IEG 환경지질연구정보센터

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(1)Jour. Korean Earth Science Society, v. 25, no. 8, p. 774−783, December 2004. J

(2). 7j$ R ¶ò¢ Ï~ \ 6 ³êf 6æ> \` ¿ÿ; ~\~ £ æ> ßW ; \ K* Ö&v ·ÊR", 573-701 *§ Ö úÿ ç 68®æ. S-wave Velocity and Attenuation Structure from Multichannel Seismic surface waves: Geotechnical Characteristics of NakDong Delta Soil Heeok Jung* 'HSDUWPHQW RI 2FHDQ 6\VWHP (QJLQHHULQJ .XQVDQ 1DWLRQDO 8QLYHUVLW\ .XQVDQ &KRQ%XN .RUHD −1. $EVWUDFW The S wave velocity and Qs structure of the uppermost part of the soil in Nakdong Delta area have been obtained to determine the characteristics of the forementioned soil. The phase velocities and attenuation coefficients of −1 multichannel seismic records were inverted to obtain the S wave velocity and Qs structure of the soil. The inversion results have been compared with the borehole measurements of the area. The seismic signal of the nearest geophone from a seismic source was used as the source signal to obtain the attenuation coefficients. Amplitude ratios of the signal at each geophone to the source signal were plotted as a function of distance for the frequency range between 10 Hz and 45 Hz. The slope of a linear regression line which fits the amplitude ratio-distance relationship best for a given frequency was used as the attenuation coefficients for the frequency. The dispersion curve of Rayleigh waves and the attenuation coefficients were inverted to obtain the S-wave velocity and Qs−1, respectively, in the uppermost 8 meter of soil layer. The borehole measurements of the area show that there are two distinct layers; the upper 4 meter of silty-sand and the lower 4 meter of silty-clay. The inversion results indicate that the shear wave velocity of the upper layer is 80 m/sec and 40 m/ sec in the lower silty-clay layer. The spacial resolution of the shear wave velocity structure is very good down to a depth of 8 meter. The Qs−1 in the upper silty-sand layer is 0.02 and increase to 0.03 in the lower silty-clay layer. The spacial resolution of quality factor is relatively good down to a depth of 5 meter, but very poor below the depth. In this study, the S-wave velocity is higher in the silty-sand than in the silty-clay and the Qs−1 is smaller in the silty-sand than in the silty-clay. However, much more data should be analyzed and accumulated before making any generalization on the shear wave velocity and Qs−1 of the sediments. ,FZXPSET s wave velocity, attenuation, surface waves, dispersion, inversion, weak soil º £ 7j6 êW ¶ò¢ Ï~ ¿ÿ; ~ â'" æ £æ>~ æ> ßWj ~V *~ S ³êf Qs−1 ¢ ~ ¢ ºÒ Ö"f jv~& . 7j6 ^~ ªÖFj Ö~ S ³ê¢ ~ 6 æ>(attenuation coefficient)¢ ~& . 7j6 ^ 7 rööB &Ë &rÚ ^¢ V& ^ ;~ 10 HzöB 45 Hz Ò~ " >ö &~ Òö V¢ V& ^ö & ê ~ j& 6²~º ;ê¢ ¾æÚº VÞV¢ ~ 6 æ>¢ Ö;~& . 6æ>¢ Ö~ æ> ç¦ 8 m [~ S ³êf þ Qs−1¢ ~& . æ~ º Òö ~~ æ~ æ[f ² ç¦ 4 m Þî Î¾[" ~¦ 4 m Þî 6Æ[b ¾*Úê . R Ö ö ~ ê S ³êf Qs−1¢ ºÒ Ö"f jv, ç¦ Þî Î¾[öB S ³êº £ 80 m/sec ~¦. Þî 6Æ[~ ³ê 40 m/sec ç&'b ¸f 8j . ' [öB S ³ê~ *' çêº Â]~ . Qs−1 º ç¦ Þî Î¾[öB £ 0.02¢ ~¦ Þî 6Æ[öB 0.03b Ã&~º ·çj . Qs−1~ * ' çêº ç¦ £ 5 m *öBº ·^~¾ pf öBº *' çê& j" Ôjæº ©j " > ® . *E-mail: [email protected] Tel: 82-63-469-1750 Fax: 82-63-469-1750.

(3) 7j$R ¶ò¢Ï~\4 ³êf6æ>\¿ÿ;~\~£æ>ßW. . −1. ÒæöBº Þî Î¾[öB Þî 6Æ[ ¸f S ³ê& ¾æ¾ Ôf Qs 8j . ¾, æ> −1 −1 ~ S ³êf Qs ¢ Ö;~º ôf º ®bæ ¢ ¢>z~V *Bº £æ>~ S ³êf Qs ö & ¶òf & ÷'>Ú¢ © . ºÚ S. ³ê, 6, R , ªÖ, Ö, £æ>. * "ö ¢ÚÂ æê ~ bçj ÚÚ æê ~ b¢ Af æ~ æ> ßW" ê~ Ã ; ê& æê~ b;êö ~º 'Ë Ö º ©j r > ® . 7öBê 7º æ>~ æ>º damping ratio . Damping ratio¢ G;~º O»ö º resonant column test, torsional shear test ®. . Hardin and Drnevich(1972), Seed et al.(1986), Ò Vucetic and Dobry(1991) þ O»j Ï~ æ>~ damping ratioö 'Ëj " º º ö &~ ~& . þò¢ Ï~º O»f ò ;W";öB Vº v¦ Î " B *Ë~ 8j ~V ÚJÚ 6 ®. . 6 j" ·f ¦ª~ ò 9f æ~ *Ë 8j &~º 8j ¾æÚV ÚJÚ 6 ® . 9f æ~ damping ratio¢ G;~V * *ËÒ O»b crosshole¾ downhole öÒöB. Ú2~ 6æ>¢ Ï > ® . Hoar and Stokoe(1984), Redpath and Lee(1986), Mok et al. (1988), Liu et al.(1994) ê 6 ;ê (amplitue decay), Ê¿Þ" ãÒ ;ê(spectral slope), 2; Ö(waveform inversion), 6º pulse rise time j Ï~ æ>~ 6æ>¢ *ËöB ~& . 1960j&¦V æbÒ¶¾ æê¶ (Anderson et al., 1965; Herrmann and Mitchell, 1975; Lee and Solomon, 1975; Cheng and Mitchell, 1987)f Ë"V 2¢ Ï~ æ'" æ~ 6æ>¢ ~&. . f 100 sec ç~ "V¢ Ï~ > W km p~ 6æ>¢ ~& . Mokhtar et al. (1988), Al-Eqabi and Herrmann(1993), Ò Malagnini(1966) f Bj Ï~ BÎ £ * f "V~ 2¢ Ï~ æ ¦" > km~ S2 ³êf 6æ>¢ ~& . "ö æ> ßW (geotechnical characterization) ö ' ç¦[ æ~ damping ratioö & & B® Úæ ® (Rix et al. 2000; Lai. et al., 2002; Rix et al., 2001). f êÿVf >ê V¢ Ï~ ³ .¢Ò2¢ Ö~ æ¦" ~ S2 ³êf 6æ>¢ ÿö ~& . 2¢ Ï~ æ>~ 6æ>¢ ~º O» f ºj Ï~º O»" jv~ &æ Ë 6j &ê . Ñ, ºj Ï O»öB z® ¾æÆ > ®º º" >êV*~ ÖÎ" (coupling effect)¢ J~æ pjê >, ~, 2¢ Ï þöB ÒÏ~º "2>~ ' º Ï ÒÏ~º "2>. B æêöB ¾ æ¾º "2>ö & º Ò . 6 2 O »f þjÏ¾ K º O» '² ² º> j2Z' . öBº 7º rö(weight-drop)" 24j6 êW2 öÒV¢ Ï~ ³ .¢Ò2~ *ç³ êf êj Ï~ æ>~ S2 ³êf 6æ> ¢ ~º O»" O»j ¿ÿ; ~~ £æ >ö 'Ï Ö"¢ VF~& .. \æ ¶ò³; ~ &çæf ¿ÿ; ~ â'"ö *~ ~ Fig. 1ö ¾æ¾® . æf â'" æb 50 m ç~ vâÚ * '[b Ú r. . º¶ò(Fig. 2)ö ~~ ç¦ 4 m~ Þî Î ¾f ~¦ 4 m~ Þî 6Æ[b W>Ú ®r j r > ® . SPT numberº 10~~ Ôf 8j p 8 möB . ¸jr. Ôjê . ¶ò³j *~ röf *V ÎVf Ê*çj Ï weight-dropj ÒÏ~& . Fêÿ> 4.5 Hz~ >ç; >êV¢ ÒÏ~&b, 24B~ 7j 6 êW2 öÒV¢ Ï~ ^¢ V~& . Shot offsetf 27 m, ¶ò³ *Ïf 500 micro seconds, >êV *Ïf 0.5 mî . êW2 ¶ò(Fig. 3)¢ ÚÚ Ö £ Î¾ [ö ~~ . 5 >Ò2º ~ 6>Ú ¾æ ¾æ p 300 msec êö 2& ¾æÂ . .

(4) . ;\K. Fig. 1. Map of the study area. (a) Map of the Korean peninsula. (b) Detail map of the experimental site. The cross(x) represents the experimental site.. Fig. 2. Soil profile showing the soil description (a) and SPT numbers (b).. æ~ ªÖF (Fig. 4)f &¦ª~ ö.æ& 7 Hz öB 40 Hz Òö ª>Ú ® 7 HzöB 60 m/ sec~ *ç³ê& 40 HzöB 40 m/sec 6² . ªÖFf ² 6²~º © jî¢ 6² ~. Ã&~, 6 6²~º ² Ç ;¢ & .. Fig. 3. Seismogram analyzed in the study.. êW2 ¶ò~ ªÖFj ~º ";" ªÖF j Ö~º ";f ;K(2003)ö ¶^® VF>Ú.

(5) 7j$R ¶ò¢Ï~\4 ³êf6æ>\¿ÿ;~\~£æ>ßW. Fig. 4. S-wave phase velocity. Plus signs(+) show the phase velocities with the maximum energy for frequency analyzed.. . Fig. 6. Dispersion curve showing the field data (asterisks) and the prediction from the inversion result (line).. ² ¾æ¾º ©j " > ® . Fig. 6öº B ªÖF" Ö~ S2 ³ êö & ªÖF~ .G 8 ¾æ¾ ® . ¢ ÚÚ *Ú' ªÖF~ Î·f ¢~~¾ B ªÖFöB ¾æ¾º *ç³ê& ·f b Ã& 6²~º *ç" & ¢~~æº pº ©j r > ® .. .¢Ò 6æ> /;. Fig. 5. S wave velocity vs. depth (a) and special resolution functions for 6 layers used in the velocity inversion (b).. ® . ¢^öBº Öb S2 ³ê¢ &; ãÖ .G>º ªÖF" B &G8"~ JN ¢ *B ÿö *' çê¢ ¸º O»j ÒÏ~& (;K, 2001). ªÖF ¶ò¢ Ö~ S2 ³ê f *' çê& Fig. 5af 5bö ¾æ¾ ® . S2 ³ê¢ ÚÚ æ ç¦ 1 m *öB S2 ³ê 40 m/sec¢ ¾æÚ ~¦ 3 m *öB S 2 ³ê& 80 m/sec Ã& . £ 4 m pöB. S2 ³ê& 40 m/sec 6²~ £ 7-8 m p öB 65 m/sec Ã& . S2 ³ê~ *' çê¢ ÚÚ '[~ pöB ~& Â]~. æ>öB B~º æê2~ 6º &® Ç *ç . 6º ² V~' ¢öÎ"(geometrical spreading)ö ~ 6f Ú¦ îV(material damping) ö ~ 6 ¾*Úê . Ú¦îVö ~ 6º Æ· «¶ Ò~ îV" Æ·«¶f Ò¢ j Ö ®º Ú Ò~ ç&' Úÿö ~ B~ º ©b *"B (Stoll, 1974; Johnstone et al., 1979; White, 1983). ¢>'b æê2~ 6¢ ¾æÚV *~, 6 æ>(attenuation coefficient), damping ratio, Ò −1 Qs f ?f Bv ÒÏ> ®b, ç> Ò öº r" ?f &ê& ® . æê2~ damping ratioº r" ? ;~B . ∆E D = ---------4πE. (1). VB, ∆E: "V ÿnö OÖ(dissipate)B ö.æ, E: "V ÿn &ËB &~ æ;ö.æ(strain.

(6) . ;\K. energy) . −1 Q º damping ratiof r" ?f &ê¢ &ê . ∆E −1 Q = ---------- = 2D 2πE. (2). 6 z® ÒÏ>º 6æ>f damping ratiof~ &êº damping ratio~ 8 ·j ãÖ(D < 10%). r" ? F > ® . αc D = -----ω. (3). VB, α: 6æ>. c: 2~ *2³ê ω: '³ê . æê2& æ>j Û" r, ¢Ú¾º 6º r " ? F > ® (Rix et al., 2000). −α(ω)r. | uz(r,ω) | = FzG(r,ω)Áe. (4). VB, Fz: rööB B~º ß; "2>~ ê, G(r,ω): V~' ¢öÎ", −α(ω)r e : Ú¦ îVö ~ 6(material damping) . V~' ¢öÎ" G(r,ω) º r" ? F > ® (Rix et al., 2000). 0.5. m m.    ∑ ∑ r1 ( ki, ω )r1 ( kj, ω )r2 ( ki, ω )r2( kj, ω )cos [ r ( ki – kj ) ]   = j=  Fz - G ( r, ω ) = --------------  i-----------------------------------------------------------------------------------------------------------------------k i k j ( Vi U i I i ) ( V j U j Ij ) 4 2πr       VB, Vi: *ç³ê, Ui: ³ê, Ii: i ® Îf &B first integral(Aki and Richard, 1980) ki: 2>(wave number), r1(ki,ω), r2(ki,ω): [Îj &; .¢Ò2~ *2 ~ öB ¾æ¾º eigen function . VB, (5)~ G(r,ω) ¦ªf .¢Ò2~ V~ ' ¢öÎ"ö ~ 6ö ~ r ö >j f . 7*^ n~ f .¢Ò2 *2ö &NB eigen functionj ~, 1Nö [ç¢ &;~ VÎ òj J ãÖ ωf k~ > Ò ö &Bº ¢;~ . (4)~ e−α(ω)rf Ú¦ îVö ~ 6(material damping)ö &NB . (4)~ |uz(r,ω)|¢ Ò ö V V~' ¢ö Î"ö & ; ê, ·æ j Fzb ¾* ¶¢ ~ −α(ω)r. ln(|uz(r,ω)|/Fz) = ln G(r,ω) + ln(e. ). (6). & B . ;ê "2>ö &~ (6)~ ¢Þ ~ 8j Ò~ > ¾æÚ, (6)~ JÞö. (5). Bf ? Ò~ ¢N >& > r, VÞVº −αω& B . öBº 6æ>¢ ~V *~ röb¦V &Ë &rÚ >êV~ ^¢ Ò ö æ~~ ' "2>~ Fz8b ÒÏ~& . 24B j6~ êW2 Vj Òö æ~~ ê Ê¿Þ "j ~ Òö V V~' ¢ö Î"¢ ;~& . ' "2>ö &~ Î j6~ êj Fz ¾*Ú & r, ê~ j¢ Ò~ > ¾ æÚî . Fig. 7j ÚÚ &¦ª~ "2>öB ê j& F;' ãËj " ®b¾, 20 Hz f 25 HzöB F;öB £* ½Ú¾º ãËj . . Fig. 8ö 10 HzöB 45 Hzræ "2>'ö & 6æ>f 1 σ .GJN& >Ú ® . ¢ ÚÚ 10 HzöB 6æ>~ 8 £ 0.05 /m "2>& Ã&ö V¢ Ã&~ 40 HzöBº £ 0.15 /m& >º ©j r > ® .. 6æ> Ö 6æ>¢ Ï~ æ>j ;W~ ®º ' [~ −1 Qs ¢ ~V *Bº Ö"; jº~ . .¢Ò 2~ damping ratioº P2~ damping ratiof S2~ damping ratio¢ Ï~ r" ? ¾æâ > ® ..

(7) 7j$R ¶ò¢Ï~\4 ³êf6æ>\¿ÿ;~\~£æ>ßW. . Fig. 7. Amplitude ratios (squares) vs. distance for 6 frequencies. Lines represent the linear regression of the data.. ∂VR ρVP Zi --------- = --------------∂VP i 2UIK2 ∫Zi – 1 ∂VR ρVS Zi --------- = --------------∂VS i 2UIK2 ∫Zi – 1. dr 2 kr1 + -------2 dz dz. (7). 2. dr  kr – dr -1 – 4kr1 -------2 dz (8)  2 -----dz dz . N.  ∂V ∂V ω αR ( ω ) = ------2  ∑ VP, i  ---------R K + VS, i  ---------R DS, i  ∂VP i ∂VS i VR   i (9) VB, i ® [~ S2 ³ê VS: VR: i ® [~ .¢Ò2 *ç³ê VP: i ® [~ P2 ³ê Ds,i: i ® [~ S2 damping ratio K: S2~ damping ratioö & damping ratio~ j. P2~. ∂VR --------- : ' [öB P2 ³êæzö & .¢Ò2 ∂VP. ³êæz~ "6ê ∂VR --------- : ' [öB S2 ³êæzö & .¢Ò2 ∂VS ³êæz~ "6ê . (9)~ &*^ n~ Ñ ® ~ Kº S2 damping ratio¢ Ö~º ®Ú ~ 'Ëj ~ æ pº ©b rJ^ ® (Spang, 1995). F º .¢Ò2~ *ç³ê& P2 ³ê~ æzö ~ ∂V 'Ëj Aæ pV r^ö ---------R ~ 8 j" ·jæ ∂VP Vö K¢ ©ê 1 R ·f 8 > æ öBº K8j 1 ;~B Öj > ¯~& . (9)º ¢>zB Ö (Aki and Richard, 1980; Menke, 1989)ö ~~ ¯R~ ; r" ? *F > ® . d = Gm. (10).

(8) . ;\K. Fig. 8. Observed attenuation coefficients (asterisks) and one sigma uncertainty estimates (lines).. VB vector dº 6æ> nB~ data mf Öb ~¶ ~º ' [~ S2 damping ratio & B . Gº Ö~ kernel ¯R (7), (8)j (9)~ &*^ nö ã«~ > ® . Ö Ö" −1 −1 ê Qs & Fig. 9ö ¾æ¾® . Qs f þ ~ *' çê& þ ¾æ¾® . Qs−1 f ³ê¢ ? jv~ S2~ ³ê& 40 m/sec ;êö ê~º æ ç¦ [ £ 1 m * öB Qs−1f 0.04~ ¸f 8j ¾æÞ . j¾ S 2~ ³ê& £ 65 m/sec Ã& * £ 3 m −1 Ò~º, öBº Qs ~ 8 0.02 6²~ º ©j . æj¾ £ 4 möB £ 7 mræº S2~ ³ê& £ 40 m/sec 6²~º −1 *öBº Qs £ 0.03 Ã& . j¾ öB S2 ³êº 65 m/sec Ã&~¾ Qs−1f j" £* Ã&~º Î·j ¾æÞ . Qs−1ö & *' çê(Fig. 9b)¢ ÚÚ Ñ ® [öB ^ ® [ræº ' [ö ~º pöB Â] ~¢ *' çê& ±rj r > ® b¾ J ® [ j¾öBº çê& æ ±æ prj r > ® .. º¶òB ÖÖ~ jL *öB æ~ S2 ³êf Qs−1 ¢ æ~ ºÒÖ"(Fig. 2)f jv~ ~ . æf ¿ÿ; ~~ â'" æ& *'[ 50 m ç vó² 9®º . .¢Ò2~ ªÖF~ "2> '~ ê ~ ö. −1 Fig. 9. Qs vs. depth (a) and resolution functions for six layers used in the inversion (b).. −1. Bº £ 8 m præ~ S2 ³êf Qs ¢ > ®î . 8 mræ pöB '[f ² v [b ª>, ç¦ £ 4 mº ¶Î Þî Î¾ W >Ú ® . [~ ç¦öBº 6Æ& £* bÒ> Ú® . ~¦ £ 4 mº £ Þî 6Æ W> Ú ®b £*~ Î¾& D® . '[~ Wb −1 î" S2~ ³ê, Qs ¢ jv~ ç¦ Þî Î¾[~ S2~ ³ê& ~¦ Þî 6Æ[ ¸ f ©j r > ® . æ ç¦ 1 m *öB ¾ æ¾º Ôf ³êº æ> ^ææ p Ö ¶ Î çö V~º ©b . Qs−1 f ºÒ¢ jv~ S2 ³ê& ç&'b 8(80 m/sec) j ¾æÚº ç¦ 4 m Þî Î ¾[öB Qs−1f 0.02~ 8j . S2 ³ê& 40 m/sec Ôjæº ~¦ 4 m~ Þî 6Æ[öB −1 Qs f 0.03b Ã& . æ ç¦ 1 m *ö −1 B S2~ ³êº 40 m/sec Qs f 0.04~ ¸f 8j ¾æÞ . *öBº æ[ ~¦~ æ[. ^ææ p ¶Î çB S2~ ³ê& ¶ −1 Ò ¸f 6& ¢Ú¾º ©b . Qs ~ *' çê¢ ÚÚ p 5 mræº '[öB çê& ¸b¾ pf öBº çê& / Ï® ¾æº ©j " > ® . ºÖ"f S2~ ³êf 6¢ jv~V*~ Fig. 10ö pö V æ>~ Wª ßW" SPT, S2~ ³ê, Ò.

(9) 7j$R ¶ò¢Ï~\4 ³êf6æ>\¿ÿ;~\~£æ>ßW. . −1 Fig. 10. (a). Soil description. (b). SPT numbers. (c). S wave velocity and resolution. (d) Qs and resolution.. −1 Qs ¢ þ ¾æÚî . p 4 m¢ ãê ç¦~. Þî Î¾[~ Qs−1 8 ~¦~ Þî 6Æ[~ −1 Qs 8 ·f Fº 6Æ¢ ~º [ Î¾ ¢ ~º [ z ¸f 6¢ ¾æÚº ©b C >ê ®b¾, [j W~º bîö. ö, , ~ Î·, ~ z;ê 2~ 6ö 'Ëj "º &æ º²& ô ® V r^ö ¢ ¢>z~Vº Ú[ . £æ>~ 2 ~ ³êf 6ö & ôf ¶ò& >÷>Ú æ æ[~ Wbî" ³ê, 6~ &ê& ¦z ç^~ ² C&î > ®j © .. Ö öBº 7j6 êW2 ¶ò¢ Ï~ −1 æ>~ S2 ³êf Qs ¢ ~º O»j ¿ÿ; ~ â'" æ~ £ æ>ö 'Ï~ æ>~ S2 ³êf Qs−1¢ ~ ºÒ Ö"f jv~. r" ?f Öj áî . Ñ, 7j6 ^¢ ÒÏ~ S2~ ³êf Qs−1 ¢ > ®î . ";öB rööB &Ë &r Ú ^¢ V& ^ ;~ ' ÒöB~ ^ ¢ Òö æ~ ¾Ò~ ' "2>ö ~º ê j ~& . ¢ V& ^~ Ê¿Þ"b ¾*. Ú & r ¶¢ ~ ¢ Ò~ > ¾æÚî . r Òö V¢ ê j& 6²~º ;ê¢ ¾æÚº VÞV¢ 6æ> ;~& . 6æ>¢ æ> ç¦ 8 m [~ S2 ³êf þ Ö~ [~ Qs−1¢ ~& . −1 ~, Öö ~~ S2 ³êf Qs ¢ Ò æ~ ºÒf jv~& . ºÖ"ö ~~ æ~ '[ ç¦ 8 m vþ~ æ[f ². Þî Î¾[" Þî 6Æ[b ¾*Úê . .¢ Ò2~ ªÖFj Ö~ S2 ³ê ö ~~ ç¦ 4 m~ Þî Î¾[öB S2 ³êº £ 80 m/sec ~¦ 4 m~ Þî 6Æ[~ ³ê 40 m/sec ¸f 8j . ' [öB S2 ³ê~ *' çêº jv' ¸ . Qs−1º ç¦ 4 m~. Þî Î¾[öB £ 0.02¢ ~¦ 4 m~ Þ î 6Æ[öB 0.03b Ã&~º ·çj . −1 Qs ~ *' çêº ç¦ £ 5 m *öBº · ^~¾ pf öBº *' çê& j " Ôjæº ©j " > ® . æ[ ç¦ 1 m p öBº ç&'b Ôf S2 ³êf ¸f Qs−1¢ ¾æÚº, ©f ç¦ [ ^ææ pf Ö" C > ®j © . q, Ö Ö"f ºÒ¢ jv~ , * Ú'b Þî Î¾[ Þî 6Æ[ ¸f.

(10) . ;\K −1. S2 ³ê¢ ¾æÚ Ôf Qs 8j ®b¾, æ>~ S2 ³êf Qs−1¢ Ö;~º ôf º. ®bæ ¢ ¢>z~V *Bº ôf £ −1 æ>~ S2 ³êf Qs ö & ¶òf & ÷' >Ú¢ © .. Ò Ò ¢^f Ö&v ‘êj * ·BB ² 2003j ßêÒë’ æöö ~ >¯>î rj C¿î . ¢^j Ò~ >;ö êæj " ^ ª~ Ò*ö (fêê, "ÿ", î)þ p f 6Ò¢ ãî .. ^ ^ò ;\K, 2001, .;~ ÂW '[~ £æ>ö & : R Öö ~ S ³êf çê, æ "²æ, 22², 3^, 179-186. ;\K, 2003, R öÒO»j Ï~ S ³ê f ºÖ"~ jv ,æ"²æ, 24², 6^, 549-557. Aki, K. and Richard, P. G., 1980, Quantitative Seismology, W. H. Freedman and Company, 259-333 p. Al-Eqabi, G. I., and Herrmann, R. B., 1993, Ground roll: A potential tool for constraining shallow shear wave structure, Geophysics, 58 (5), 713-719. Anderson, D. L., Ben-Menahem, A., and Archambeau, C. B., 1965, Attenuation of seismic energy in the upper mantle., Journal of Geophysical Research, 70, 14411448. Cheng. C. C. and Mitchell, B. J., 1987, Crustal Q structure in the United States from multimode surface waves, Bulletin of Seismological Society of America, 71, 161-181. Hardin, B. O. and Drnevich, V. P., 1972, Shear modulus damping in soils: Measurement and parameter effects, Journal of Soil Mechanics and Foundation Division., ASCE 98 (6), 603-624. Herrmann, R. B. and Mitchell, B. J, 1975, Statistical analysis and interpretation of surface wave and elastic attenuation data for the stable interior of North America, Bulletin of Seismological Society of America, 65, 11151128. Hoar, R. J. and Stokoe, K. H. II, 1984, Field and laboratory measurements of material damping of soil in shear wave propagation., Proc. 8th World Conference on Earthquake Engineering., Prentice Hall, Englewood Cliffs, N. J. Vol III, 47-54.. Johnstone, D. H., Toksoz. M. N., and Timur. A., 1979, Attenuation of seismic waves in dry and saturated rocks: II. Mechanism, Geophysics, 44 (4), 691-711. Lai, C. G., Rix, G. J., Foti, S. and Roma, V., 2002, Simultaneous measurement and inversion of surface wave dispersion and attenuation curves, Soil Dynamics and Earthquake Engineering, 22, 923-930. Lee, W. B. and Solomon, S. C. 1975, Inversion schemes for surface wave attenuation and Q in the crust and in the mantle. Geophysical Journal of Royal Astronomy Society, 43, 47-71. Liu, H. P., Warrick, R. E., Westerlund, R. E. and Kayen, R. E., 1994, In site measurement of seismic shear wave absorption in the San Fransisco Holocene bay mud by the pulse broadening method, Bulletin of Seismological Society of America, 86 (5), 62-75. Malagnini, L., 1996, Velocity and attenuation of very shallow soils: Evidence of frequency-dependent Q, Bulletin of Seismological Society of America, 86 (5), 14711486. Mok, Y. J., Sanchez-Salieno, I., Stokoe, K. H. II, and Roesset, J. M., 1988, In situ measurement in crosshole seismic method, Earthquake Engineering and Soil Dynamics II - Recent Advances in Ground Motion Evaluation, Geotechnical Special Publication, No. 20, J. L. Von Thun, ed. ASCE, New York, 305-320. Menke, W., 1989, Geophysical data analysis: discrete inverse theory, Academic Press, Sandieo, California, 248 p. Mokhtar,T. A., Herrmann. R. B., and Russel, D. R., 1988, Seismic velocity and Q model for the shallow structure of Arabian Shield from short period Rayleigh waves, Geophysics, 53 (11), 1379-1387. Redpath, B. B. and Lee, R. C., 1986, In situ measurements of shear wave attenuation at a strong motion recording site., Earthquake Notes, 57, 8. Rix, G. J. and Lai, C. G., and Foti, S., 2001, Simultaneous measurement of surface wave dispersion and attenuation curves, Geotechnical Testing Journal, 24 (4), 350-358. Rix, G. J., Lai, C. G., and Spang, A. W., 2000, In situ measurement of damping ratio using surface waves, Journal of Geotechnical and Geoenvironmental Engineering, 126 (5), 472-480. Seed, H. B., Wong, R. T., Idriss, I. M, and Tokimasu, K., 1986, Moduli and damping factors for dynamic analyses of cohesionless soils, Journal of Geotechnical Engineering, ASCE 112 (11), 1016-1032. Stoll, R. D., 1974, Acoustic waves in saturated sediments. Physics of sound in marine sediments, Plenum, New York, 19-39 p. Spang, A. W. Jr. 1995, In situ measurements of damping ratio using surface waves, Ph. D. dissertation, Georgia.

(11) 7j$R ¶ò¢Ï~\4 ³êf6æ>\¿ÿ;~\~£æ>ßW. Institute of Technology, Atlanta, 346 p. Vucetic, M. and Dobry, R., 1991, Effect of soil plasticity on cyclic response, Journal of Geotechnical Engineer-. . ing, ASCE, 117 (1), 89-107. White, J. E., 1983, Underground sound: Applications of seismic waves, Elsevier Science, Amsterdam, 287 p.. 2004j 7ú 31¢ ö 7> 2004j 11ú 13¢ >;ö 7> 2004j 11ú 13¢ ö j.

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