正交介质方位傅里叶反射系数及裂缝密度预测
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摘要
利用傅里叶级数展开法,对正交介质裂缝参数进行预测。当地层中发育着两组相互垂直的高角度裂缝时,可以近似地将其等效为正交各向异性介质。从线性滑移理论出发,将裂缝视为旋转对称的平行柔性面,引入无量纲参数法向弱度和切向弱度,通过忽略高阶项,可以推导得到纵波方位反射系数的傅里叶级数表示形式;进一步结合有缝隙介质的Hudson模型,推导得到反射系数傅里叶级数项与两个正交方向裂缝密度之间的关系,并由此计算得到不同方向的裂缝密度。模型试算结果表明,正交介质的傅里叶级数反射系数公式能够准确地描述正交裂缝的方位各向异性特征,由该方法进行裂缝密度预测,其结果是可靠的。
Azimuthal Fourier coefficients are utilized to predict fracture parameters for orthotropic media. If there are orthogonal fractures in purely isotropic layer, the fractured medium can be described as orthorhombic. Based on the Schoenberg's linear slip theory, two dimensionless quantities, normal and tangential weaknesses, are introduced, and by ignoring the high order terms, the Fourier series of P-wave azimuthal reflection coefficient formula for the orthorhombic model was derived from general reflection coefficients for weakly anisotropic elastic media.Furthermore, combining with Hudson's fracture model, the relationship between the Fourier coefficients and fracture density is presented, and the fracture densities in different directions can then be calculated. The model tests show that the azimuthal Fourier coefficients can well describe the azimuthal anisotropy of the orthogonal fractured medium, and the prediction results of fracture density in different directions are accurate and reliable.
Azimuthal Fourier coefficients are utilized to predict fracture parameters for orthotropic media. If there are orthogonal fractures in purely isotropic layer, the fractured medium can be described as orthorhombic. Based on the Schoenberg's linear slip theory, two dimensionless quantities, normal and tangential weaknesses, are introduced, and by ignoring the high order terms, the Fourier series of P-wave azimuthal reflection coefficient formula for the orthorhombic model was derived from general reflection coefficients for weakly anisotropic elastic media.Furthermore, combining with Hudson's fracture model, the relationship between the Fourier coefficients and fracture density is presented, and the fracture densities in different directions can then be calculated. The model tests show that the azimuthal Fourier coefficients can well describe the azimuthal anisotropy of the orthogonal fractured medium, and the prediction results of fracture density in different directions are accurate and reliable.
引文
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[10] SCHOENBERG M,SAYERS C M.Seismic anisotropy of fractured rock[J].Geophysics,1995,60(1):204-211.
[11] GRECHKA V,BAKULIN A,TSVANKIN I.Seismic characterization of vertical fractures described as general linear-slip interfaces[J].Geophysical Prospecting,2003,51(2):117-130.
[12] BAKULIN A,TSVANKIN I,GRECHKA V.Estimation of fracture parameters from reflection seismic data—part I:HTI model due to a single fracture set[J].Geophysics,2000,65(6):1788-1802.
[13] BAKULIN A,TSVANKIN I,GRECHKA V.Estimation of fracture parameters from reflection seismic data—part II:fractured models with orthorhombic symmetry[J].Geophysics,2000,65(6):1818-1830.
[14] BAKULIN A,TSVANKIN I,GRECHKA V.Estimation of fracture parameters from reflection seismic data—part III:fractured models with monoclinic symmetry[J].Geophysics,1999,65(6):1818-1830.
[15] HSU C J,SCHOENBERG M.Elastic waves through a simulated fractured medium[J].Geophysics,1993,58(7):964.
[16] P?ENCíK I,MARTINS J L.Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media[J].Studia Geophysica et Geodaetica,2001,45(2):176-199.
[2] SCHOENBERG M.Elastic wave behavior across linear slip interfaces[J].Journal of the Acoustical Society of America,1980,68(5):1516-1521.
[3] HUDSON J A.Overall properties of cracked solid[J].Mathematical Proceedings of the Cambridge Philosophical Society,1980,88(2):371-384.
[4] HUDSON J A.Wave speeds and attenuation of elastic waves in material containing cracks[J].Geophysical Journal of the Royal Astronomical Society,2010,64(1):133-150.
[5] THOMSEN L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-1966.
[6] RüGER A.P wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry[J].Geophysics,1997,62(3):713-722.
[7] 印兴耀,刘婵娟,王保丽.基于混合遗传算法的叠前随机反演方法[J].中国石油大学学报(自然科学版),2017,41(4):65-70.YIN Xingyao,LIU Chanjuan,WANG Baoli.Pre-stack stochastic inversion based on hybrid genetic algorithm[J].Journal of China University of Petroleum(Edition of Natural Science),2017,41(4):65-70.
[8] 张繁昌,张汛汛,翁斌,等.基于匹配追踪的叠前道集吸收补偿和频散校正[J].中国石油大学学报(自然科学版),2017,41(4):71-77.ZHANG Fanchang,ZHANG Xunxun,WENG Bin,et al.Prestack seismic gather absorption compensation and dispersion correction based on matching pursuit[J].Journal of China University of Petroleum (Edition of Natural Science),2017,41(4):71-77.
[9] DOWNTON J E,ROURE B.Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters[J].Interpretation,2015,3(3):ST9-ST27.
[10] SCHOENBERG M,SAYERS C M.Seismic anisotropy of fractured rock[J].Geophysics,1995,60(1):204-211.
[11] GRECHKA V,BAKULIN A,TSVANKIN I.Seismic characterization of vertical fractures described as general linear-slip interfaces[J].Geophysical Prospecting,2003,51(2):117-130.
[12] BAKULIN A,TSVANKIN I,GRECHKA V.Estimation of fracture parameters from reflection seismic data—part I:HTI model due to a single fracture set[J].Geophysics,2000,65(6):1788-1802.
[13] BAKULIN A,TSVANKIN I,GRECHKA V.Estimation of fracture parameters from reflection seismic data—part II:fractured models with orthorhombic symmetry[J].Geophysics,2000,65(6):1818-1830.
[14] BAKULIN A,TSVANKIN I,GRECHKA V.Estimation of fracture parameters from reflection seismic data—part III:fractured models with monoclinic symmetry[J].Geophysics,1999,65(6):1818-1830.
[15] HSU C J,SCHOENBERG M.Elastic waves through a simulated fractured medium[J].Geophysics,1993,58(7):964.
[16] P?ENCíK I,MARTINS J L.Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media[J].Studia Geophysica et Geodaetica,2001,45(2):176-199.
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