基于双曲Radon变换的混采地震数据重建
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摘要
采用多级中值滤波分离混采数据,可以很好地保持单炮的有效信息;对分离后的单炮数据,采用双曲Radon变换进行地震数据道重建,可以在Radon域获得极高的分辨率从而准确地重建地震数据。单炮道重建时,通过稀疏约束控制Radon变换来提高地震数据的重建精度。双曲Radon变换计算耗时较长,在算子求解时,本文采用快速迭代收缩阈值算法(FISTA),明显加快收敛速度,提高计算效率。模拟数据和实际数据表明,采用多级中值滤波和双曲Radon变换的方法重建混采地震数据可以获得较高的重建精度。
The effective information of single shot record can be kept well by multilevel median filter in blended data separation. The seismic data track reconstruction of separated single shot seismic data can be done by hyperbolic Radon transform,which can get a high resolution in Radon region and improve the accuracy of reconstruction. The reconstruction accuracy of seismic data can be improved by using sparsity-constraint Radon transform in the single shot reconstruction. Hyperbolic Radon transform takes large amount of calculation time. During the operator solving,FISTA algorithm is used to speed up the rate of convergence and improve the calculation efficiency.The results of simulated data and real data demonstrate that the reconstruction of blended data by using multilevel median filter and hyperbolic Radon transform can achieve high reconstruction accuracy.
The effective information of single shot record can be kept well by multilevel median filter in blended data separation. The seismic data track reconstruction of separated single shot seismic data can be done by hyperbolic Radon transform,which can get a high resolution in Radon region and improve the accuracy of reconstruction. The reconstruction accuracy of seismic data can be improved by using sparsity-constraint Radon transform in the single shot reconstruction. Hyperbolic Radon transform takes large amount of calculation time. During the operator solving,FISTA algorithm is used to speed up the rate of convergence and improve the calculation efficiency.The results of simulated data and real data demonstrate that the reconstruction of blended data by using multilevel median filter and hyperbolic Radon transform can achieve high reconstruction accuracy.
引文
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[18]孙成禹,尚新民,石翠翠,等.影响地震数据相位特征的因素分析[J].石油物探,2011,50(5):444-454.SUN Cheng-yu,SHANG Xin-min,SHI Cui-cui,et al.Analysis of influence factors on phase characteristics of seismic seismic data[J]. Geophysical Prospecting for Petroleum,2011,50(5):444-454.
[19]刘法启,张关泉.借助广义Radon变换进行方位角校正[J].石油物探,1996,35(4):43-51.LIU Fa-qi, ZHANG Guan-quan. Azimuth correction with the aid of generalized Radon transform[J]. Geophysical Prospecting for Petroleum,1996,35(4):43-51.
[20]张军华,吕宁,雷凌,等.抛物线拉冬变换消除多次波的应用要素分析[J].石油地球物理勘探.2004,39(4):398-405.ZHANG Jun-hua,LYU Ning,LEI Ling,et al. Analysis of application factors in multiple attenuation by parabolic Radon transform[J]. Oil Geophysical Prospecting,2004,39(4):398-405.
[21] Beck A,Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences,2009,2:183-202.
[22] Yang K C,Jiang Y,Zhao Y J,et al. Deblending using normal moveout and median filtering in common-midpoint gathers[C]//76th EAGE Conference and Exhibition. Expanded Abstracts,2014.
[23] Claudio B,Mark D,Ian M. The acquisition and processing of dithered slip-sweep vibroseis data[J]. Geophysical Prospecting,2012(4):618-639.
[24]龙云,韩立国,邓武斌,等.自适应加权改进窗口中值滤波[J].世界地质,2013,32(2):396-402.LONG Yun,HAN Li-guo,DENG Wu-bin,et al. Adaptive weighted improved window median filtering[J].Global Geology,2013,32(2):396-402.
[25]张保卫. Radon变换及其在地震数据处理中的应用:硕士学位论文[D].西安:长安大学,2007.ZHANG Bao-wei. Radon transform and its application in seismic data processing:master's degree thesis[D].Xi'an:Chang'an University,2007.
[26] Nurul Kabir M M,Verschuur D. Restoration of missing offsets by parabolic Radon transform[J]. Geophysical Prospecting,1995,43(3):347-368.
[27]熊登,赵伟,张剑锋.混合域高分辨率抛物Radon变换及在衰减多次波中的应用[J].地球物理学报,2009,52(4):1068-1077.XIONG Deng,ZHAO Wei,ZHANG Jian-feng. Hybriddomain high-resolution parabolic Radon transform and its application to demultiple[J]. Chinese Journal of Geophysics,2009,52(4):1068-1077.
[28]王立歆,李强,姬小兵,等.用Radon变换法消除沙丘鸣震的应用及效果分析[J].石油物探,2002,41(1):89-91.WANG Li-xin,LI Qiang,JI Xiao-bing,et al. Application of Radon transform to elimination of dune ringing and its effect analysis[J]. Geophysical Prospecting for Petroleum,2002,41(1):89-91.
[29] Trad D,Ulrych T,Sacchi M. Latest views of the sparse Radon transform[J]. Geophysics,2003,68(1):386-399.
[30]邢慧婷,刘财,李炳秀,等.双曲Radon变换参数分析[J].世界地质,2017,36(2):579-587.XING Hui-ting,LIU Cai,LI Bing-xiu,et al. Analysis of parameters in hyperbolic Radon transform[J]. Global Geology,2017,36(2):579-587.
[2]黄新武,吴律,牛滨华.基于抛物线拉东变换的地震道重构[J].中国矿业大学学报,2003,32(5):534-539.HUANG Xin-wu,WU Lyu,NIU Bin-hua. Reconstruction of seismic trace by parabolic Radon transform[J]. Journal of China University of Mining&Technology,2003,32(5):534-539.
[3]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.LI Yuan-qin. A non-linear Radon transform and non-zero offset VSP wave field separation[J]. Geophysical Prospecting for Petroleum,1994,33(3):33-39.
[4]曾有良,乐友喜,单启铜,等.基于高分辨率Radon变换的VSP波场分离方法[J].石油物探,2007,46(2):115-119.ZENG You-liang,LE You-xi,SHAN Qi-tong,et al. VSP wave filed separation based high resolution Radon transform[J]. Geophysical Prospecting for Petroleum,2007,46(2):115-119.
[5] Silverman D. Method of three dimensional seismic prospecting[P]. U. S. Patent,4159463,1979.
[6] Beasley C J,Chambers R E,Jiang Z. A new look at simultaneous sources[C]//68th SEG Technical Program Expanded Abstracts,1998,17(1):133-135.
[7] Beasley C J. A new look at marine simultaneous sources[J]. The Leading Edge,2008,27(7):914-917.
[8] Beasley C J. Simultaneous sources:a technology whose time has come[C]//78th SEG Annual Meeting. Society of Exploration Geophysicists. 2008.
[9] Bagaini C. Overview of simultaneous vibroseis acquisition methods[C]//76th SEG Annual Meeting. Society of Exploration Geophysicists. 2006.
[10]刘财,王典,刘洋,等.二维多级中值滤波技术在随机噪声消除中的应用初探[J].石油地球物理勘探,2005(2):163-167.LIU Cai,WANG Dian,LIU Yang,et al. Application of two-dimensional multistage median filtering in random noise elimination[J]. Oil Geophysical Prospecting,2005(2):163-167.
[11] Huo S,Luo Y,Kelamis P G. Simultaneous sources separation via multidirectional vector-median filtering[J].Geophysics,2012,77(4):V123-V131.
[12]张良,韩立国,许德鑫,等.基于压缩感知技术的Shearlet变换重建地震数据[J].石油地球物理勘探. 2017,52(2):220-225.ZHANG Liang,HAN Li-guo,XU De-xin,et al. Shearlet transform reconstruction of seismic data based on compressed sensing technology[J]. Oil Geophysical Prospecting,2017,52(2):220-225.
[13] Hampson D. Inverse velocity stacking for multiple elimination[J]. Journal of the Canadian Society of Exploration Geophysicists,1986,22(1):44-55.
[14] Kabir M M N,Verschuur D J. Restoration of missing offsets by parabolic Radon transform[J]. Geophysical Prospecting,1995,43(3):347-368.
[15] Sacchi M,Ulrych. High-resolution velocity gathers and offset space reconstruction[J]. Geophysics,1995,60(4):1169-1177.
[16]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,2007,50(3):851-859.WANG Wei-hong,PEI Jiang-yun,ZHANG Jian-feng.Prestack seismic data reconstruction using weighted parabolic Radon transform[J]. Chinese Journal of Geophysics,2007,50(3):851-859.
[17]张红梅,刘洪.基于稀疏离散τ-p变换的非均匀地震道重建[J].石油物探,2006,45(2):141-145.ZHANG Hong-mei, LIU Hong. Sparseness discretetransform in irregular seismic trace reconstruction[J].Geophysical Prospecting for Petroleum,2006,45(2):141-145.
[18]孙成禹,尚新民,石翠翠,等.影响地震数据相位特征的因素分析[J].石油物探,2011,50(5):444-454.SUN Cheng-yu,SHANG Xin-min,SHI Cui-cui,et al.Analysis of influence factors on phase characteristics of seismic seismic data[J]. Geophysical Prospecting for Petroleum,2011,50(5):444-454.
[19]刘法启,张关泉.借助广义Radon变换进行方位角校正[J].石油物探,1996,35(4):43-51.LIU Fa-qi, ZHANG Guan-quan. Azimuth correction with the aid of generalized Radon transform[J]. Geophysical Prospecting for Petroleum,1996,35(4):43-51.
[20]张军华,吕宁,雷凌,等.抛物线拉冬变换消除多次波的应用要素分析[J].石油地球物理勘探.2004,39(4):398-405.ZHANG Jun-hua,LYU Ning,LEI Ling,et al. Analysis of application factors in multiple attenuation by parabolic Radon transform[J]. Oil Geophysical Prospecting,2004,39(4):398-405.
[21] Beck A,Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences,2009,2:183-202.
[22] Yang K C,Jiang Y,Zhao Y J,et al. Deblending using normal moveout and median filtering in common-midpoint gathers[C]//76th EAGE Conference and Exhibition. Expanded Abstracts,2014.
[23] Claudio B,Mark D,Ian M. The acquisition and processing of dithered slip-sweep vibroseis data[J]. Geophysical Prospecting,2012(4):618-639.
[24]龙云,韩立国,邓武斌,等.自适应加权改进窗口中值滤波[J].世界地质,2013,32(2):396-402.LONG Yun,HAN Li-guo,DENG Wu-bin,et al. Adaptive weighted improved window median filtering[J].Global Geology,2013,32(2):396-402.
[25]张保卫. Radon变换及其在地震数据处理中的应用:硕士学位论文[D].西安:长安大学,2007.ZHANG Bao-wei. Radon transform and its application in seismic data processing:master's degree thesis[D].Xi'an:Chang'an University,2007.
[26] Nurul Kabir M M,Verschuur D. Restoration of missing offsets by parabolic Radon transform[J]. Geophysical Prospecting,1995,43(3):347-368.
[27]熊登,赵伟,张剑锋.混合域高分辨率抛物Radon变换及在衰减多次波中的应用[J].地球物理学报,2009,52(4):1068-1077.XIONG Deng,ZHAO Wei,ZHANG Jian-feng. Hybriddomain high-resolution parabolic Radon transform and its application to demultiple[J]. Chinese Journal of Geophysics,2009,52(4):1068-1077.
[28]王立歆,李强,姬小兵,等.用Radon变换法消除沙丘鸣震的应用及效果分析[J].石油物探,2002,41(1):89-91.WANG Li-xin,LI Qiang,JI Xiao-bing,et al. Application of Radon transform to elimination of dune ringing and its effect analysis[J]. Geophysical Prospecting for Petroleum,2002,41(1):89-91.
[29] Trad D,Ulrych T,Sacchi M. Latest views of the sparse Radon transform[J]. Geophysics,2003,68(1):386-399.
[30]邢慧婷,刘财,李炳秀,等.双曲Radon变换参数分析[J].世界地质,2017,36(2):579-587.XING Hui-ting,LIU Cai,LI Bing-xiu,et al. Analysis of parameters in hyperbolic Radon transform[J]. Global Geology,2017,36(2):579-587.