* BISQ, 133 BISQ BISQ BISQ BISQ BISQ : PACC: 43, 665, 913 1. [1], * (:4743). 119 133 431-8449917 431-898966 431-8941554 Email cuizwjlu@sina.com; kexiew@public.cc.jl.cn
[] [3 4] Dvorkin Nur [5 6] - BISQ [7-13] [7-9], [1] BISQ [11 1] BISQ BISQ BISQ BISQ BISQ [13] [14] [15] [, 16]
BISQ Dvorkin Nur 1993 [5] BISQ ( ) BISQ BISQ M M M M S ( ω, R) 1 S ( ω, R) 1 J ( R) λrj ( λr) 1 λ λ ω ρ ~ ω R ( ) M Dvorkin [6] ρ ~ ( ω ) ρ ~ ( ω ) iη ωκ ( ω ) 3 ( ) κ ω ) 1 [ F iω ρ α ηφ] ( ω ) κ ( ω ) κ κ 4 α κ η ρ φ F(ω [ 17] BISQ [18] BISQ H u + ω ρu + C C u + ω ρ u + M w + ω ρ w + ω w ρ ~ w 5a 5b ρ ρ φρ + 1+ φ ρ ρ s ( ) w φ( U u U C αm H K + 4G / 3 + α ) s b M α 1 K b / K s b K, K s 3
kˆ u ( r t ) u kˆ, i e ( k r ωt ) w ( r ) k ˆ i( k r ωt ) t w e 6, 5a b w Y u ( ) ( ~ ) ~ H M C Y H + M ρ C ρ Y + ρρ ρ ρ 7 k 1, ω Y1, P ( k ) Re( Y ) V ω Re 1 Q 1 Im( k) Re( k ) 8 3 [18], ωρ κ ηφ << 1 7 ( K + 4G / α ) Y 1 ρ b 3 + M [ ωκ ( 1 α M H ) M ] iη ωκ M Y 9 iη / 4 J ( x) xj ( x) 1+ x 8 + 48 + L 1 x S ( ω, R) ( iηωr κ M ) 8 + ( ηωr κ M ) 48, x λr 1 S( ω ) V P ω κ / η Im( S ) S Re( S ) 11a M 1 Q P [ Im( S ) Re( S )] 11b ω, 1 VP 3 M κ ηr Q P 4M κ ηr ω 1 1,, V ω M ( 1 α M / ) κ / η Q P H P 4
BISQ BISQ 8 4 φ.15 5 1-15 m κ K b η.1pa.s 16 1 9 Pa 38 1 9 Pa K s 14.61 1 G 9 Pa 65Kg/m 3 3.67 1- ρ s α 5 1 3 4 (U / u ) a b 1 1 1a 1b BISQ a b 5
BISQ BISQ BISQ [11] 3 3 3a 3b R <1Hz / π π 4 4 4a 4b BISQ 1 BISQ 6
1Hz R 3mm 3 1 4 35 BISQ [13] 5 5 5 1 5a,5b BISQ [15] Pride [] 5 η ~ ρ α ρ / φ 1 M λ ω α ρ Mφ M ( ω ) n n λ j M R j 7
J ( j n ) n 1,,3L J ( λr) J J 1 M j n M M > H u M 1 λr < j.45 J1( λr) λrj ( λr) 13 λr BISQ w BISQ 5a 5b u u + ω ρ u C u + ω ρ u 14 u k ω ρ / ω ρ C 15 H / BISQ C H 15 M ( ω ) ( 1 / K ) K b s K ( b + 4G / 3 ρ / ρ + K b / K 1) s 16 16 BISQ [16] 6, 8
BISQ BISQ BISQ A BISQ 1993 Dvorkin Nur z P P C u + M w M ( w + α u) C αm α 1 K / K A-1 b s r 9
u r, w r A- u η w P ρ A-3 t κ ( ω) t A- A-3 P r η κ w ( ω ) t r A-4 w ( z, r, t ) w ( r ) r r i e ( lz ωt ) ω ) P ( z, r, t ) P ( r i( lz t ) e A-5 A-5 A-4 w ( r r ) ω ~ ρ 1 P ( r) ( ω) r A-6 ( ω) κ ρ (ω ) [16] A-6 A-4 [5] Dvorkin z P ( r ) w ( r r ) r u w z u ( z, t) D 1 i e ( lz t ω ) i( lz ωt ) w z ( z, t) D e A-8 D A-8A-1 θ A-6 D1 r d dr P 1 dp ~ ω ρ( ω) + + P ( ) ~ il D + αd1 ω ρ( ω) A-9 r dr M r R P R A-9 1
J P ( z, r, t) ( λr) wz u z M 1 + α λ ω ~ ρ M A-1 λrj ( λr) z z P () r r P av 1 πr ( z, t) R J π rp ( z, r, t)dr 1( λr) wz u z M 1 + α A-11 λrj ( λr) z z A-11 A-1 M J 1( λr) M 1 λrj ( λr) A-1 ( ) 1 F ω Dvorkin Nur 1993 [1] Qiao W X, Wu W Q, Wang Y J 1996 Progress in Physics 16 386(in Chinese)[ 1996 16 386] [] M A. 1956 J. Acoust. Soc. Am. 8 168 [3] Wang K X, Dong Q D1986 Acta Petrolei Sinica 7 59 (in Chinese)[,, 1986 7 59] [4] Zhou Y F, Wang Y J, Ma L et al Acta Phys.Sin. 49 48(in Chinese)[ 49 48] [5] Dvorkin J., and Nur A. 1993 Geophysics 58 53 [6] Dvorkin J., R. Nolen-Hoeksema, and Nur A. 1994 Geophysics 59 48 [7] J.O. Parra Geophysics 65 [8] Yang D H, Zhang Z J Chinese. Science.Bulletin 45 1333(in Chinese)[,, 45 1333] 11
[9] Yang D H, Zhang Z J Wave Motion 35 3 [1] Cheng Y F, Yang D H, and Yang H Z Chin.Phy.Lett 19 445 [11] Yang K D, Yang D H, Wang S Q Chinese J Geophysics 45 853(in Chinese) [ 45 853] [1] Meng Q S, He Q D, Zhu J W et al 3, Journal o Jinlin University(Earth Science Edition)33 17(in Chinese)[,, 3 ( ) 33 17] [13] Cui Z W and Wang K X, 3, Int.J.Eng.Sci 41 179 [14] Wang K X, J. E. White, Wu X Y 1996 Acta Geophysica Sinica 39 133(in Chinese) [ J. E. White, 1996 39 133] [15] Hu H S 3 Acta Phys.Sin. 5 1954(in Chinese) [ 3 5 1954] [16] Hu H S, Wang K X, Liu J Q Chinese J.Comput.Phys(in Chinese)19 3(in Chinese) [,, 19 3] [17] Hu H S, Wang K X 1 Chinese J Geophysics 44 135(in Chinese)[, 1 44 135] [18] Cao Z L, Wang K X 1 Annual J Chin. Geophys.Soc.31[ 1 31] [19] Dutta N C. and Odé H. 1979 Geophysics 44 1777 [] Pride S.R. 1994 Phys.Rev.B 5 15678 1
Slow waves propagation in BISQ poroelastic model * Cui Zhi Wen Wang Ke Xie Cao Zheng Liang Hu Heng Shan (Department o Acoustics & Microwaves, School o Physics, Jilin University, Changchun, 133, China) Abstract The slow compressional wave (P-wave) in Porous media based on BISQ model is investigated. The low requency approximate expression or velocity and attenuation o P-wave is given. Comparing with model, BISQ model predicts that: the attenuation o P waves is very large at low requency and decrease with characteristic uirt low length (R) increasing, velocity dispersion are weaken and the velocity low requency limit is not zero and decrease with R increasing, the ratio o pore luid-displacement and bulk-displacement is similar to attenuation and phase is dierent obviously; The seepage low induced by P wave at the luid-porous media interace is more large than that o model, which can be induced larger accompanying electric ield. For the sake o contrast, the properties o the ast compressional wave are also presented. Two conclusions are induced rom BISQ model: there is no uirt mechanism in in-viscid luid-saturated porous media and there is no dynamic compatibility phenomenon in viscid luid-saturated porous media. Keywords: Porous medium, Squirt low, Slow compressional waves, Dynamic compatibility PACC: 43..Jr, 6.65, 91.3 *Project supported by the National Natural Science Foundation(Grant No.4743) 13
41 45 (1a) Vp1(m/s) 4 395 39 385 38 1 1 1k 1k 1k 1M Vp(m/s) 6 5 4 3 1 (1b) R(mm) 1. 3. 6. 1. 1 1 1k 1k 1k 1M 1 14
.5 (a).4 Q p1-1.3..1. 1 1 1k 1k 1k 1M Q p -1 1M 1k 1k 1k 1 (b) R(mm) 1. 3. 6. 1. 1 1 1m 1 1 1k 1k 1k 1M 15
5 4 3 R(mm) 1. 3. 6. 1. 1 18 18 178-9 -1-11 -1-13 -14-15 -16-17 -18 (3a) 1 1 1k 1k 1k 1M (3b) 1 1 1k 1k 1k 1M 3 16
1. U p1 /u p1.95.9.85 (4a) 1 1 1k 1k 1k 1M U p /u p 1M 1k 1k 1k 1 1 (4b) 1 1 1k 1k 1k 1M R(mm) 1. 3. 6. 1. 4 17
.1 1E-3 (5a) 1E-4 Wp1/Ui 1E-5 1E-6 1E-7 1E-8 1 1 1k 1k 1k 1M.1 (5b) Wp/Ui.1 1E-3 1E-4 R1mm 3mm 6mm 1mm 1 1 1k 1k 1k 1M 5 18