基于高分辨率Radon变换的VSP波场分离方法
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摘要
讨论了时间域线性Radon变换、频率域最小平方Radon变换和频率域高分辨率Radon变换等方法的基本原理。Radon变换在频率域通常采用最小平方反演的方式来实现,但由于最小平方法对于不同的p值(视慢度)范围采用相同的阻尼因子,得到的解不够精确。高分辨率Radon变换对这一缺陷进行了改进,即通过对不同的p值范围采用不同的加权值来提高解的稀疏性和精确性。具体方法是:在反演迭代过程中,根据前一次迭代的结果,通过Bayes原理将加权矩阵与前一次迭代的结果联系起来,得到新的加权矩阵;然后求解这个加权矩阵方程,得到频率域的稀疏解。设计了一个3层水平地层的地质模型,利用高分辨率Radon变换进行了VSP波场分离。τ-p域的结果表明,能量得到了很好的收敛。在分离出来的上、下行波波场记录上,波形恢复得很好,上、下行波波场的相互干扰被完全消除。
Principles of Radon transformation methods, including linear Radon transform in time domain, least square Radon transformation and high-resolution Radon transformation in frequency domain are discussed. Radon transformation in frequency domain is usually implemented by least square inversion. However, for different values of p (slowness), the least square uses the same dummy factor, making the solution inaccurate. High-resolution Radon transformation can improve the deficiency. Different weights varied with the range of p values are used to enhance the accuracy and sparseness of the solution. In the inversion iterations, according to the previous solution, the weighted matrix is linked to the result of previous iteration by Bayes rule, resulting in a new weighted matrix. Then the sparse solution in frequency domain can be obtained through computing the weighted matrix equation. A three-layer acline geological model was designed so as to carry out the VSP wavefield separation by using high-resolution Radon transformation. The re- suits inτ-p domain show that the energy can be converged well. In the separated up and down wave field record, the waveform is well recovered, with the interference being completely eliminated.
Principles of Radon transformation methods, including linear Radon transform in time domain, least square Radon transformation and high-resolution Radon transformation in frequency domain are discussed. Radon transformation in frequency domain is usually implemented by least square inversion. However, for different values of p (slowness), the least square uses the same dummy factor, making the solution inaccurate. High-resolution Radon transformation can improve the deficiency. Different weights varied with the range of p values are used to enhance the accuracy and sparseness of the solution. In the inversion iterations, according to the previous solution, the weighted matrix is linked to the result of previous iteration by Bayes rule, resulting in a new weighted matrix. Then the sparse solution in frequency domain can be obtained through computing the weighted matrix equation. A three-layer acline geological model was designed so as to carry out the VSP wavefield separation by using high-resolution Radon transformation. The re- suits inτ-p domain show that the energy can be converged well. In the separated up and down wave field record, the waveform is well recovered, with the interference being completely eliminated.
引文
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10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
11王维红,首皓,刘洪等．线性同相轴波场分离的高分辨率τ-p变换法[J]．地球物理学进展,2006,21(1):74～78．
12 Carswell A, Tang R, Dillistone C,et al. A new method of field separation in VSP data processing[J]. Expanded Abstracts of 54th Annual Internat SEG Mtg, 1984,40-42
13 Thorson J R, Claerbout J F. Velocity -stack and slant stack stochastic inversion [J]. Geophysics, 1985, 50 (12):2 727 -2 741
14 Beylkin G. Discrete radon transform[J]. IEEE Trans Acoust, Speech and Signal Processing, 1987, 35 (2): 162-172
15 Kostov C. Toeplitz structure in slant -stack inversion [J]. Expanded Abstracts of 60th Annual Internat SEG Mtg,1990,1 618-1 621
16 Sacchi M,Ulrych T. High-resolution velocity gathers and offset space reconstruction[J]. Geophysics, 1995, 60(4): 1 169~1177
17 Trad DQ,Ulrych T J,Sacchi M D. Accurate interpo- lation with high resolution time -variant Radon trans-forms[J]. Geophysics,2002,67(4) :644~656
18 Sacchi M D, Ulrych T J. Model re -weighted least-squares Radon operators [J]. Expanded Abstracts of 65th Annual Internal SEG Mtg, 1995,616-618
2罗省贤,李录明．F-K域多波变速波场分离[J]．物探化探计算技术,1995,21(2):127～132
3吴律．τ-p变换及应用[M]．北京:石油工业出版社, 1993．110～114
4陈遵德,段天友,朱广生等．SVD滤波方法的改进及应用[J]．石油地球物理勘探,1994,29(6):783～792
5张卫红,陈林,高志凌．垦71井区三维VSP资料波场分离方法应用研究[J]．石油物探,2006,45(5):532～536
6姚忠瑞,何惺华,左建军等．多方位Walk-away VSP处理方法[J]．石油物探,2006,45(4):380～384
7李远钦．一种非线性Radon变换及非零偏移距VSP波场分离[J]．石油物探,1994,33(3):33～39
8许世勇,李彦鹏,马在田等．τ-q变换法波场分离[J]．中国海上油气(地质),1999,13(5):334～337
9孙显义,陈可为,许世勇．采用τ-q变换法进行纵、横波波场分离[J]．大庆石油地质与开发,2002,21(4):76～77
10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
11王维红,首皓,刘洪等．线性同相轴波场分离的高分辨率τ-p变换法[J]．地球物理学进展,2006,21(1):74～78．
12 Carswell A, Tang R, Dillistone C,et al. A new method of field separation in VSP data processing[J]. Expanded Abstracts of 54th Annual Internat SEG Mtg, 1984,40-42
13 Thorson J R, Claerbout J F. Velocity -stack and slant stack stochastic inversion [J]. Geophysics, 1985, 50 (12):2 727 -2 741
14 Beylkin G. Discrete radon transform[J]. IEEE Trans Acoust, Speech and Signal Processing, 1987, 35 (2): 162-172
15 Kostov C. Toeplitz structure in slant -stack inversion [J]. Expanded Abstracts of 60th Annual Internat SEG Mtg,1990,1 618-1 621
16 Sacchi M,Ulrych T. High-resolution velocity gathers and offset space reconstruction[J]. Geophysics, 1995, 60(4): 1 169~1177
17 Trad DQ,Ulrych T J,Sacchi M D. Accurate interpo- lation with high resolution time -variant Radon trans-forms[J]. Geophysics,2002,67(4) :644~656
18 Sacchi M D, Ulrych T J. Model re -weighted least-squares Radon operators [J]. Expanded Abstracts of 65th Annual Internal SEG Mtg, 1995,616-618
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