含孔隙、裂隙介质弹性波动的统一理论——Biot理论的推广
摘要
地球表层的岩石介质往往是即含孔隙又含裂隙,这种现象对弹性波传播产生重要影响.本文在Biot孔隙介质的波动理论基础上,利用该理论中介质在排水(干燥)条件下的弹性模量引入裂隙对弹性性质的影响,并对裂隙在弹性波动作用下的"挤喷流"(squirt flow)效应进行了具体分析,导出了一个描述孔隙、裂隙并存时的弹性波统一理论.该理论既能描述裂隙对介质弹性的影响,又能模拟挤喷效应导致的弹性波衰减和频散,并且指出,这种挤喷效应是由裂隙介质的两个最重要的参数,裂隙密度和纵横比所控制.这一统一理论的另一重要特性是该理论保持了Biot理论的基本特征,即慢速纵波的传播特征及孔隙渗透率的影响.模拟计算结果及与实际数据的对比表明,这一孔隙、裂隙弹性波动的统一理论能较好地描述实际岩石介质中弹性波的传播,从而在地球介质中地震和声波测量中比Biot理论有着更为广泛的应用前景.
引文
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2Walsh J B.The effect of cracks on the compressibility of rock.J Geophys Res,1965,70,2:381–389
3O’Connell R J,Budiansky B.Seismic velocities in dry and saturated cracked solids.J Geophys Res,1974,79:4626–4627
4Budiansky B,O’Connell R J.Elastic moduli of a cracked solid.Int J Solids Structures,1976,12:81–97
5O’Connell R J,Budiansky B.Viscoelastic properties of fluid saturated cracked solids.J Geophys Res,1977,82:5719–5736
6Budiansky B,O’Connell R J.Bulk dissipation in heterogeneous media.Solid Earth Geophys Geotech,1980,42:l–10
7O’Connell R J.A viscoelastic model of anelasticity of fluid saturated porous rocks.Physics and Chemistry of Porous Media,AIP Conf.Proceedings,1984.166–175
8Biot M A.Theory of propagation of elastic waves in a fluid saturated porous solid:A.Low-frequency range.J Acoust Soc Am,1956,28:168–179
9Biot M A.Theory of propagation of elastic waves in a fluid saturated porous solid.B.Higher frequency range.J Acoust Soc Am,1956,28:170–191
10Biot M A.Generalized theory of acoustic propagation in porous dissipative media.J Acoust Soc Am,1962,34:1254–1264
11唐晓明,郑传汉,著.定量测井声学.赵晓敏,译.北京:石油工业出版社,2004.76–78
12Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms.Geophysics,1993,58,4:524–533
13White J E.Computed seismic speeds and attenuation in rocks with partial gas saturation.Geophysics,1975,40:224–232
14Johnson D L.Theory of frequency dependent acoustics in patchy-saturated porous media.J Acoust Soc Am,2001,110:682–694
15Carcione J M,Helle H B,Pham N H.White’s model for wave propagation in partially saturated rocks:Comparison with poroelastic numerical experiments.Geophysics,2003,68:1389–1398
16Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks.Geophys J R Astr Soc,1981,64:133–150
17Hudson J A.A higher order approximation to the wave propagation constants for a cracked solid.Geophys J R Astr Soc,1986,87:265–274
18Hudson J A.Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks.Geophys J Int,1990,102:465–469
19Kuster G T,Toks?z M N.Velocity and attenuation of seismic waves in two-phase media:I.Theoretical formulation.Geophysics,1974,39:587–606
20Mavko G,Nur A.Wave attenuation in partially saturated rocks.Geophysics,1979,44:161–178
21Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.I.Governing equations and acoustic attenuation.Phys Rev E,2003,68:036603
22Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.II.Fluid transport equations.Phys Rev E,2003,68:036604
23Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.J Geophys Res,1995,100(B12):24611–24627
24Berryman J G.Effective medium theories for multicomponent poroelastic composites.J Eng Mech,2006,132:519–531
25巴晶.复杂多孔介质中的地震波传播机理研究.博士学位论文.北京:清华大学,2008
26巴晶.双重孔隙介质波传播理论与地震响应实验分析.中国科学:物理学力学天文学,2010,40:1–12
27Thomsen L.Biot-consistent elastic moduli of porous rocks:Low-frequency limit.Geophysics,1985,50,12:2797–2807
28Mavko G,Jizba D.Estimating grain-scale fluid effects on velocity dispersion in rocks.Geophysics,1991,56,12:1940–1949
29Johnson D L,Koplik J,Dashen R.Theory of dynamic permeability and tortuosity in fluid saturated porous media.J Fluid Mech,1987,176:379–402
30Brie A,Pampuri F,Marsala A F,et al.Shear sonic interpretation in gas-bearing sands.Proceedings of SPE Annual Technical Conference&Exhibition,1995,SPE30595:701–710
31陈顒.地壳岩石的力学性能—理论基础与实验方法.北京:地震出版社,1988.140–157
32Tang X,Cheng C H.A dynamic model for fluid flow in open borehole fractures.J Geophys Res,1989,94,B6:7567–7576
33崔志文,王克协,曹正良,等.多孔介质BISQ模型中的慢纵波.物理学报,2004,53,9:3084–3089
34Garland G D.地球物理学引论.陈顒,唐晓明,赵晓敏,译.北京:地震出版社,1987.117–120
35Schubnel A,Benson P M,Thompson B D,et al.Quantifying damage,saturation and anisotropy in cracked rocks by inverting elastic wave velocities.Pure Appl Geophys,2006,163:947–973
36Cheng C H,Toksoz M N.Inversion of seismic velocities for the pore aspect ratio spectrum of a rock.J Geophys Res,1979,84(B13):7533–7543
2Walsh J B.The effect of cracks on the compressibility of rock.J Geophys Res,1965,70,2:381–389
3O’Connell R J,Budiansky B.Seismic velocities in dry and saturated cracked solids.J Geophys Res,1974,79:4626–4627
4Budiansky B,O’Connell R J.Elastic moduli of a cracked solid.Int J Solids Structures,1976,12:81–97
5O’Connell R J,Budiansky B.Viscoelastic properties of fluid saturated cracked solids.J Geophys Res,1977,82:5719–5736
6Budiansky B,O’Connell R J.Bulk dissipation in heterogeneous media.Solid Earth Geophys Geotech,1980,42:l–10
7O’Connell R J.A viscoelastic model of anelasticity of fluid saturated porous rocks.Physics and Chemistry of Porous Media,AIP Conf.Proceedings,1984.166–175
8Biot M A.Theory of propagation of elastic waves in a fluid saturated porous solid:A.Low-frequency range.J Acoust Soc Am,1956,28:168–179
9Biot M A.Theory of propagation of elastic waves in a fluid saturated porous solid.B.Higher frequency range.J Acoust Soc Am,1956,28:170–191
10Biot M A.Generalized theory of acoustic propagation in porous dissipative media.J Acoust Soc Am,1962,34:1254–1264
11唐晓明,郑传汉,著.定量测井声学.赵晓敏,译.北京:石油工业出版社,2004.76–78
12Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms.Geophysics,1993,58,4:524–533
13White J E.Computed seismic speeds and attenuation in rocks with partial gas saturation.Geophysics,1975,40:224–232
14Johnson D L.Theory of frequency dependent acoustics in patchy-saturated porous media.J Acoust Soc Am,2001,110:682–694
15Carcione J M,Helle H B,Pham N H.White’s model for wave propagation in partially saturated rocks:Comparison with poroelastic numerical experiments.Geophysics,2003,68:1389–1398
16Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks.Geophys J R Astr Soc,1981,64:133–150
17Hudson J A.A higher order approximation to the wave propagation constants for a cracked solid.Geophys J R Astr Soc,1986,87:265–274
18Hudson J A.Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks.Geophys J Int,1990,102:465–469
19Kuster G T,Toks?z M N.Velocity and attenuation of seismic waves in two-phase media:I.Theoretical formulation.Geophysics,1974,39:587–606
20Mavko G,Nur A.Wave attenuation in partially saturated rocks.Geophysics,1979,44:161–178
21Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.I.Governing equations and acoustic attenuation.Phys Rev E,2003,68:036603
22Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.II.Fluid transport equations.Phys Rev E,2003,68:036604
23Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.J Geophys Res,1995,100(B12):24611–24627
24Berryman J G.Effective medium theories for multicomponent poroelastic composites.J Eng Mech,2006,132:519–531
25巴晶.复杂多孔介质中的地震波传播机理研究.博士学位论文.北京:清华大学,2008
26巴晶.双重孔隙介质波传播理论与地震响应实验分析.中国科学:物理学力学天文学,2010,40:1–12
27Thomsen L.Biot-consistent elastic moduli of porous rocks:Low-frequency limit.Geophysics,1985,50,12:2797–2807
28Mavko G,Jizba D.Estimating grain-scale fluid effects on velocity dispersion in rocks.Geophysics,1991,56,12:1940–1949
29Johnson D L,Koplik J,Dashen R.Theory of dynamic permeability and tortuosity in fluid saturated porous media.J Fluid Mech,1987,176:379–402
30Brie A,Pampuri F,Marsala A F,et al.Shear sonic interpretation in gas-bearing sands.Proceedings of SPE Annual Technical Conference&Exhibition,1995,SPE30595:701–710
31陈顒.地壳岩石的力学性能—理论基础与实验方法.北京:地震出版社,1988.140–157
32Tang X,Cheng C H.A dynamic model for fluid flow in open borehole fractures.J Geophys Res,1989,94,B6:7567–7576
33崔志文,王克协,曹正良,等.多孔介质BISQ模型中的慢纵波.物理学报,2004,53,9:3084–3089
34Garland G D.地球物理学引论.陈顒,唐晓明,赵晓敏,译.北京:地震出版社,1987.117–120
35Schubnel A,Benson P M,Thompson B D,et al.Quantifying damage,saturation and anisotropy in cracked rocks by inverting elastic wave velocities.Pure Appl Geophys,2006,163:947–973
36Cheng C H,Toksoz M N.Inversion of seismic velocities for the pore aspect ratio spectrum of a rock.J Geophys Res,1979,84(B13):7533–7543
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