裂缝及介质非均匀散射
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摘要
为配合地球物理衍射CT的研究，本文对几何非均匀（尤指裂缝）引起的散射及介质非均匀（尤指弹性系数摄动）所产生的散射场，运用弹性动力学得到了解析式与数值结果。裂纹散射场可用裂纹张开位移COD与Green应力张量的褶积表示。其远场特性的研究在油气勘探中对预测裂隙位置、方向及大小均有重要意义。
To play a supporting role in the research on geophysical diffraction tomography we have analytically formulated the scattered field caused by inhomogeneity either in geometry of media(esp the cracks) or in property of media (e. g. the purturbation of clastic parameters) based on the principle of elastodynamics and a set of numerical solutions is thus obtained. The scattered field caused by a crack can be expressed in terms of the convolution of crack opening displacement (COD) with Green stress tensor. The study on its far field fcatures is of significance to the prediction for the position, orientation, and size of a crack.
To play a supporting role in the research on geophysical diffraction tomography we have analytically formulated the scattered field caused by inhomogeneity either in geometry of media(esp the cracks) or in property of media (e. g. the purturbation of clastic parameters) based on the principle of elastodynamics and a set of numerical solutions is thus obtained. The scattered field caused by a crack can be expressed in terms of the convolution of crack opening displacement (COD) with Green stress tensor. The study on its far field fcatures is of significance to the prediction for the position, orientation, and size of a crack.
引文
[1] 刁顺、杨慧珠、许云.弹性波衍射CT,石油物探,1994年第3期。
[2] K. Sezawa, Scattering of elastic waves and some allied problems, Bull. Earthquake Res. Inst.Tokyo Univ., 1927.
[3] L. Knopoff, Scattering of compressional waves by spherical obstacles, Geophysics, 1959, Vol.24, 30- 39.
[4] J. W. Miles, Scattering of clastic waves by small inhomogeneities, Geophysics, 1960, Vol. 25,642- 648.
[5] J. A. Hudson,Scattered waves in the coda of P, J. Geophys., 1977,Vol. 43, 359-374.
[6] Y. H. Pao et al., Diffeaction of elastic waves and dynamics stress concentration, Crane andRussak,New York, 1973.
[7] S. Crampin, A review of wave motion in anisotropic and crack elastic -media, Wave Motion,1981,Vol. 3. 343- 391.
[8] S. Itou, Diffraction of an antiplane shear waves by two coplana Griffith cracks in an infiniteelastic medium,Int. J. Solids struc., 1986,Vol. 16,No. 8, 1147- 1159.
[9] D. Gross, Diffraction of SH waves by a system of cracks, Int. J. Solids Struc., 1988, Vol. 24,No. 1, 41 - 53.
[10] C. H. Zhang et al., Scattering by multiple crack configurations,ASME,J. Appl. Mech., 1988,Vol. 55,No. 1, 104- 117.
[11] E. I. Neerhoff, Diffraction of Love waves by a stress-free crack of finitc with the planeinterface of a layered composite,Appl. Sci. Res., 1979,Vol. 35,No. 2, 237- 250.
[12] A. Bostrom, Elastic wave scattering from an interface crack, ASME, J. Appl. Mech. 1987,Vol. 54, 503- 519.
[13] S. Diao,Study on seismie diffraction tomography and seismic wave scattering, Ph. D. Thsis,China Univ. of Geoscienccs (Beijing), 1993.
[14] J. D. Achenback et al.,Ray methods for wavcs in elastic solids,Pitman Publishing Inc., 1982.
[15] R. S. Wu and K. Aki, Elastic wave scattering by a random medium and the small scaleinhomogeneities in the lithosphere,J. Geophys. Res., 1985, 10261～10273.
[16] R. S, Wu and K. Aki (ed),Scattering and attenuation of seismic waves, Birkhauser, Boston,Part Ⅰ - Ⅳ. 1989.
[2] K. Sezawa, Scattering of elastic waves and some allied problems, Bull. Earthquake Res. Inst.Tokyo Univ., 1927.
[3] L. Knopoff, Scattering of compressional waves by spherical obstacles, Geophysics, 1959, Vol.24, 30- 39.
[4] J. W. Miles, Scattering of clastic waves by small inhomogeneities, Geophysics, 1960, Vol. 25,642- 648.
[5] J. A. Hudson,Scattered waves in the coda of P, J. Geophys., 1977,Vol. 43, 359-374.
[6] Y. H. Pao et al., Diffeaction of elastic waves and dynamics stress concentration, Crane andRussak,New York, 1973.
[7] S. Crampin, A review of wave motion in anisotropic and crack elastic -media, Wave Motion,1981,Vol. 3. 343- 391.
[8] S. Itou, Diffraction of an antiplane shear waves by two coplana Griffith cracks in an infiniteelastic medium,Int. J. Solids struc., 1986,Vol. 16,No. 8, 1147- 1159.
[9] D. Gross, Diffraction of SH waves by a system of cracks, Int. J. Solids Struc., 1988, Vol. 24,No. 1, 41 - 53.
[10] C. H. Zhang et al., Scattering by multiple crack configurations,ASME,J. Appl. Mech., 1988,Vol. 55,No. 1, 104- 117.
[11] E. I. Neerhoff, Diffraction of Love waves by a stress-free crack of finitc with the planeinterface of a layered composite,Appl. Sci. Res., 1979,Vol. 35,No. 2, 237- 250.
[12] A. Bostrom, Elastic wave scattering from an interface crack, ASME, J. Appl. Mech. 1987,Vol. 54, 503- 519.
[13] S. Diao,Study on seismie diffraction tomography and seismic wave scattering, Ph. D. Thsis,China Univ. of Geoscienccs (Beijing), 1993.
[14] J. D. Achenback et al.,Ray methods for wavcs in elastic solids,Pitman Publishing Inc., 1982.
[15] R. S. Wu and K. Aki, Elastic wave scattering by a random medium and the small scaleinhomogeneities in the lithosphere,J. Geophys. Res., 1985, 10261～10273.
[16] R. S, Wu and K. Aki (ed),Scattering and attenuation of seismic waves, Birkhauser, Boston,Part Ⅰ - Ⅳ. 1989.
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