线性同相轴波场分离的高分辨率τ-p变换法
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摘要
基于最小二乘τ-p变换和τ-p域模型稀疏分布的假设,本文给出高分辨率τ-p变换的推导及其模型空间域的离散采样公式,同时给出了保振幅线性同相轴波场分离的算法流程.在求解本文给出的高分辨率τ-p正变换时,由于待求解的矩阵不具备最小平方法所具有的Toeplitz结构,故采用Cholesky分解法进行计算.本文模拟了井间地震和阵列声波测井中的Stoneley上下行波的分离算法过程,高分辨率正反τ-p变换且滤波所得结果显示本文算法误差小和保振幅的特点.对于在τ-p域距离很近或时间域同相轴近于水平的线性波场,高分辨率算法的聚焦作用使得所分离波场畸变小,体现本文算法精度高的优点.理论模型试算表明本文给出的高分辨率τ-p变换线性波场分离算法具有稳定性、精度高和保振幅的特点.
The formula derivation of high resolution τ-p transform is given in this paper based on the assumption of sparse distribution of model space in linear Radon domain,and also the high fidelity algorithm of the Linear events wavefield separation.Cholesky decomposition algorithm is adopted to solve the high resolution forward τ-p transform because the Toeplitz structure of the 2D matrix in least square method is destroyed.The wavefield separation of up and down-going wave separation is modeled in array sonic logging and the crosswell seismic data.The method presented in this paper has the advantage of small error or high fidelity for the forward τ-p transform.The focusing of high resolution makes the wavefield's distortion smaller when the two events is very closer to each other or when some events are horizontal in x-t domain which the traditional least square method cannot separate them efficiently.Stability,high accuracy and high fidelity of the high resolution τ-p transform are demonstrated by the synthetic linear wavefield examples in this paper.
The formula derivation of high resolution τ-p transform is given in this paper based on the assumption of sparse distribution of model space in linear Radon domain,and also the high fidelity algorithm of the Linear events wavefield separation.Cholesky decomposition algorithm is adopted to solve the high resolution forward τ-p transform because the Toeplitz structure of the 2D matrix in least square method is destroyed.The wavefield separation of up and down-going wave separation is modeled in array sonic logging and the crosswell seismic data.The method presented in this paper has the advantage of small error or high fidelity for the forward τ-p transform.The focusing of high resolution makes the wavefield's distortion smaller when the two events is very closer to each other or when some events are horizontal in x-t domain which the traditional least square method cannot separate them efficiently.Stability,high accuracy and high fidelity of the high resolution τ-p transform are demonstrated by the synthetic linear wavefield examples in this paper.
引文
[1]唐金良,曹辉,王立华,等.中值滤波在井间地震资料处理中的应用[J].石油物探,2005,44(1):47~50.
[2]余春昊,李长文.利用斯通利波信息进行裂缝评价[J].测井技术,1998,22(4):273~277.
[3]Deans S R.The Radon transform and some of its applications[M].New York:John Wiley and Sons Inc,1983.
[4]刘喜武,刘洪,李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用[J].地球物理学进展,2004,19(1):8~15.
[5]周龙泉,刘福田,刘劲松,等.利用τ-p波场反演法确定东沙群岛的地壳速度模型[J].地球物理学进展,2005,20(2):503~506.
[6]黄新武,吴律,宋炜.拉东投影法三维叠前深度偏移[J].地球物理学报,2004,47(2):321~326.
[7]吴律.τ-p变换及应用[M].北京:石油工业出版社.1993.
[8]Schultz P S,Claerbout J F.Velocity estimation and downwardcontinuation by wavefront synthesis[J].Geophysics,1978,43(3):691~714.
[9]Stoffa P L,Buhl P,Dibold J B,et al.Direct mapping of seis-mic data to the domain of intercept time and ray parameter:Aplane wave decomposition[J].Geophysics,1981,46(4):255~267.
[10]Kostov C.Toeplitz structure in slant-stack inversion[J].60th Annual Internat.Mtg.,Soc.Expl.Geophys.,Ex-panded Abstracts,1990,1618~1621.
[11]Hampson D.Inverse velocity stacking for multiple elimina-tion[J].Journal of the Canadian Society of Exploration geo-physicists,1986,22:44~55.
[12]Kabir M M N,Verschuur D J.Restoration of missing offsetsby parabolic Radon Transform[J].Geophys Prosp,1995,43:347~368.
[13]王维红,刘洪.抛物Radon变换法近偏移距波场外推[J].地球物理学进展,2005,20(2):289~293.
[14]Trad D,Ulrych J,Sacchi M.Accurate interpolation withhigh-resolution time-variant Radon transforms[J].Geophys-ics,2002,67(2):644~656.
[15]刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究[J].地球物理学报,2004,47(2):299~305.
[2]余春昊,李长文.利用斯通利波信息进行裂缝评价[J].测井技术,1998,22(4):273~277.
[3]Deans S R.The Radon transform and some of its applications[M].New York:John Wiley and Sons Inc,1983.
[4]刘喜武,刘洪,李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用[J].地球物理学进展,2004,19(1):8~15.
[5]周龙泉,刘福田,刘劲松,等.利用τ-p波场反演法确定东沙群岛的地壳速度模型[J].地球物理学进展,2005,20(2):503~506.
[6]黄新武,吴律,宋炜.拉东投影法三维叠前深度偏移[J].地球物理学报,2004,47(2):321~326.
[7]吴律.τ-p变换及应用[M].北京:石油工业出版社.1993.
[8]Schultz P S,Claerbout J F.Velocity estimation and downwardcontinuation by wavefront synthesis[J].Geophysics,1978,43(3):691~714.
[9]Stoffa P L,Buhl P,Dibold J B,et al.Direct mapping of seis-mic data to the domain of intercept time and ray parameter:Aplane wave decomposition[J].Geophysics,1981,46(4):255~267.
[10]Kostov C.Toeplitz structure in slant-stack inversion[J].60th Annual Internat.Mtg.,Soc.Expl.Geophys.,Ex-panded Abstracts,1990,1618~1621.
[11]Hampson D.Inverse velocity stacking for multiple elimina-tion[J].Journal of the Canadian Society of Exploration geo-physicists,1986,22:44~55.
[12]Kabir M M N,Verschuur D J.Restoration of missing offsetsby parabolic Radon Transform[J].Geophys Prosp,1995,43:347~368.
[13]王维红,刘洪.抛物Radon变换法近偏移距波场外推[J].地球物理学进展,2005,20(2):289~293.
[14]Trad D,Ulrych J,Sacchi M.Accurate interpolation withhigh-resolution time-variant Radon transforms[J].Geophys-ics,2002,67(2):644~656.
[15]刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究[J].地球物理学报,2004,47(2):299~305.
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