Synopses of Master Papers

Bulletin of IISEE, 47, 31-36, 2013

LOCAL MAGNITUDE SCALE FOR MONGOLIA AND
DETERMINATION OF MWP AND M S (BB)Dashdondog Mungunsuren ∗MEE11606

Supervisor: Tatsuhiko HARA ∗∗ABSTRACTWe determined a new local magnitude (M L ) scale for the regional network of Research Center of
Astronomy and Geophysics of Mongolian Academy of Sciences (RCAG, MAS). We used amplitude
data from the Mongolian seismic network recorded by short-period seismographs from 143 local andregional earthquakes that occurred during 2005–2012. The magnitude range is between 3.5 and 6.7.
We derived − log A0 distance correction function for M L based on its original definition. We obtained
the following formula for determining M L in Mongolia:

M L = log A − 1.11log(r / 100) + 0.00061(r − 100) + 3
where A is the maximum amplitude (mm) observed on the horizontal component, r is the hypocentral
distance (km). We found that the residuals of magnitudes determined using the above formula do nothave a significant epicentral dependence. The magnitudes determined by the above formula areslightly larger (by about 0.15) than those determined by the current formula.
Since RCAG has started deployment of its broadband seismic network recently, in order toenhance its seismic monitoring capability, we determined M wp and M s (BB) for five local earthquakes
using waveform data from a single broadband station in Mongolia. The estimated magnitudes are
relatively consistent with the moment magnitudes of the Global CMT solutions, which implies thatthese magnitude determination methods will work well for monitoring larger earthquakes, for which
M L will saturate. The routine determination of M L , M wp and M s (BB) is important and effective forearthquake monitoring in and around Mongolia.
Keywords: M L , Distance correction, M wp , M s (BB), broadband station,

1. INTRODUCTION
The Research Center of Astronomy and Geophysics (RCAG) has been deploying its digital seismic
network and conducting earthquake monitoring in and around Mongolia since 1994. Digital seismic
stations have been calibrated so that digital records can be converted to ground velocities from one
station to the other. This step is important in the constitution of the seismic catalogue with a magnitude
determination. At present, the following formula is used at RCAG to determine local magnitude: A
M L = log  + 0.816 log ∆ + 0.00045∆ − 1.22
T 

(1)

where A is the maximum amplitude in nm, measured for period T on horizontal components, ∆ isthe epicentral distance in km. Ulziibat (2001) obtained this formula using data from digital stations
operational since 1994. We found that the magnitudes determined by the above formula have∗

Research Center of Astronomy and Geophysics of Mongolian Academy of Sciences (RCAG, MAS).
International Institute of Seismology and Earthquake Engineering, Building Research Institute (IISEE, BRI)∗∗

significant epicentral distance dependence. In order to reduce this dependency, we developed a new
local magnitude scale for Mongolia.
In addition, we determined broadband moment magnitude M wp and surface-wave magnitude
M s (BB) from a broadband station in Mongolia. M wp gives quick and accurate size estimates forearthquakes both in regional (Tsuboi et al., 1995) and teleseismic (Tsuboi et al., 1999) distance
ranges.
2. DATAIn this study, we used two kinds of dataset. First, we selected 143 local and regional earthquakes that
occurred in 2005 – 2012. The magnitude range is between 3.5 and 6.7. We used 699 amplitude datafrom 23 short-period stations of the Mongolian seismic network.
We also used five earthquakes that occurred in and around Mongolia during 2004-2012. The
magnitude range is 5.5 and 6.7. We retrieved waveform data recorded at a broadband seismic station,
ULN from the Incorporated Research Institutions for Seismology (IRIS) Data Management Center(DMC).

3. METHODSIn this study, we determined the three different magnitudes.
1. We followed the procedure of Miao and Langston (2007) to determine a formula of M L . Richter(1935, 1958) used the local-magnitude M L defined by:

M L = log A − log A0 + S(2)where A is the maximum amplitude observed in mm, logA 0 is an empirically determined distancecorrection function and S is an empirical station correction.
There are several different techniques to determine an empirical distance correction function
for M L (e.g., Kanamori and Jennings, 1978; Hutton and Boore, 1987). In this study, following Miaoand Langston (2007), we used the approach suggested by Hutton and Boore (1987); the above
equation can be expressed with an explicit distance correction function as:− log Aij = n log(rij / 100) + K (rij − 100) + 3.0 − M Li

(3)

where n and K are parameters related to the geometrical spreading and anelastic attenuation, Aij is
the horizontal maximum amplitude of the i th event observed at the j th station, rij is the epicentral
distance from the i th event to the j th station component. M Li is the local magnitude of the i th
event.
They conducted a one-step linear inversion without iteration to determine the coefficientsfor a distance correction function under the condition that a local magnitude is 3 when maximum
amplitude is 1 mm at a distance of 100 km. We did not include station corrections in the unknown
model parameters to be determined due to limitation of the available data.
2.

We followed Tsuboi et al. (1995) to calculate the broadband moment magnitude. The broadband
moment magnitude, M wp , gives quick and accurate size estimates for both regional (Tsuboi et al.,1995) and teleseismic (Tsuboi et al., 1999) earthquakes. It determines the seismic moment from
P-wave of broadband seismograms and calculates the moment magnitude estimate. The seismic
moment is read as peak amplitude of the integrated P-wave of displacement seismograms. We
used the following equation to calculate approximate seismic moment M 0 :M 0' =| max(∫ u z ( xr , t )dt | ⋅4πρα 3 r(4)where u z is the vertical component record, x r is the receiver location, ρ is the density, α is the
P-wave velocity, and r is the epicentral distance. We adopted ρ = 2.6kg / cm 3 and α = 6.0km / sec ,respectively, considering that earthquakes in and around Mongolia usually occur in the upper crust.
This equation means that we can have an estimate of seismic moment from the first peak of the
P-wave portion of the velocity seismogram integrated twice. Using an estimate from this equation
we can obtain an estimate of moment magnitude by using the standard moment-magnitude formula(Kanamori, 1977):

2
M w' = log M 0' − 10.73
3(5)where the unit of M 0' is dyne centimeters. To compensate for the correction of the radiation pattern,
we followed Tsuboi et al. (1995); they suggested the correction for radiation pattern is adding 0.2 toM w' :

M wp = M w' + 0.2
3.

(6)

We followed the recommendation of the Working Group on Magnitudes, International
Association of Seismology and Physics of the Earth’s Interior (IASPEI) to calculate thesurface-wave magnitude, M s (BB), using digital broadband velocity seismograms. The standard
equation for M s (BB) is as follows:

M s ( BB) = log( A / T ) max + 1.66 log ∆ + 3.3(7)

where ( A / T ) max = (Vmax / 2π ) , where V max = ground velocity in µm / s associated with the
maximum trace-amplitude in the surface-wave train as recorded on vertical-component
seismogram that is proportional to velocity, and where the period T, 3s < T < 60s, should bepreserved together with A or V max in bulletin data-bases. The applicable epicentral distance range∆ is larger than or equal to 2 degrees and smaller than or equal to 160 degrees. The focal depth
should be less than 80 km.

4. RESULT & DISCUSSION
In this study, we derived a local magnitude scale for Mongolia based on the original definition of local
magnitude (M L ), and we also determined M wp for earthquakes in and around Mongolia analyzing
waveform data from IRIS station. Also we determined surface-wave magnitude M s (BB) frombroadband seismograms.
4.1 Determination of Local magnitude (M L )In this study, we derived a local magnitude scale for Mongolia. We performed linear inversion underconstraints. Based on preliminary calculations and previous studies we set 3, 0.001, and 5 to thestandard deviations of n, K, and magnitude before inversion, respectively. We obtained the following
distance correction term:− log A0 = 1.11log(r / 100) + 0.00061(r − 100) + 3(8)

-logAo

where r is the hypocentral distance in km. The coefficient 1.11(±0.79) for the log(r) term is almost thesame as that for Southern California (Hutton and Boore, 1987). The second coefficient
0.00061(±0.00071) is much smaller than that of Hutton and Boore (1987). Although it is difficult tohave a tight constraint for this coefficient, we obtained a larger variance reduction for the observed
amplitude measurements using the above
formula than the formula of Hutton and
Boore (1987). Thus, this smaller
coefficient is likely to reflect the lower
dissipation of seismic wave energy in the
study area.
Figure 1 shows the distance-correction
functions for southern California (Booreand Hutton, 1987), Central California(Bakun and Joyner, 1984), Central
United States (Miao and Langston, 2007),
Japan (Y. Fujino and R. Inoue, 1985,
given as “written communication” which
Boore and Hutton, 1987) and Mongolia(from our study). The attenuation curve
computed for Japan by Fujino and Inoue
Hypocentral(1985) is similar to that of our study.
Figure1. Comparison of logA 0 of this study to thosefrom pevious studies.
Using the above distance correction, we propose the following formula for determining a local
magnitude in Mongolia.

M L = log A − 1.11log(r / 100) + 0.00061(r − 100) + 3(9)where A is the maximum amplitude in mm on the horizontal component records, r is the hypocentral
distance in km. We calculated the M L residuals using Eq. (9). Magnitude residuals were computed as
the difference between magnitude assigned by a single station for a given earthquake and the averagemagnitude of the same earthquake.
Figure 2 shows the hypocentral
distance dependence of the residuals.
The magnitude residuals do nothave any significant hypocentral
distance dependence, i.e., theresiduals are close to zero for each
hypocentral distance except for the
distance range between 0 and 100
km. In this range, there are only
three measurements. Therefore, it isdifficult to judge whether thedeviation of the residuals from zerois significant or not. Further
accumulation of data will benecessary.
Figure 2. Local magnitude residuals as a function of
hypocentral distance.

Then we compared our results of local magnitude to local magnitudes computed using thecurrent formula, body-wave magnitude m b by USGS, respectively (Figures 3 and 4).

Figure 3. Comparison between M L (this study)
and M L calculated using Eq. (1)Figure 4. Comparision between our results oflocal magnitude M L (this study) and m b by
USGS.

4.2 Determination of M wp from broadband P-waveform
We used five local earthquakes which occurred in and around Mongolia in between 2006 to 2012.

Figure 5 shows that there is a relatively goodcorrelation between them. The RMS of theirdifferences is 0.38. These results indicate that M wp
gives a relatively good estimate of moment
magnitude for these five earthquakes. Although it ispreliminary since the number of earthquakes is few,
this result suggest that the procedure to determine
M wp is also applicable to the study area.

Figure 5. Comparison between M wp (this study)
and M w (GCMT) from the Global CMT solutions.
4.3 Determination of M s (BB) from broadband seismograms
We determined surface-wave magnitude, M s (BB), using broadband seismograms. By picking thelargest peak from the surface-wave train, we measured V max (μm/sec), and then calculated M s (BB). We
compared our results (Figures 6 and 7). They are in relatively good agreement.

Figure 6. Comparison between M s (BB) andothers magnitude scales.

Figure 7. Comparison between M s (BB) andM w (GCMT) from the Global CMT solution.

5. CONCLUSION
In the present study, we determined − log A0 , distance correction function for M L using 699 amplitude
measurements for 143 local and regional earthquakes from the Mongolian seismic network. The
magnitude range is between 3.5 and 6.7. Referring to the Richter’s original condition that a magnitude
3 event would produce 1 mm of motion at 100 km, we obtained the following distance correction:− log A0 = 1.11log(r / 100) + 0.00061(r − 100) + 3
where r is hypocentral distance in km. Then, the following formula is proposed for the local
magnitude in Mongolia.

M L = log A − 1.11log(r / 100) + 0.00061(r − 100) + 3
where A is the maximum amplitude (mm) observed on the horizontal component, r is the hypocentral
distance in km. We found that the residuals of magnitudes determined using the above formula do nothave a significant epicentral dependence. On the other hand, the residuals of magnitudes determinedusing the current M L formula adopted by RCAG have a significant epicentral dependence. The
magnitudes determined by the above formula are slightly larger (by about 0.15) than those determinedby the current formula.
Since RCAG has started deployment of its broadband seismic network, in order to enhance
its seismic monitoring capability, we determined M wp and M s (BB) for five local earthquakes using
waveform data from a single broadband station in Mongolia. The estimated magnitudes are relatively
consistent with the moment magnitudes of the Global CMT solutions, which implies that thesemagnitude determination methods will work for monitoring larger earthquakes, for which M L will
saturate.
The routine determination of M L , M wp and M s (BB) by RCAG is important and effective forearthquake monitoring in and around Mongolia, which will provide fundamental information forseismic hazard evaluation in Mongolia.

ACKNOWLEDGEMENT
I would like to express my sincere gratitude to Dr. Toshiaki Yokoi and Dr. Bunichiro Shibazaki for
their valuable comments that improved the clarity of this manuscript.

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