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,**1 P 2 Q +. RST+ ,**2 P + Q 2 RS ,Simpliﬁed test on tilt response of CMG.*T seismometers
Hiroshi AOYAMA῍
Deformation under the ground excites not only translational motion but also tilt changes, although
seismologists usually analyze recorded waveforms under an assumption that seismogram only expresses translational motion. Since broadband seismometers have high enough sensitivity to tilt changes, the seismograms are
sometimes contaminated by tilting motion at a seismic station. To check the e#ect of tilt change on seismogram
recorded by a broadband velocity seismometer, we performed a simple experiment with a CMG.*T seismometerand a tilt sensor of surface mount type. Tilt changes yield one-sided oscillation of the pendulums in a horizontaltransducer. Such particular oscillation is clearly identiﬁed in the displacement trace calculated from the original
velocity seismogram. Theoretical consideration predicts that slow temporal changes in tilt angle correlate with atime function of the apparent displacement of seismogram. Since results of our experiment well agree with theprediction, we estimate the conversion coe$cient from the apparent displacement to tilt angle and conﬁrm that the
coe$cient obtained experimentally well corresponds with the value from theoretical prediction. As a possible
example in an active volcano, we consider slow isotropic volume change near a seismic station and calculate
synthetic seismogram due to the volume change.
Key words : broadband seismometer, tilt response+ῌ ῐ ῎ ῑ ῏?@UNV( ;<W XYZ[\]^_) ?@UN`aK+ bcdef(gh*- Rodgers (+302) i ;<K?@UNjkl*mfno?@U p - bcdefNqrsZt uvw xyN +  p - Rodgers (+302)

ih+ z{|N? }~(z{K$ + ?Nm i ?@U+ |N? }~(N ?@U d"" _&'(?@U4 - Z ?@UK  (d")*- IJ K+ LM@ ?@9NO+ @ Wd(d)Of+ ?@9wCD;<OJNo?@U d""*?@$HGX+ ?@U d""*K p dNXd - Bouchon and Aki

(+32,) N;<K+ WN()*;<N +Graizer, ,**0,- p - "K?@ih ?@$Nr 

N U(Y+   ?N+  + Boroschek and Legrand, ,**0 ;?@$? N¡ ?@UN¢$£jk(¤¥ K+   (}¦ §¨ [ m©ª«  &'K  i &'¬¥­®( Wd)- IJ K Boroschek andd¯°±*- )²)w"+ mfnoN?@U

Legrand (,**0)  0 Nm ®(UN N³ XL´¡)~(WdK¹a²"º"Of+ mfnN »¼°. /*0*ῌ*2+*

012 3 4 +* 56 2 7018989: 9;<:=>?@AB;<CD
EFGH
Institute of Seismology and Volcanology, Graduate
School of Science, Hokkaido University, N+*W2, Kita-

jkµ¶(Y+ ?@$%_·¸+ L !" #$%  &'()*ku, Sapporo, Hokkaido *0*ῌ*2+*, Japan.
Corresponding author : Hiroshi Aoyama
e-mail : aoyama@uvo.sci.hokudai.ac.jp

+ 

36

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    Aster et al. (,**-)$ Chouet et al. (,**-) !12L%89) IS$
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CMG.*T ,-./012 3456
Table +.

Response properties of seismometers.

78 ! 99" w* :;<=>?@A" h :BCDA ! 91AEF " ,/0:G?@
AHIJ

37

Table ,.

Poles and zeros of CMG.*T seismometer.

KGLM ! (,) N1A Xd (w):OP?@A/01A7E " ,QOPRSTU
VFWXY (u(t) # d (t)$ ,Z[\]2! ^_" ,`abc,`dabe2 ?@A/0

1A 8297fg ! hiN,,`abeῌ
2 /01A:" (,) Njk U (w)#iwU(w) 7lg
m  no"
%w$
%w$
&iw
Xvw$# ῌ##Uw$
iwUw$ w,*',ihw*w&w,-ῌ CMG.*T ΐῑῐ῍῎῔῏ῒ(-)

 ! ῏

7z {" ^_,`dabe2 /01A:"
Xaw$#Güralp Systems Inc. p CMG.*T ,:" qrs`tuvE OPwv x WyHI,|}{" ;<=>?@A

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%w$
&+
#
#
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7z !
N,?@A/01A:" ,`[7Z[8 ! ,Z[ D2 

+* Hz ~~ *.*--

_$  97" y῍

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CMG.* T ,,`abe2?@A/01A[SRjg 72 " OP?@A

:" - J7῎R ! 9:(,/01A: D8E Table , E Edw$#G78

&iw,
w*',ihw* w&w,

! CMG .* T ,
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2 /01A:"Evw$#G&w,,
w*',ihw* w&w,

iww,*',ihw* w&w,

(0)

iw&zi$iw&z,$iw&z-$
iw&pi$iw&p,$iw&p-$(2)

;ªR + 7zE«2(2) N8

?@A/01A;ª­®: Fig. + W¨¬A

!

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const. 7z" f **.*-- Hz :῍Cv (w)῍+w, 7z ! 2zµ¶=>?@AEfj· ?@AHI:,`ab῍{WZ[R" =>?@AEf

7z !
¸/0­® [¹º?@AHI7BCDA
f7½

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78 ! 99 A : + Hz © ?@A/01A

78" ,`dabe2 /01A:"
Eaw$#G¡W?@A/01

A:" 9¢ x

jῌ2 7" Table + E7¨ !

j» ?@AHI:" ,`ddab ¼b$ 
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= >

38

?

Fig. ,. Schematic of - component transducers in aseismic sensor.
ῌ
ῌ
ῌ
ῌ
ῌ ῌ
ῌ
x-5,w- h-x-5w,- x-67ῌ
u-5ῌ8+7cosY+97Y+l-5ῌ
u,qFig. +. Amplitude component of velocity response
function of the CMG.*T seismometer.

@A: (3) BC

Yj DAEF + cosYj῍+

7Yj,ῌ, GH'':
ῌY+ ῌ
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7Y+ l-5ῌu,q,,. 

(+*)



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 ;FV!-@WKX'(YK; WW

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m +"#$%no$% YJ

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03R- uj (t): m$%- xj (t) @
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u+
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x,5,w, h,x,5w, x,67u,

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x+5,w+ h+x+5w+, x+6ῌY,ῌῌῌ
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sinYj GH'T

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(+,)

(+-)

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uj (t)67ῌY (t) '@3%x_Ebª+: QNῌ

CMG.*T

39

 !"#$%&'()*+,-ῌ
u (t)ῌYH (t)./"01 2)3 !"ῌ
45*+%&6789ῌῌῌ
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ῌY
iww*,,iw* h* ww,(+/)

KLM( .N (.) 9 HIJ

Fig. -. Amplitude component of tilt response function of CMG.*T.

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XTw 
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iw

(+0)

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ETw 

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IdN *.,,- mm e1VEf"g./:h  ijkl1( CMG.*TῌY
ῌY
Eaw 
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iw
w,/Yp./"q1 CMG .* T"`3( .N + mrad E7"ab)*+ CMG.*T(+1)

m HIJKcnRHIE7oOPN
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"E_:

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(+2)





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:(XP"r01c

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/ Applied Geomechanics ¶· 1*+῍,´µ:¸0@¹º»¼ ½ -* cm

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40

Fig. ..

)

Schematic representation of the simple experiment in this study.

Fig. /. Waveform examples of the tilting test.
First and second traces are output from thebiaxial tiltmeter. Three traces in the middle arevelocity outputs of CMG.*T. Bottom two traces
are displacements of horizontal components calculated from the velocity traces.

Fig. 0. Velocity amplitude spectra of two horizontal
components of CMG.*T.

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41

Results of the experiments.

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Fig. 2 (a). Calculated waveforms at each step of simulating procedure. This is the case for signal duration of 0*
seconds. A and B are schematics of isotropic volume change and associated deformation. C and D are
expected tilt change and translational displacement, respectively. E is apparent displacement trace due to tiltchange. Tilt response of CMG.*T is convolved. F is velocity trace derived from translational displacement.
G is apparent velocity trace due to tilt change. H is translational velocity ﬁltered by CMG.*T response. I iscombined velocity seismogram that will be output from CMG.*T, and J is displacement seismogram.

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44

Fig. 2 (b).

Same to Fig 2a. Signal duration is -* seconds.

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Fig. 2 (c).

῏

45Same to Fig. 2a. Signal duration is +* seconds.

῎ 

!"#$%&'(!)*+,-.* -*/012
3456789 , :;:<=>?@ ABC!DE$%FG HIJK&LM!)*+,-.* N.OPQ)*.-ῌ ῑ ῐ ῍Aki, K. and Richards, P.G. (,**,) Quantitative seismology, Second Eds., University Science Books, 1**p.
Aster, R., Mah, S., Kyle, P., McIntosh, W., Dunbar, W.,
Johnson, J., Ruiz, M. and McNamara, S. (,**-) Verylong period oscillations of Mount Erebus Volcano, J.
Geophys. Res., +*2, ,/,,, doi : +*.+*,3/,**,JB**,+*+.
Boroschek, R.L. and Legrand, D. (,**0) Tilt motion

e#ects on the double-time integration of linear accelerometers : an experimental approach. Bull. Seism. Soc.
Am., 30, ,*1,ῌ,*23.
Bouchon, M. and Aki, K. (+32,) Strain, tilt, and rotation
associated with strong ground motion in the vicinity ofearthquakes faults. Bull. Seism. Soc. Am., 1,, +1+1ῌ+1-2.
Chouet, B., Dawson, P., Ohminato, T., Martini, M.,
Saccorotti, G., Giudicepietro, F., De Luca, G., Milana,
G. and Scarpa R. (,**-) Source mechanisms of explosions at Stromboli Volcano, Italy, determined frommoment-tensor inversions of very-long-period data. J.
Geophys. Res., +*2, ,*+3, doi : +*.+*,3/,**,JB**+3+3.
Graizer, V.M. (+313) Determination of the true grounddisplacement by using strong motion records. Izv. USSR
Acad. Sci., Physics Solid Earth, +/, 21/ῌ22/.
Havskov, J. and Alguacil, G. (,**.) Instrumentation inearthquake seismology. Modern approaches in geophys-

 

46

ics, ,,, Springer, -/2p.
Graizer, V.M. (+323) On inertial seismometry. Izv. USSR
Acad. Sci., Physics Solid Earth, ,/, ,0῍,3.
Graizer, V.M. (+33+) Inertial seismometry methods. Izv.
USSR Acad. Sci., Physics Solid Earth, ,1, /+῍0+.
Graizer, V. (,**0) Tilts in strong ground motion. Bull.
Seism. Soc. Am., 30, ,*3*῍,+*,.
Rodgers, P.W. (+302) The response of the horizontal pendulum seismometer to Rayleigh and Love waves, tilt, andfree oscillations of the earth. Bull. Seism. Soc. Am., /2,+-2.῍+.*0.
Usher, M. J., Burch, R.F. and Guralp, C. (+313) Wideband feedback seismometers. Phys. Earth Planet. Int., +2,-2῍/*.
Wielandt, E. and Forbriger, T. (+333) Near-ﬁeld seismic
displacement and tilt associated with the explosive activity of Stromboli. Ann. Geoﬁs., .,, .*1῍.+0.
Wiens, D.A., Pozgay, S.H., Shore, P. J., Sauter, A.W. andWhite, R.A. (,**/) Tilt recorded by a portable broadband seismograph : the ,**- eruption of Anatahan Volcano, Mariana Islands. Geophys. Res. Lett., -,, L+2-*/,
doi : +*.+*,3/,**/GL*,--03.
st'u (+320) o1v)wxw w -* S+*+ῌ
S++3.
Appendix : 

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