裂缝介质的有效弹性常数
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摘要
目前研究平行裂缝或定向裂纹对地震波传播影响的常用模型有三种 :1具有平面分布的细小、孤立的滑移面或裂纹的裂缝模型 ;2具有平面分布的、非连续接触的裂纹的裂缝模型 ;3把平面界面当作由黏性液体或软材料组成的连续薄层的裂缝模型。本文从较普遍的理论出发 ,导出了裂缝介质中柔度系数的解析表达式 ;利用这些解析式计算了上述三种模型的有效裂缝柔度系数和刚度系数 ,并证明上述三种模型均可归结到统一的表达形式。研究还表明 ,当已知裂缝表面一些信息时 ,就可将宏观测得的柔度系数直接与裂缝的微观结构特征联系起来
Existing common used fractured models are three types when studying effect of parallel fracture or oriented fracture on seismic wave propagation: ① fracture model having a small, isolate sliding surface or cracks with plane distribution; ② fracture model having non continuous contacting cracks with plane distribution; ③ fracture model putting plane interface as a continuous thin layer consisting of viscous liquid or soft material. Starting directly from more common theory, we deduced analytic expressions of coefficients of softness in fractured material. The effective fractured coefficients of softness and stiffness of three above mentioned models has been calculated by using these analytic expressions and it has been proved that three above mentioned models can be integrated into results of the paper. Our studying results show hat macroscopically measured coefficients of softness can be directly connected with microscopic structural feature of fracture when information on surface of fracture has been known.
Existing common used fractured models are three types when studying effect of parallel fracture or oriented fracture on seismic wave propagation: ① fracture model having a small, isolate sliding surface or cracks with plane distribution; ② fracture model having non continuous contacting cracks with plane distribution; ③ fracture model putting plane interface as a continuous thin layer consisting of viscous liquid or soft material. Starting directly from more common theory, we deduced analytic expressions of coefficients of softness in fractured material. The effective fractured coefficients of softness and stiffness of three above mentioned models has been calculated by using these analytic expressions and it has been proved that three above mentioned models can be integrated into results of the paper. Our studying results show hat macroscopically measured coefficients of softness can be directly connected with microscopic structural feature of fracture when information on surface of fracture has been known.
引文
1 Queen JH,Rizer W D and De Martini D.Geophysical methods of fracture detection and estimation.TheL eading Edge,1992 ,11:19～ 2 1
2 Hudson JA,Liu E and Crampin S.Transmission properties of a plane fault.Geophys J Int,1996 ,12 5559～ 56 6
3 Hudson JA,L iu E and Crampin S.The mean transmission properties of a fault with imperfect facialcontact.Geophys J Int,1997,12 9:72 0～ 72 6
4 Hudson JA and Knopoff L.含小尺度包体或裂纹的复合介质总体特性的推测 .吴如山 ,安艺敬一主编 :地震波的散射与衰减 (上 ) ,地震出版社 ,1993,6～ 2 8
5 Schoenberg M and Sayers C.Seismic anisotropy of fractured rock.Geophysics,1995,6 0 :2 0 4～ 2 11
6 Hudson JA.Wave speeds and attenuation of elastic waves in material containing cracks.Geop hys J RoyAstr Soc,1981,6 4 :133～ 150
7 Nishizawa O.Seismic velocity anisotropy in a medium containing orientedcracks:transversely isotropiccase.J Phys Earth,1982 ,30 :331～ 347
8 Stoll R D.Stress- induced anisotropy in sediment acoustics.J Acoust Soc Am,1989,85:70 2～ 70 8
9 Yoshioka N.Elastic behavior of contacting surfaces under normal loads,a computer simulation usingthree- dimensional surface topographies.J Geophys Res,1994 ,99
10 White JE.Underground sounding— Application of seismic waves,Elsevier,1983
11 L iu E,Crampin S and Hudson JA.Diffraction of seismic waves by cracks with application to hydraulicfracturing.Geophysics,1997,6 2 :2 53～ 2 6 5
12 Groenenboom Jand Fokkema JT.Monitoring the width of hydraulic fractures with acoustic waves.Geo-physics,1998,6 3:139～ 148
13 L iu E et al.The effective elastic compliance of fractured rock.Exp anded Abstract6 6 th Ann Int SEGMeeting ,1996 ,1882～ 1885
14 Backus G.L ong- wave anisotropy produced by horizontal layering.J Geophys Res,196 2 ,6 6 :4 4 2 7～ 4 4 40
2 Hudson JA,Liu E and Crampin S.Transmission properties of a plane fault.Geophys J Int,1996 ,12 5559～ 56 6
3 Hudson JA,L iu E and Crampin S.The mean transmission properties of a fault with imperfect facialcontact.Geophys J Int,1997,12 9:72 0～ 72 6
4 Hudson JA and Knopoff L.含小尺度包体或裂纹的复合介质总体特性的推测 .吴如山 ,安艺敬一主编 :地震波的散射与衰减 (上 ) ,地震出版社 ,1993,6～ 2 8
5 Schoenberg M and Sayers C.Seismic anisotropy of fractured rock.Geophysics,1995,6 0 :2 0 4～ 2 11
6 Hudson JA.Wave speeds and attenuation of elastic waves in material containing cracks.Geop hys J RoyAstr Soc,1981,6 4 :133～ 150
7 Nishizawa O.Seismic velocity anisotropy in a medium containing orientedcracks:transversely isotropiccase.J Phys Earth,1982 ,30 :331～ 347
8 Stoll R D.Stress- induced anisotropy in sediment acoustics.J Acoust Soc Am,1989,85:70 2～ 70 8
9 Yoshioka N.Elastic behavior of contacting surfaces under normal loads,a computer simulation usingthree- dimensional surface topographies.J Geophys Res,1994 ,99
10 White JE.Underground sounding— Application of seismic waves,Elsevier,1983
11 L iu E,Crampin S and Hudson JA.Diffraction of seismic waves by cracks with application to hydraulicfracturing.Geophysics,1997,6 2 :2 53～ 2 6 5
12 Groenenboom Jand Fokkema JT.Monitoring the width of hydraulic fractures with acoustic waves.Geo-physics,1998,6 3:139～ 148
13 L iu E et al.The effective elastic compliance of fractured rock.Exp anded Abstract6 6 th Ann Int SEGMeeting ,1996 ,1882～ 1885
14 Backus G.L ong- wave anisotropy produced by horizontal layering.J Geophys Res,196 2 ,6 6 :4 4 2 7～ 4 4 40