occurred on 18 September 2009, its origin time is 11:53:51.8 GMT (USGS). The 2ndevent is an Mw 5.9 recorded on 31 May 2010, its origin time of 10:16:03.4 GMT (USGS). Bothearthquakes have clear seismic data recorded for the three components, which is an essential todetermine the focal mechanism solution.
3. THEORY AND METHODOLOGY
3.1 Time Domain Moment Tensor Inversion
We used the time domain moment-tensors inversion code TDMT_INVc developed by Dreger (2003)
to determine seismic moment tensors by inversion of three-component broadband waveform. The code
is designed to obtain reliable solutions using a minimal number of stations based on the paper ofDreger and Helmberger (1993). In this study we used three component broadband seismogram from asingle station.
3.1.1 Data Preparation
Preparation of the observed waveforms consists of thefollowings: 1) removing the instrument response, 2)
rotation of the horizontal components to radial andtransverse components, 3) integration to convert
displacement, 4) passband filtering between 0.02 Hz
and 0.05 Hz, 5) re-sampling the data to 1 sample persecond to match the Green’s functions. The Green’s
functions are filtered with the same passband filter forthe observed data. Figure 1 shows the observed
waveforms and the filtered seismograms.
3.1.2

Computation of Green’s Function2Figure 1. The observed waveform for the event
18 September 2009 (the upper three traces).
The lower three traces are the time series
obtained after the procedure explained in 3.1.1
is applied.

We generate a suite of Green’s function over a rangeof source depth for each source-station distance using
the available crustal models for the calculation of theGreen’s function to model the observed waveforms.
The frequency-integration program (Saikia 1994) isused to compute the Green’s functions to invert thesynthetic waveform data. Subsequently, inverse Fast
Fourier Transform (FFT) was performed to construct
an eight-component waveform data in ASCII format.
The ordering of the components is as follows:transverse component vertical strike slip (tss) andFigure 2. Green’s functions for thevertical dip slip (tds) faults, radial component verticalstrike-slip (xss), vertical dip-slip (xds) and 45-degree
eight components. (see text for details)
dip-slip (xdd) faults, vertical component vertical strike
slip (zss), vertical dip-slip (zds), and 45-degree dip slip (zdd) faults (Jost and Hermann 1989). An
acausal (two pass) 4th order Butterworth filter is applied using Seismic Analysis Code (Goldstein et al.,2007) for the seismic waveform analyses. The frequency passband for both data and Green’s function
use the same filter. Figure 2 shows am example of the filtered functions for the eight components. Theordering of the components is described as the same manner as mentioned in the computation forGreen’s function. The same passband filter is applied to the Green’s function.
3.1.3 Moment Tensor Inversion
The observed seismograms are assumed to be represented by the following equation,(1)
where,

Un is the observed nth component of displacement.
Gnij is the nth component Green’s function for specific force couple orientations.
Mij is the scalar seismic moment tensor.
i, j indices refer to the geographical directions.

Mij describes the strength of the force-couples. The general force-couples for a deviatoric
moment tensor are represented by vertical strike-slip, vertical dip-slip and 45 degree dip-slip. Linear
least squares for deviatoric moment tensors are performed for Eq. (1).
To determine the source depth, inversions are performed over a range of source depths taking
the best solution with the largest variance reduction (e.g., Dreger and Helmberger 1993) defined by:(2)
where,datai is the observed waveform.
synthN is the synthetic waveform.
VR is the variance reduction.
and the summation is performed for all components.
Another useful measurement for determining source depth is the RES/Pdc or variance ofresiduals divided by the percent double-couple defined by:(3)
where, RES is the residual variance and Pdc is the percent double-couple (the ratio of double couple
component to total seismic moment). Dividing the variance by percent double–couple tends to deepen
the minimum. The datai and synthN are the data and Green’s function time series.

33.2 Construction of 1-D crust models
We constructed velocity models using CRUST2.0. This global crustal model uses a type key to assign
crustal structure at a 2x2 degree model which composed of 360 key one-dimensional profiles, where
one of these profiles is assigned to each 2x2 degree cell (Bassin et al. 2000).
Figure 3 shows the assigned crust types in our study region. The crustal velocity comprisesof model J1 for an island arc, model S1 for the continental slope with a transition of 1 km sediments.
In addition, model iasp91 model (Kennett et al. 1991) was also used in this study for earth structurecomparisons. Figure 4 shows P-wave velocities of the three models. The water layer for model S1 wasremoved since the ray path travels mainly beneath the land area. This model was used as a possiblemodel with a thinner crust.

Figure 3. The key codes of CRUST2.0 for thestudy region. The upper right panel shows thelocation of the study region in the red rectangular.
4.

Figure 4. The red lines, dashed green lines
and blue lines denote P-wave velocities ofmodels J1, S1 and iasp91, respectively.

RESULTS AND DISCUSSION

4.1 Event 18 September 2009
Figure 5 shows the focal mechanism obtained for modelJ1 in case a depth is set to 5 km, which gives the largest
variance reduction for this model. The comparison
between the observed waveform denoted by the solid
curves, and the synthetic waveform denoted by the dashedcurves, is also shown in the same figure. The obtained
focal mechanisms for model J1 at different depths areshown in Figure 6.
We applied a passband filter with cornerfrequencies between 0.02 Hz and 0.05 Hz to the observed
seismograms. We found a better solution when thispassband filter was used. In terms of variance reduction
and focal mechanism, model J1 provides the better
solution than the other two models. Figure 7 shows thevariance reduction for model J1. For both models S1 andiasp91, the largest variance reductions are obtained for a
depth of 5 km. Their focal mechanisms are shown in
Figure 8 and Figure 9.

Figure 5. Moment tensor solution formodel J1 with a depth of 5 km. The
Global CMT solution is also shown.

Figure 6. Variation of moment tensor solutions
with different depths for model J1.

Figure 7. Variance reduction for model J1

4

Figure 9. Moment tensor solution formodel iasp91 with a depth of 5 km.

Figure 8. Moment tensor solution formodel S1 with a depth of 5 km.
4.2 Event 2010 May 31

Figure 10 shows the focal mechanism obtained for the model J1 in case a depth is set to 9 km, whichgives the largest variance reduction for this model. The comparison between the observed waveform
denoted by the solid curves, and the synthetic waveform denoted by the dashed curves, is also shownin the same figure. The obtained focal mechanisms for model J1 at different depths are shown in
Figure 11. The focal mechanism obtained for the model S1 at depth of 5km is shown in Figure 12.
Figure 13 is the focal mechanism obtained for models iasp91 when depth is set to 23 km. Among thethree crust models used, model J1 provides the better solution. Figure 14 shows change of variancereduction as a function of depth for the three crust models used.

Figure 10. Moment tensor solution for the J1model with depth of 9 km. The Global CMT
solution is also shown.

Figure 11. Variation of moment tensor
solutions with different depths for model J1.

Figure 12. Moment tensor solution for model S1
with depth of 5 km.

Figure 13. Moment tensor solution for model
iasp91 with depth of 23 km.

5

(a)

(b)

(c)

Figure 14. Change of variance reduction a function of depth for (a) model J1 (b) model S1 (c) model
iasp91, respectively.
5. CONCLUSIONSIn this study, we performed time domain moment tensor inversion using a broadband waveform data
recorded at one of the broadband seismic stations in the Philippines. We applied time domain moment
tensor inversion code (TDMT_INVc) developed by Dreger (2003). We utilized broadband waveform
data recorded at DAV seismic station. The seismograms were requested and retrieved fromIRIS-DMC.
We analyzed two crustal earthquakes. They are the events on September 18, 2009, Mw 5.7 andMay 31, 2010 Mw 5.9. Three one-dimensional crust structures were used for the calculation ofGreen’s function to model observed waveform data. They are model iasp91and the two models (J1 andS1) from CRUST2.0. The results of our focal mechanism were compared to the Global CMT solution
to investigate its reliability. Among the three crust structures used, model J1 provided the bettersolutions. We generated a suite of Green’s function over a range of source depth. Our result shows thatthe variance reduction as functions of depths shows the clear peaks, which implies that it is possible todetermine a good focal depth. On the other hand, the behavior of the variance of residuals divided by
the percent double-couple seems complex.
Recently, another seismic station in the study area has been upgraded to a broadband station;
data from this station will help to improve the accuracy of focal mechanism determination by theprocedure used in this study.
ACKNOWLEDGEMENT
I would like express my sincere gratitude to Toshiaki Yokoi, Dr. Nobuo Hurukawa, Dr. Bartolome C.
Bautista, Dr. Ma. Leonila P. Bautista, Mr. Ishmael Narag and Dr. Renato U. Solidum Jr for the supportand valuable comments. We used Generic Mapping Tools (GMT) (Wessel and Smith 1998) for someof the figures in this study.
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