用边界元数值模拟验证Hudson裂缝介质理论
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摘要
裂缝介质各向异性的研究对于油气勘探与开发及地下工程建设均有重要意义。边界元法具有输入数据少、精度高等优点。本文依据Hudson裂缝介质模型,建立了纵波在裂缝介质中传播的边界元法数值模型,模拟了裂缝密度、裂缝纵横比以及裂缝填充物对纵波的传播速度和衰减因子的影响,探讨了波长与裂缝特征尺度的关系。结果显示,边界元法可以很好地模拟含裂缝非均匀介质中波的传播问题。波长和裂缝特征尺度的比值是等效介质理论能否成立的一个重要因素,裂缝饱和水后各向异性程度下降,裂缝密度对纵波传播速度及衰减因子有一定的影响。在地震长波长情况下,相同特征尺度的圆形干裂纹比薄的干裂纹对弹性波衰减更有效。
Studying anisotropy of fractural medium has important meaning for oil/gas exploration and development as well as underground engineering construction. The boundary element method is characterized by fewer input data and high precision. Based on Hudson fractural medium model, the paper creates numeric model of boundary element method that the P-wave propagates in fractural medium, simulates the influence of fractural density, aspect and infill on propagation velocity and attenuation factor,and probes the relationship between the wavelength and characteristic fractural scale. The results showed the boundary-element method can better simulate the issue of wave propagating in heterogeneous fracture-bearing medium. The wavelength-to-characteristic fractural scale ratio is an important factor whether the equivalent medium theory is correct or not, the anisotropic degree decreased when the fracture is water saturated, the fractural density has certain influence on P-wave propagation velocity and attenuation factor. Under the circumstance of seismic long wavelength, the circular dry fracture is more effective in attenuation of elastic wave than thin dry fracture when the characteristic scale is same.
Studying anisotropy of fractural medium has important meaning for oil/gas exploration and development as well as underground engineering construction. The boundary element method is characterized by fewer input data and high precision. Based on Hudson fractural medium model, the paper creates numeric model of boundary element method that the P-wave propagates in fractural medium, simulates the influence of fractural density, aspect and infill on propagation velocity and attenuation factor,and probes the relationship between the wavelength and characteristic fractural scale. The results showed the boundary-element method can better simulate the issue of wave propagating in heterogeneous fracture-bearing medium. The wavelength-to-characteristic fractural scale ratio is an important factor whether the equivalent medium theory is correct or not, the anisotropic degree decreased when the fracture is water saturated, the fractural density has certain influence on P-wave propagation velocity and attenuation factor. Under the circumstance of seismic long wavelength, the circular dry fracture is more effective in attenuation of elastic wave than thin dry fracture when the characteristic scale is same.
引文
[1]刘恩儒,曾新吾.裂缝介质的有效弹性常数.石油地球物理勘探,2001,36(1):37~44
[2]郝守玲,赵群.裂缝介质对P波方位各向异性特征的影响.勘探地球物理进展,2004,27(3):189~194
[3]范国章,牟永光.裂缝各向异性介质中纵波速度的变化及其对共中心点道集叠加的影响.石油物探,2002,41(1):49~55
[4]Crampin S.Evidence for aligned cracks in the earth′scrust.First Break,1985,3:12~15
[5]Sayers C M.Stress-induced ultrasonic wave velocity anisotropyinfractured rock.Ultrasonic,1988,26:311~317
[6]韩开锋,尹梓安,曾新吾.间接边界元法模拟含裂缝介质中弹性波的传播.国防科技大学学报,2005,27(3):92~95
[7]Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks.Geophys J Roy Astr Soc,1981,64:133~150
[8]Hudson J A.A higher order approxi mation to the wave propagation constants for cracked solid.Geo-phys J R Astr Soc,1986,87:265~274
[9]何樵登,张中杰.横向各向同性介质中地震波及数值模拟.吉林长春:吉林大学出版社,1996
[10]Pointer Liu E,Hudson J A.Numerical modeling of seismic waves scattered by hydrofractures:application of the indirect boundary element method.Geophys J Int,1998,135:289~303
[11]Kiyoshi Yomogida and Rafael Benites.Scattering of seismic waves by cracks with the boundary integral method.Pure appl geophys,2002,159:1771~1789
[12]Crampin S.Effective anisotropic elastic constants for wave propagation through cracked solids.Geophys J R Astr Soc,1984,76:135~145
[2]郝守玲,赵群.裂缝介质对P波方位各向异性特征的影响.勘探地球物理进展,2004,27(3):189~194
[3]范国章,牟永光.裂缝各向异性介质中纵波速度的变化及其对共中心点道集叠加的影响.石油物探,2002,41(1):49~55
[4]Crampin S.Evidence for aligned cracks in the earth′scrust.First Break,1985,3:12~15
[5]Sayers C M.Stress-induced ultrasonic wave velocity anisotropyinfractured rock.Ultrasonic,1988,26:311~317
[6]韩开锋,尹梓安,曾新吾.间接边界元法模拟含裂缝介质中弹性波的传播.国防科技大学学报,2005,27(3):92~95
[7]Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks.Geophys J Roy Astr Soc,1981,64:133~150
[8]Hudson J A.A higher order approxi mation to the wave propagation constants for cracked solid.Geo-phys J R Astr Soc,1986,87:265~274
[9]何樵登,张中杰.横向各向同性介质中地震波及数值模拟.吉林长春:吉林大学出版社,1996
[10]Pointer Liu E,Hudson J A.Numerical modeling of seismic waves scattered by hydrofractures:application of the indirect boundary element method.Geophys J Int,1998,135:289~303
[11]Kiyoshi Yomogida and Rafael Benites.Scattering of seismic waves by cracks with the boundary integral method.Pure appl geophys,2002,159:1771~1789
[12]Crampin S.Effective anisotropic elastic constants for wave propagation through cracked solids.Geophys J R Astr Soc,1984,76:135~145
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