弹性波衍射CT
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摘要
本文直接从等价于弹性动力学Navier方程的耦合齐次与非齐次矢量波动方程组出发，围绕弹性波衍射CT展开了理论研究。尤其是其非齐次方程合有震源项，同时适合P波和S波，考虑爆炸震源，引进塑性半径，运用张量运算，推导了Born近似下散射波港与目标函数的关系。得到二种数据采集方式下的层析成像FBP公式，可同时适用于P波和S波，尽管与以往不涉及震源项的结果相似，但本结果更符合地震勘探情况。
Starting directly from the coupled homogeneous and inhomogeneous vecter wave equations which are equivalent to Navier cquation of elastodynamics ,we have made a theoretical study of elastic watre diffraction tomography, espccially, when the inhomogeneous equation contains a source term and is accordingly applicable to both P-waves and S-waves. Considering explosive source is used, we introduce the concept plastic radius. And along with the tensor operation, we cstablish the relationship between sccatering spectrum and objective function under Born approximation. In addition, tomography FBT formulae are derived for two kinds of data acqpisition geometries. Although the results are similar to those obtaind in the absence of source term, they are more reasonable in seismic survey.
Starting directly from the coupled homogeneous and inhomogeneous vecter wave equations which are equivalent to Navier cquation of elastodynamics ,we have made a theoretical study of elastic watre diffraction tomography, espccially, when the inhomogeneous equation contains a source term and is accordingly applicable to both P-waves and S-waves. Considering explosive source is used, we introduce the concept plastic radius. And along with the tensor operation, we cstablish the relationship between sccatering spectrum and objective function under Born approximation. In addition, tomography FBT formulae are derived for two kinds of data acqpisition geometries. Although the results are similar to those obtaind in the absence of source term, they are more reasonable in seismic survey.
引文
[1] K. T. Ladas, and A. J. Devaney, Gencralized ART algorithm for diffraction tomography, lnverseProblems 7,P109~ 121, 1991
[2] K. T. Ladas, and A. J. Dcvaney, Application of an ART algorithm in an experimental study ofultrasonic diffraction tomography,Ultrasonic Imaging 15,P48~ 58, 1993
[3] A. J, Devaney,and D. X. zhang,Gcophysical diffraction tomography in a laycred background,WaveMotion 14,243~265, 1991
[4]R. G. Pratt and N. R, Goulty,Combining wavc-equation imaging with traveltime tomography toform high-resolution imagcs from crosshole data,Gcophguics,Vol. 56,No. 2,P208~ 224, 1991
[5]Y. luo and G. T. Schuster,Wave equation travel time invcrsion,Geophysics,Vol. 56,No. 5,P645~653, 1991
[6]A. Tarantola, 1987, Inverse problem t heory,In: Methods for data fitting and parameter estimation,Elscvier Science- Publishers
[7]P. R. Mora, Nonlincar two-dimensional elastic invcrsion of multioffset seismic data, Geophysics,52,No. 3,P1211 ~ 1228, 1987
[8]S. Diao,Study on seismic diffraction tomography and seismic wave scattcring,Ph. D. Thesis,ChinaUniv. of Geosciences (Beijing ), 1993
[9]S. X. Pan and A. C. Kak, 1993, A computational study of rcconstruction algorithms for diffractiontomography: interpolat ion versus fi1tercd back propagation, IEEE,ASSP - 31,P 1262~ 1275
[10]R. S. Wu and M. N. Tokoz,Difftaction tomography and mu1tisource holography applied to scismicimaging, Geophysics, 52, No- 1, P 11 ~ 25
[11]Y. Xu and S. Diao,The application of plasticity in scismic diffraction tomography,The Pro. ofAsia-Pacific Samp. On Advances in Eng. plasticity and its Application,Hong Kong, 1992,P801~814
[2] K. T. Ladas, and A. J. Dcvaney, Application of an ART algorithm in an experimental study ofultrasonic diffraction tomography,Ultrasonic Imaging 15,P48~ 58, 1993
[3] A. J, Devaney,and D. X. zhang,Gcophysical diffraction tomography in a laycred background,WaveMotion 14,243~265, 1991
[4]R. G. Pratt and N. R, Goulty,Combining wavc-equation imaging with traveltime tomography toform high-resolution imagcs from crosshole data,Gcophguics,Vol. 56,No. 2,P208~ 224, 1991
[5]Y. luo and G. T. Schuster,Wave equation travel time invcrsion,Geophysics,Vol. 56,No. 5,P645~653, 1991
[6]A. Tarantola, 1987, Inverse problem t heory,In: Methods for data fitting and parameter estimation,Elscvier Science- Publishers
[7]P. R. Mora, Nonlincar two-dimensional elastic invcrsion of multioffset seismic data, Geophysics,52,No. 3,P1211 ~ 1228, 1987
[8]S. Diao,Study on seismic diffraction tomography and seismic wave scattcring,Ph. D. Thesis,ChinaUniv. of Geosciences (Beijing ), 1993
[9]S. X. Pan and A. C. Kak, 1993, A computational study of rcconstruction algorithms for diffractiontomography: interpolat ion versus fi1tercd back propagation, IEEE,ASSP - 31,P 1262~ 1275
[10]R. S. Wu and M. N. Tokoz,Difftaction tomography and mu1tisource holography applied to scismicimaging, Geophysics, 52, No- 1, P 11 ~ 25
[11]Y. Xu and S. Diao,The application of plasticity in scismic diffraction tomography,The Pro. ofAsia-Pacific Samp. On Advances in Eng. plasticity and its Application,Hong Kong, 1992,P801~814
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