LOCAL MAGNITUDE CALCULATIONS FOR
EARTHQUAKES IN AND AROUND BANGLADESH
AND THEIR INFERENCE FOR DISTANCE
CORRECTION FUNCTION
Suman SAHAMEE17706

Supervisor:Tatsuhiko HARAABSTRACT
We calculated local magnitudes for events that occurred in and around Bangladesh from January 2007
to December 2010. We retrieved waveform data from the Incorporated Research Institutions for
Seismology (IRIS) Data Management Centre (DMC) and calculated synthetic Wood-Anderson
seismograms. We selected 30 events for which there are at least 5 waveform data with the high signal tonoise ratio. First we used the distance correction function obtained for southern California to calculate
local magnitudes. We calculated a magnitude residual which is a difference between a magnitude
estimate of each station and the median magnitude of that event. The hypocentral distance dependenceof magnitude residuals is small, which suggests that the distance correction function for this area issimilar to that of southern California. Then, we conducted a grid search for the coefficients of thedistance correction function. The set of the coefficients with the minimum root mean square of themagnitude residuals is similar to that for southern California. We also compared local magnitude
estimates to body wave magnitudes in the ISC catalog to find their correlation.
Keywords: Local magnitude, Distance correction function, Grid search.

1. INTRODUCTION
The Seismic Observatory and Research Centre, Bangladesh Meteorological Department (BMD) isresponsible for providing earthquake information, tsunami advisory and warnings to the government
and public and determines earthquake parameters (epicenters, magnitudes, etc.) of local earthquakes.
The objective of this study is to calculate local magnitude of earthquakes in and around Bangladesh toinfer an appropriate distance correction function of local magnitude for the study area. We also
compare local magnitudes to body wave magnitudes to investigate their correlation.

2. METHODOLOGY
2.1. Local magnitude and recommendations of IASPEIMagnitude is one of important earthquake source parameters. Magnitude scale for earthquakes was
first introduced by Richter (1935, 1958). The equation of the local magnitude
based on themaximum trace amplitude (A) on horizontal components of the Wood-Anderson seismogram inmillimeters is given as:
Bangladesh Meteorological Department (BMD), Bangladesh.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

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(1)
whereis a distance correction function and S is a station correction. The local magnitude
saturates at around 7 (e.g., Hanks and Boore, 1984).
In 2013, the International Association of Seismology and Physics of the Earth’s Interior(IASPEI) Commission on Seismological Observations and Interpretations approved “Summary ofMagnitude Working Group Recommendations on Standard Procedures for Determining Earthquake
Magnitude from Digital Data” which was proposed by the Working Group on Magnitudes. Hereafter
we refer to this procedure as IASPEI (2013). According to IASPEI (2013), the formula of the local
magnitude of the crustal earthquakes for regions where the attenuative properties of seismic waves are
similar to that of southern California is as follows(2)
where A is the maximum trace amplitude in nanometer measured from a horizontal component
seismogram for which the instrumental response of the Wood-Anderson seismograph is convolved(after removing the instrument response by deconvolution) and r is hypocentral distance. The
applicable distance range ofis up to 1000 km. The coefficients are obtained for southern
California by Hutton and Boore (1987). The constant term is based on the static magnification of theWood-Anderson torsion seismometer (Uhrhammer and Collins,1990).
The formula proposed by IASPEI (2013) for regions where the attenuative properties aredifferent from that of southern California is of the form:(3)
where A is the maximum amplitude in nanometer on the vertical component of the Wood-Anderson
seismogram, andis a distance correction function.
2.2. Local magnitude calculations using distance correction function for southern California
We first calculate
using the distance correction function given in Eq. (2). We did not include
station corrections in the calculation. We use the median of the magnitude estimates for an event as theestimate for that event. Then we calculate local magnitude residual which is defined as the difference
between each estimatedfor a seismic station and the estimate for the same event. We calculate
the root mean square (RMS) of the magnitude residuals.
2.3. Grid search method for determination of the distance correction function
The equation ofdistance correction used by Hutton and Boore (1987) has the following form:(5)

where n and K are the coefficients for geometrical spreading and attenuation of seismic waves,respectively.
Table 1. The range of n and K withWe set up an appropriate range for theseincrements used in the grid search.
unknown parameters to conduct grid search, which Coefficients Lower Upper Increments
is shown in Table 1. For each set of the coefficients
bounds bounds
we calculated, their medians for each event,
0.7
20.25
nandresiduals by the same process described in
0.001
0.004
0.00005
KSection 2.2.

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We fit a straight line to obtain distance dependence of magnitude residuals. Finally, we
calculated the RMS of the magnitude residuals, slope, a, and the intercept, b, for each set of thecoefficients.

3. DATA
3.1. Data acquisition

The range of latitude and longitude of the study area is 19 degrees to 28 degrees and 87 degrees
to 95 degrees respectively. Waveform data of seventy one events that occurred between January 1,
2009 and December 31, 2010 were available at the Wilber 3 of the Data Management Centre (DMC) of
Incorporated Research Institutions for Seismology (IRIS). The range of the focal depth is set to thatbetween 0 and 40 km. The magnitude range is that between 4.0 and 6.9. At that time, one project wasoperational by the name of network code XI “Collision of the Burma Arc accretionary prism andfoldbelt with the Ganges-Brahmaputra Delta in Bangladesh” (Seeber et al., 2007). For that project, inBangladesh 16 seismic stations with three components broadband seismometers were deployed andoperated by the Lamont Doherty Earth Observatory (LDEO), Columbia University. In addition, the data
was taken from the other stations of all available networks.
3.2. Data retrieval
We retrieved SAC waveform data from the IRIS DMC. There were 1136 vertical component waveform
data from 148 stations of 10 networks in the hypocentral distance range up to 1000 km. In thisstudy, we used the data from short period channels and broadband channels. We used Seismic Analysis
Code (SAC, Goldstein and Snoke, 2005) to calculate synthetic Wood-Anderson seismograms. We
downloaded the event information from the catalog of International Seismological Centre (ISC) for thecomparison of magnitudes.
3.3. Data processing and amplitude measurement procedure.
The instrument response was first removed from the observed waveform data by deconvolution. Thenthe frequency response of the Wood-Anderson seismogram obtained by Uhrhammer and Collins(1990) was used to calculate synthetic Wood-Anderson seismograms. An example of the waveform
data from station JAFL of network XI for the event that occurred at 18:51:51 UTC on 26th August,2008 (4.8; depth 18 km) in Bangladesh is shown in Figure 1.
(b)(a)

Figure 1. (a) The upper trace and the lower trace show an example of observed waveform data andsynthetic Wood-Anderson seismograms, respectively. (b) The same waveform data shown in (a) arepresented in the different time range. The maximum trace amplitude is measured on the simulated
Wood-Anderson seismogram by the peak and trough, which are marked by T8 and T9 in the lowertrace, respectively.

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Then we evaluated the noise level (N) by the RMS of the time series in between 10sec and5sec before the theoretical P wave arrival time. We evaluated the signal level (S) by the RMS of thetime series in between 5sec and 10sec after the theoretical P wave arrival time. Then we obtained thesignal to noise ratio (S/N).
We used only data with. Finally, we selected the events under the condition thatthe minimum number of stations for a particular event is five. In total 424 vertical component waveform
data (378 broadband and 46 short period) of 30 events are used. The epicenters are shown in Figure 2.
The data were recorded by the 95 stations of the 8 networks (Figure 3).

Figure 2: The epicenters of 30 events selected in Figure 3: The locations of the 95 stations of the 8this study.
networks in this study.

4. RESULTS AND DISCUSSION
4.1. Forward calculations
The procedure to calculate local magnitudes was described in Section 2.2. Figure 4 represents local
magnitude residuals as a function of hypocentral distance.
The hypocentral distance dependence of the magnitude residuals is very small. It suggeststhat the distance correction function appropriate for the study area is similar to that for southern
California. Figure 5 shows the frequency distribution of theresiduals. The RMS of the magnituderesiduals is 0.3021.

Figure 4. Local magnitude residuals with respect to Figure 5: Frequency distribution of themagnitude residuals.
hypocentral distance.

44.2. Grid search for coefficients n and K
A grid search was conducted to find the appropriate value of the coefficients n and K. The procedureof grid search was described in Section 2.3. Table 2 represents the five set of the coefficients n and K
with the smallest RMSs ofresiduals .
Table 2. The value of coefficients of n and K obtained from the grid search method.
n1.1
1.15
1.025
1.05
1.2

K
0.001800.001750.001850.001850.00170RMS
0.300970.30100
0.30104
0.30104
0.30104|a*1000|
0.030
0.034
0.044
0.027
0.039

b0.044
0.047
0.053
0.040
0.050

These coefficients are similar to those for southern California obtained by Hutton and Boore(1987), which is consistent with the inference suggested in Section 4.1, although the coefficients are
not tightly constrained as is shown in Table 2. In neighboring countries, different distance correction
functions are used for local magnitude calculations (e.g., Baruah et al., 2012; Baillard et al., 2017).
The difference between this study and their formula is likely to partly reflect that the area in this study
is rather wide including different tectonic regions.
Figure 6 shows that the distribution ofresiduals with hypocentral distance for thecoefficients n = 1.1 and K = 0.0018, which provides the minimum RMS of theresidual. Figure 7
shows the frequency distribution ofresiduals.

Figure 6. Local magnitude residuals with respect tohypocentral distance using the coefficients providing the Figure 7. Frequency distribution of theminimum RMS of the magnitude residuals in this study.
magnitude residuals.
4.3. Comparison between

calculated and body wave magnitude from ISC

We compared thecalculated for n = 1.1 and K = 0.0018 with the body wave magnitudes in thecatalog of the International Seismological Centre to find that they are correlated and comparable(Figure 8).

5Figure 8. Comparison between local magnitudes (this study) and body wave
magnitudes in the ISC catalog.

5. CONCLUSIONSIn this study we conducted local magnitude calculations and a grid search for the coefficients of a
distance correction function in and around Bangladesh. We selected data based on the signal to noise
ratios. We used only events for which there are at least five amplitude data. We used 424 verticalcomponent waveform data for 30 earthquakes. The observed waveform data were used to computesynthetic Wood-Anderson seismogram for measuring maximum amplitudes.
We first calculated local magnitudes using the distance correction for southern California.
We computed a median using the magnitudes of all stations for an event and calculated theirmagnitude residuals. The weak distance dependence of the magnitude residuals suggests that thedistance corrections is similar to that of southern California. We used the grid search to confirm thisinference. We calculated RMSs of the magnitude residuals for each set of the coefficients. The set ofcoefficients which provides the minimum RMS residuals is similar to that for southern California. We
also compared the calculated local magnitudes to body wave magnitudes in the ISC catalog. The local
magnitudes and the body wave magnitudes were correlated.

ACKNOWLEDGEMENTS
I wish to pay my sincere gratitude to the supervisor and advisor Tatsuhiko Hara for his continuous
support, valuable suggestion and instruction during my study. I retrieved the waveform data from theIRIS-DMC and used SAC software for the analysis of data.

REFERENCES
Baruah, S., Baruah, S., Kalita, A., 2012, Geomatics, Natural Hazards and Risk, 3, 365-375.
Baillard, C., Lyon-Caen, H., Bollinger, L., Rietbrock, A., 2017, Geophys. J. Int., 209, 1111-1125.
Goldstein, P., and Snoke, A., 2005, SAC, https://ds.iris.edu/ds/newsletter/vol7/no1/193/.
Hutton, L.K., and Boore, M.D., 1987, Bull. Seismol. Soc. Am., 77, 2074-2094.
Hanks T.C., and Boore D.M., 1984, J. Geophys. Res., 89, 6229-6235.
IASPEI, 2013, htttp://iaspei.org/pub/commissions/CSOI/Summary_WG_recommendations_20130327.pdf.
Incorporated Research Institutions for Seismology (IRIS), https://www.iris.edu.
Richter, C.F., 1935, Bull. Seismol. Soc. Am., 25, 1–31.
Richter, C.F., 1958, Elementary Seismology, Freeman, W. H. San Francisco, p578.
Seeber, L., Steckler, M., and Kim W., 2007, FDSN, XI_2007, https://doi.org/10.7914/SN/XI_2007.
The International Seismological Centre, http://www.isc.ac.uk/.
Uhrhammer, R.A., and Collins, E.R., 1990, Bull. Seismol. Soc. Am., 80, 702–716.

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