DETERMINATION OF SOME COMMONMAGNITUDE SCALES USING BROADBAND
DIGITAL SEISMOGRAMS
Afsar Khan∗
MEE06002

Supervisor: Toshiaki Yokoi∗∗

ABSTRACTPakistan Meteorological Department (PMD) has started establishing the new digital seismic network
including broadband stations in Pakistan after the 2005 Kashmir earthquake. This study was aimed tosummarize the basic information to make a strategy for an appropriate way of the routinary tasks ofthe new seismic network. In this paper, we have checked some magnitude scales commonly used withbroadband seismograms today and their operability. For this purpose, we have analyzed the 2005
Kashmir earthquake taking data from seventeen broadband stations through IRIS to determine themoment magnitude in the time domain using few sets of density and P-wave velocity as well as in thefrequency one. As a whole we have made a comparison between the various magnitude scales like Mw,Mwp, Ms(BB) and Ms20. In conclusion, we emphasize on Mw determination and its application in
future for the PMD new network which will be a first step towards the disaster mitigation based on thequick and rapid determination.
Keywords: Broadband, Seismic Moment, Seismograms, Frequency domain, Time domain
INTRODUCTION
After the 2005, Kashmir earthquake, Pakistan Meteorological Department (PMD) obtained a set of
new digital seismometers to monitor the on going seismic activities in and around Pakistan. However,
the observational job on the modern seismic equipments has not been established well. The seismic
staff of PMD was familiar with the old analog network, but the operation of the new digital seismic
network and its handling were a challenge. Therefore, the objective of this paper is to support andovercome the problems of determination of different kinds of magnitudes and other parameters, and tobring PMD to the position to join the modern seismological society. Therefore in this paper we aregoing to through light on the way of determination of magnitudes.
NEW DIGITAL SEISMIC NETWORK OF PAKISTAN
After the 2005 Kashmir earthquake, PMD has started upgrading the seismic network by installingsome new set of digital seismometers and accelerometers for fast calculations of the seismic activities
Figure 1* Seismic Section, Pakistan Meteorological Department∗∗International Institute for Seismology & Earthquake Engineering (IISEE), BRI, Japan

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LEGEND
Broadband
Short period
Short period
ProposedAcccelerographs

Figure 1 Planned Seismic network of PMD (analog+digital) mapped on a politicalmap downloaded from http://geography.about.com/library/cia/blcpakistan.htm
EXPECTATIONS FOR THE NEWLY INSTALLED DIGITAL SEISMIC ETWORKThe newly established digital system will have a good impact on the output of the PMD seismological
data. The newly installed broader band system will be more powerful according to its bigger numberand response and it will cover the complete seismic spectrum from very low frequency to high. The
collected data can be easily handled for research purposes and can be stored for long duration.
EXAMPLES OF ANALYSISDATA
In this paper, 2005 Kashmir earthquake was used for analysis which was obtained from the DataManagement Center of Incorporated Research Institutions for Seismology (IRIS) network.
Determination of Mwp in the time domain
We used sac2000 software for analysis (http://www.llnl.gov/sac/). At first the raw waveform data wasconverted to velocity seismograms (Figure 2 and Figure 3).
We analyzed, the event using Tsuboi et al (1995), Kanjo et al (2006) and by using the Preliminary
Reference Earth Model (PREM) (e. g., Bormann 2002) and the Mwp was obtained as shown in theFigure 5 and the result was compared with (USGS). The mathematical equation for moment is givenby Tsuboi (1995) as

Mo' = max ∫ u z (r , t )dt ⋅ 4πρα 3r(1)Where uz is a vertical component of ground displacement
The values for the constants the density (ρ) and P-Wave velocity (α) are given in Table 1

Div_G0V-seismogram

PZZEESN2N

Figure 2 Raw wave form data from WMQfrom WMQ Broadband station

Figure 3 Velocity seismogram (m/sec)
from WMQ broadband station

From the P-wave train we removed the mean and the trend. After applying the integration twice, we
got the absolute value and further by multiplying with 4πρα3r, where ρ density, α P-wave velocity andr hypocentral distance, the seismic moment was obtained using Eq 1 as shown in Figure 4. The peakgave Mo = 2.5 x 1020N-m. (Mwp=7.6, Figure 5). Average values of magnitudes are given in Table 1.
Mo=2.5E20 N-m

7.6

ZNEFigure 4 Mo obtained from the doubly
integrated P-wave

Figure 5 Integrated displacements (m-sec)from WMQ showing magnitude (Mwp 7.6)

Determination of Mw in Frequency Domain
We analyzed the same event and same seventeen seismic stations except ENH using the Fast Fourier
Transform (FFT;Sac2000) from the P-wave train from vertical component and we found the value ofseismic moment Mo (Mo=3x1020 N-m) from low frequency asymptote, as shown in Figure 6. Using
the famous Eq (2) of Keilis-Borok (1960) for moment determination.
Mo=4πρα3rΩo/Rθφ(2)alLbFigure 6 Fourier spectra of the P-Wave from WMQ station
An then using the famous Eq.(3) of Kanamori (1977) we found the Mw
Mw = 2/3 (1og10 Mo -9.1)

3(3)We got average Mw= 7.3.
Results for the moment magnitude
Figure 7 shows the variation of Mwp and Mw determined by the four cases that are summarized inTable 1. The right most column shows the determined values that are the means over the. Only in thecase 4 it was determined in the frequency domain with the material properties used by Hanks andWyss (1972).In comparison with Mw determined by USGS, the case 2 and 3 gave the best estimate,
the case 1 gave slightly smaller ones but with trivial difference. The case 4 gave significantly smaller
value due to the small value of ρ and α.
Table 1

input parameters for analysis

S.No ρ(Kg/m3) α(Km/sec) Refeference for ρ and α
MethodMagnitude
Case 1 3400
7.9
Tsuboi et al.(1995)
Mwp in the time domain
Mwp 7.5
Case 1' 3400
7.9
Tsuboi et al.(1995)
Mw in the frequency domain Mw 7.6
Case 2 3880
8.11 PREM modelMwp in the time domain
Mwp 7.6
Case 2' 3880
8.11 PREM model
Mw in the frequency domain Mw 7.7
Case 3 3400 0.16Δ+7.9 Kanjo et al.(2006)
Mwp in the time domain
Mwp 7.6
Case 4 2700
6Hanks and Wyss(1972) Mw in the frequency domain Mw 7.3

Figure 7 Mwp and Mw obtained for 16 stations
Determination of Surface Wave Magnitude Ms (BB) from Broadband Instrument
We determined Ms (BB) in the time domain using SAC2000 from broadband velocity seismograms.
Picking the largest peak from the surface-wave train, we found the Vmax (μm/sec) Figure 8. This wasconverted to Ms(BB) using Eq 4 (Working Group; IASPEI) given as follow
Ms (BB) =log10 (Vmax/2π) +1.66log10 ∆ +3.3(4)Where (A/T) max = V max/2π), where v max = ground velocity in μm/ sec. The average value forMs(BB) was 7.4, while Mw determined by USGS was 7.6.
SURFACE WAVES, KASHMIR E/Q 2005

54/2 mm4x10 -4Z Comp

Vmax= 500 μm/sec , after calculations

Figure8 Peak amplitude of surface wave train

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Determination of mB Intermediate Period / Broadband Body Wave Magnitude
We determined mB in the time domain using SAC2000 from broadband velocity seismograms.
We found the Vmax (µm/sec), Figures 9. This value was converted to mB using Eq 5 (WG ISPAEI)mB = log10 (A/T)max + Q (h, ∆)(5)

Where (A/T) max can be replaced with (Vmax/2π), Vmax is ground velocity in μm/s. The average value
was determined 6.9 and Figure 10 shows the scattering of Ms(BB) and mB over the azimuth.
Ms (BB)_mB V Az
Velocity Seismogram after dividing by G 08Reading with ruler in mm 5518x10^ -610848/2 mmmB64ZMs

200100200300

400az i mut
Selecting the largest P wave amplitude
55 mm:18x106-6:: 24 :X _______ V max

Figure 9, max amplitude from body wave,
KIV station (IRIS)

Figure 10 Ms (BB) and mB against Azimuth

DISCUSSIONS AND CONCLUSION
The information of the conventional teleseismic magnitude scales mb, Ms(20) and their broadband
version mB and Ms(BB) is mainly for the global observation, e. g., international vigilance of nuclear
test ban, whereas the rapid moment magnitude Mwp is used for tsunami warning due to distant greatearthquake. For the latter the quickness is necessary but not so severely as local damaging earthquake.
The only demand is to be observed by a broadband seismograph and this will be fulfilled after
establishment of new network. Considering on the simplicity of processing mB and Ms(BB) may haveadvantage, whereas mb and Ms(20) are more famous although they need the instrumental correction(Table 2).
Table 2 Comparison among the common magnitude scales. * A way ofcorrection was proposed by Whitmore et al. (2002).
Magnitude
type
Mw
Mwp
mB

Domain Seismometer
typefreq.
BB
time
BB
time
BB

DistanceRange
No Limit
No Limit21<∆<100

Ms(BB)

timeBB

2<∆<160mbtime

WWSSN_SP21<∆<100Ms(20)
Ml

time
time

Md

time

WWSSN_LP 20<∆<100
WA
0<∆<100
Not
SpecifiedLocal Event

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Phase usedPPP
SurfacewaveP
Surfacewave
Body wave
Duration

Processing Remarks
requiredFFT
Integration Saturate*
No needSaturate
Saturate
No needInst. Corr. Saturate
Saturate
Inst. Corr.
Inst. Corr.
Easy

SaturateIn general, it is better to use Mwp for tsunami warning rather than mb, mB, Ms(20) or Ms(BB) that are
currently not used, because Mwp corrected may not saturate for great earthquakes (Whitmore et al.
2002). Moreover, in seismological context Mw relates directly to the seismic moment Mo that is thephysical quantity of earthquake size and Mwp is a way to estimate Mw rapidly. The difference of Mwand Mwp exists only in the way of calculation; the former is done in the frequency domain and thelatter in the time domain.
Consequently, all the above discussions prove that advantages of moment magnitude and otherseismic parameters from the digital seismic records will improve not only the quality of seismic data
but also will help in the rapid and reliable information regarding earthquake hazards and its mitigation.
REFERENCES
Working Group (WG IASPEI) international Association of Seismology and Physics of Earth Interior(IASPEI).
Bormann, 2002, New manual of seismological observatory (MNSOP) Vol 1, international Associationof Seismology and Physics of Earth Interior (IASPEI).
Geller R. J. and H. Kanamori, 1977, magnitudes of the great shallow earthquakes from 1904 to 1952,
Bull. Seism. Soc. Am., 67, 587-598.
Hanks T.C and M.Wyss 1972. The use of body wave spectra in the determination of seismic source
parameters.

Kanjo, K. T. Furudate and S. Tsuboi, 2006, Application of Mwp to the Great December 26,
2004 Sumatra Earthquake, Earth Planets Space, 58, 121-126.
Keilis-Borok, V.1. (1960). Investigation of the mechanism of earthquakes, Sov.Res. Geophys. Englishtransl.) 4,29.
Tsuboi et al, Rapid Determination of Mw from Broadband P Waveform, Bull. Seism. Soc. Am., 83,606-613.
Tsuboi, S. P. M. Whitmore and T. J. Sokolowski, 1999, Application of Mwp to Deep and Teleseismic
earthquakes, Bull. Seism. Soc. Am., 89, 1345-1351.
Whitmore, P. M., S. Tsuboi, B. Hirshorn and T. J. Sokolowski, 2002, Magnitude-Dependent
Correction for Mwp, Science of Tsunami Hazard, 20, 187-192.

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