DETERMINATION OF LOCAL MAGNITUDE SCALEFOR UGANDANYAGO Joseph
MEE12609

Supervisor:

Tatsuhiko HARAABSTRACT
We have derived a local magnitude ML scale for Uganda using waveform data recorded by atemporary broadband seismic network deployed in Uganda and a permanent broadband station. We
used 54 earthquakes recorded between July 2007 and November 2008. First, we determined
hypocenters of these earthquakes using P and S phase arrivals. Most of their locations are associatedwith the western rift of the East African Rift System. We compared the hypocenters of sevenearthquakes determined by this study to those reported by NEIC’s PDE catalog and IDC bulletins.
They do not differ much, and they are roughly consistent with each other. To develop the ML scale, weremoved instrument responses in the waveforms and then applied the frequency response of thestandard Wood-Anderson torsion seismograph for amplitude measurements. We obtained 529
amplitude data from horizontal components of 52 earthquakes whose focal depths are up to 34 km. We
performed simultaneous linear inversion to determine the coefficients of distance correction function
and local magnitudes to obtain the formula M L  logA  0.848 logr 100  0.00116 r  100  3.0 ,where A is the maximum peak amplitude (mm) observed on the horizontal component seismogram,and r is the hypocentral distance (km). The coefficients of the above formula are smaller than thoseobtained for Southern California, and closer to those obtained for Tanzania. Uganda, through the
Department of Geological Survey and Mines (DGSM), is in the process of upgrading its seismologicalmonitoring network with modern digital monitoring and data acquisition systems. Therefore, the resultof this study and its application to data from the upcoming new seismic network will be useful for
improving earthquake monitoring and seismicity study in Uganda.
Keywords: ML, amplitude, hypocenter, distance correction.
1. INTRODUCTION
The use of earthquake magnitude scales to quantify seismic energy and moment released byearthquakes is a common practice in the field of seismological data analysis. One of the most widelyused magnitude scales at local epicentral distances is the local magnitude (ML) scale, originallydefined by Richter (1935, 1958). ML scale is typically based on amplitude measurements of highfrequency S waves (Brazier et al., 2008).
The main objective of this study is to determine a local magnitude, ML scale for Uganda.
There is need to develop a magnitude scale to be able to accurately quantify earthquakes occurring
within the study area.
2. SEISMIC STATIONS AND DATA
2.1 Seismological data acquisition

Department of Geological Survey and Mines, Seismology Unit (DGSM) Entebbe, Uganda.
International Institute of Seismology and Earthquake Engineering, Building Research Institute (IISEE, BRI)
Tsukuba, Japan.
1In this study, seismic data from 12 seismic stations were used. The 11 stations were part of aseismological experiment, the AfricaArray-Uganda Broadband Seismic Study conducted between July
2007 and November 2008. We also used additional waveform data recorded by a Global
Seismographic Network (GSN) station MBAR. Figure 1 shows the location of seismic stations used inthis study.
2.2

Data retrieval

We retrieved broadband waveform datafrom the IRIS DMC in the SEED format.
We obtained waveform data for 54 local
seismic events. We used RDSEED program
to convert the SEED format data to SAC
format.
3. METHOD AND DATA ANALYSISPROCEDURE
3.1 Hypocenter determination

Figure 1. Locations of seismic stations used in thisstudy are indicated with diamonds. The Pink
diamonds denote AfricaArray temporary broadband
stations, and the green diamond denotes the IRISGSN station.

We performed hypocenter determination for
the 54 local earthquakes using the location
program, HYPOCENTER 4.0 (Lienert andHavskov, 1995). We picked arrival times of
P and S waves manually. We used iasp91 asacrustalmodel
forhypocenter
determination. For the depth range between
35 and 120 km, the velocity structures arelinearly interpolated. The starting depth for
hypocenter determination was set to 10 km.

3.2 Local magnitude, ML scale
The basic concept of ML scale was introduced by Richter (1935) and defined using the logarithm(logA) of the maximum displacement, measured on the two horizontal components of a standard
Wood-Anderson torsion seismometer (Anderson and Wood, 1925). The relationship between therelative size of an earthquake and its amplitude follows the original Richter (1935, 1958) local
magnitude, defined such that an earthquake of ML = 3 is recorded with a peak amplitude of 1mm at an
epicentral distance of 100km.
In this study, we followed the procedure of Miao and Langston (2007), in which they
followed Hutton and Boore (1987) approach. They used the following formula to derive the ML
formula:



 



- nlog rij 100  K rij  100  M Li  logAij  3.0(1)

where n and K are the parameters related to the geometrical spreading and anelastic attenuation, Aij is
the horizontal peak amplitude of the ith event observed at the jth station component, rij is the
hypocentral distance (km) from the ith event to the jth station component, MLi is the local magnitude of
the ith event. In the original definition of Richter (1935, 1958) and Miao and Langston (2007), thestation correction factors are included. In this study, we did not consider them due to the limited sizeof the dataset.

2Recently, Mungunsuren (2012) applied this method to obtain a ML scale for Mongolia.
We followed the inversion procedure for ML of this previous study.
3.3 Amplitude measurement procedure
For peak amplitude measurements, first, we removed instrument responses from the SAC waveform
data by deconvolution, and then the frequency response of the standard Wood-Anderson torsion
seismometer for displacement, (a natural period of T0 = 0.8 sec, a damping constant h = 0.8, and static
magnification of 2800) was convolved. We obtained 531 amplitude measurements from 52 crustal
local earthquakes whose focal depths fall in the range 0 – 34 km. For ML inversion, we used 529
amplitude measurements excluding 2 outliers. The hypocentral distance range of the amplitude data
used is from 14 to 700 km.
4. RESULTS AND DISCUSSION
4.1 Hypocenter solutions
Figure 2 shows the determined hypocenter solutions. Most of them are associated with the tectonic
activity of the western rift of the EARS, whose foci lie between depths of 0 and 34 km, while events
that are not associated with the western rift have depths up to 20 km. Shudofsky (1985) showed thatearthquakes associated with the EARS have focal depths as great as 25 - 30 km. Nyblade andLangston (1995) reported source parameters of some East African shallow earthquakes. Theyobserved that their foci were lying between depths of 24 and 34 km in the Archean and Proterozoic
lithosphere, where the crust could have been thinned by rifting. Lindenfeld et al. (2012) analyzed
seismicity of the Rwenzori Mountains within the western rift and reported that focal depth distribution
extends from the surface down to a depth of 32 km with a single peak around 15 km. For
determination of ML formula, we used data from earthquake events with focal depths up to 34 km.
For seven events among of the 54 earthquakes used in this study, their hypocenters were
determined by USGS and/or IDC (Table 1). Figure 3 shows the comparison of hypocenters determinedby NEIC and IDC to those determined in this study. The hypocenters do not differ much, and they areroughly consistent with each other. For some of the events, the epicenters obtained in this study arecloser to the western rift. The focal depths obtained in this study are deeper for most of the events.

Figure 2. Hypocenters solutions determined in thisstudy.
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Figure 3. Comparison of hypocenters determined by
NEIC and IDC and those determined in this study.
The stars denote epicenters determined in this study.
The red crosses denote epicenters by NEIC andsolid circles denote those by IDC.

Table 1. List of events whose hypocenters were determined and reported
by USGS and/or IDC.
Date

Origin Time

Event
No.

Year

Month

Day

HH:MM:SS

1

2008

05

11

10:34:10.37

2

2008

08

26

14:56:57.03

3
4
5
6
7

2008
2008
2008
2008
2008

08
10
10
10
10

29
01
05
05
30

16:36 13.50
14:15:53.51
00:02:12.63
00:32:25.41
00:45:48.38

Latitude(°)

Hypocenter
Longitude
(°)

0.48
0.50
2.27
2.10
-0.06
-0.81
-1.13
-1.41
0.05

29.59
29.64
30.91
30.80
29.68
33.74
29.12
29.09
30.03

Depth
[km]

10
not reported

10
not reported

0
24.7
4.0
10
0

Reporting
AgencyNEIC-PDE
IDC-SEL3
NEIC-PDE
IDC-SEL3
IDC-SEL3
NEIC-PDE
IDC-SEL3
IDC-SEL3
IDC-SEL3

4.2 Determination of Local magnitude, ML scale
In this study, we determined a local magnitude formula for Uganda. A linear inversion underconstraints (Jackson, 1979) was performed using Eq. (1). According to the preliminary calculations
and previous studies on ML scales, we set 3, 0.001, and 4 for the standard deviation of model
parameters of n, K and ML, respectively. The distance correction obtained from the inversion is asfollows:

 logA0  0.848logr 100  0.00116r  100  3.0(2)

where r is the hypocentral distance in km. The coefficients for the log(r) and r terms, 0.848 and0.00116, are smaller than those (1.11 and 0.00189) for Southern California (Hutton and Boore, 1987).
The coefficients of this study are closer to those (0.776 and 0.000902) obtained for Tanzania(Langston et al., 1998). The ML formula for Uganda is given as follows using the distance correction
expressed by Eq. (2):M L  logA  0.848 logr 100  0.00116 r  100  3.0(3)log(Aij)Cal

where A is the maximum amplitude in mm observed on the horizontal component seismogram, and r
is the hypocentral distance in km. Figure 4 shows the comparison between the observed amplitudes
and calculated amplitudes for the4
obtained n, K, and ML.
"Cal" = ''Obs"
We compute ML residual,
3
δM L by the following formula:2

δM L  M Lsta  M Lave1

where M Lsta is a ML calculated for a

0

-3

-2

-1

-1

(4)

0

1

2

3

4

log(Aij)Obs-2-3

Figure 4. Comparison between calculated and observed
amplitudes.

4

station for a particular event and M Laveis the mean ML for that event. Figure 5
shows the ML residuals as a function of
hypocentral distance. We also calculate
the mean ML residuals per 100 km bininterval as shown in Figure 6. We
observe no significant dependence of ML

residuals on hypocentral distance considering the standard deviations shown in Figure 6. This
therefore suggests that Eq. (3) is applicable to hypocentral distances up to about 700 km.

ML residual (δM)

Mean ML residuals

2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5

Hypocentral distance (km)100 200 300 400 500 600 700
Hypocentral distance (km)Figure 6. Mean ML residuals calculated per 100
km bin intervals with the standard deviations.
Figure 5. Distribution of ML residuals as afunction of hypocentral distance.

0

We compared the ML magnitudes of four earthquakes obtained from this study to the body wave
magnitudes determined by USGS and reported in PDE catalogs. Figure 6 shows the comparison
between these two magnitudes. They agree relatively well considering the errors of ML.

ML(this study)

6

5

4

3
3

4 mb(USGS)

5

6

Figure 6. Comparison of magnitudes for the selectedfour events: ML (from this study) and mb (from USGS).

5. CONCLUSION
A local magnitude scale for Uganda has been derived following the original definition of ML (Richter,1935), using simulated Wood-Anderson seismograms from broadband waveform data for local
earthquakes recorded by the AfricaArray-Uganda Broadband Seismic Experiment and the IRIS-IDA
permanent station. We retrieved waveform data from the IRIS DMC and picked P and S wave arrivals.
We determined hypocenters of 54 local earthquakes. Most of the hypocenters are associated with thewestern rift of EARS. We compared the hypocenters of seven events to those reported by the NEIC’s
PDE catalogs and IDC bulletins. They do not differ much, but are roughly consistent with each other,although the focal depths in this study are deeper, for which further studies such as effects of crustal
structure will be necessary.

5We obtained 529 amplitude data from horizontal components of 52 local earthquakes withfocal depths up to 34 km. By following Miao and Langston (2007), we performed a simultaneous
linear inversion to determine the coefficients of distance correction function and ML. The obtained
distance correction function is  logA0  0.848logr 100  0.00116r  100  3.0 , where r is the
hypocentral distance in km, and A0 is the distance correction.
From this distance correction function, the following formula was proposed for Uganda
M L  logA  0.848 logr 100  0.00116 r  100  3.0 , where A is the maximum amplitude in mm
observed on the horizontal component, and r is the hypocentral distance in km. The coefficients for thelog(r) and r terms, 0.848 and 0.00116, are smaller than those (1.11 and 0.00189) for Southern
California. They are closer to those (0.776 and 0.000902) obtained for Tanzania. We observed that theresiduals of ML are not significantly dependent on hypocentral distance up to 700 km.
At present, four broadband seismic stations are installed and recording waveform data in
Uganda. Site surveys and noise calibration exercises are being conducted to ascertain the suitability of
proposed locations of the seismic vaults to deploy more stations. It is expected that in near future
additional four stations will be installed to increase the number to eight stations including the IRIS
global seismographic station, MBAR.
Using data from these seismic stations, I plan to determine hypocenters and ML of local
earthquakes in Uganda, fully utilizing the achievements of this study. This will be an impetus towards
improving earthquake monitoring and study of seismicity rate in Uganda and the region.
ACKNOWLEDGEMENTS
I am grateful to Prof. Andrew Nyblade and IRIS DMC staff for their earlier support on data access andretrieval. I thank Dr. Toshiaki Yokoi and Dr. Bun’ichiro Shibazaki for their comments which improved
this manuscript.
REFERENCES
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Brazier, R.A., Miao, Q., Nyblade, A., and Langston, C.A., 2008, Bull. Seismol. Soc. Am., 98, 2341-2348.
Hutton, L.K., and Boore, D. M., 1987, Bull. Seismol. Soc. Am., 77, 2074-2094.
Jackson, D.D., 1979, Geophys. J. R. astr. Soc., 57, 137-157.
Kennett, B.L.N., and Engdahl, E.R., 1991, Geophys. J. Int., 105, 429-465.
Langston, C.A., Brazier, R., Nyblade, A.A., and Owens, T.J., 1998, Bull. Seismol. Soc. Am., 88, 712-721.
Lienert, B.R. and Havskov, J., 1995, Seismol. Res. Lett., 66, 26-40.
Lindenfeld, M., Rȕmpker, G., Batte, A., and Schumann, A., 2012, Solid Earth, 3, 251-264.
Miao, Q., and Langston, C.A., 2007, Bull. Seismol. Soc. Am., 97, 2137-2151.
Mungunsuren, D., 2013, Bulletin of IISEE, 47, 31-36.
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Richter, C.F., 1935, Bull. Seismol. Soc. Am., 25, 1-32.
Richter, C.F., 1958, Elementary Seismology, Freeman, W. H. San Francisco., 578.
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