逆散射级数法去除自由表面多次波
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摘要
压制多次波是地震资料处理过程中的重要环节之一,多次波去除的效果直接影响到最后成像的质量.本文研究的逆散射级数法以波动方程和Born级数为基础,构造一个与自由表面多次波相关的子序列来预测并消除多次波,该方法不需要知道地下的速度结构信息,适用于各种复杂的地下情况.在逆散射级数法的实现过程中,地震子波和近道波场是必不可少的信息,本文采用能量最低法则和带限抛物Radon变换法来弥补原始地震资料中所缺失的这些信息.合成资料和实际地震资料的处理结果表明,逆散射级数法能够在去除自由表面多次波的同时保留有效波的信息,对于地下复杂结构的情况同样有效.
Multiple removal is a key process in seismic data processing,the effect of multiple elimination directly affects the final imaging.In this paper,inverse scattering series method is based on wave equation and Born series,multiples are predicted and removed by constructing a subseries corresponding to surface-related multiples.This method does not need any subsurface information and is suitable for different kinds of complex structures.However,source wavelet and near offset traces information will be needed for applying this technique.Energyminimizing method and band-limited parabolic Radon transform is employed to meet the above two conditions.The examples of a synthetic data study and a marine data show that the free-surface multiple can be well attenuated in both prestack gathers and seismic section by implementation with inverse scattering series method.
Multiple removal is a key process in seismic data processing,the effect of multiple elimination directly affects the final imaging.In this paper,inverse scattering series method is based on wave equation and Born series,multiples are predicted and removed by constructing a subseries corresponding to surface-related multiples.This method does not need any subsurface information and is suitable for different kinds of complex structures.However,source wavelet and near offset traces information will be needed for applying this technique.Energyminimizing method and band-limited parabolic Radon transform is employed to meet the above two conditions.The examples of a synthetic data study and a marine data show that the free-surface multiple can be well attenuated in both prestack gathers and seismic section by implementation with inverse scattering series method.
引文
[1] Cohen J K,Bleistein N.Velociity inversion procedure for acoustic waves.Geophysics,1979,44(6) :1077～1087
[2] Bleistein N,Cohen J K,Hagin F G.Computional and asymptotic of velocity inversion.Geophysics,1982,47 (11) :1497～1511
[3] Moses H E.Calculation of scattering potential from reflection coefficients.Phys.Rev.,1956,102:559～567
[4] Prosser R T.Formal solutions of inverse scattering problems.Math.Phys.,1969,10:1819～1822
[5] Stolt R H,Jacobs B.Inversion of seismic data in a laterally heterogeneous medium.SEP Rep.,1980,24:135～152
[6] Weglein A B,Gray S H.The sensitivity of Born inversion to the choice of reference velocity:A simple example.Geophysics,1983,48:36～38
[7] Weglein A B,Gasparotto F A.An inverse scattering series method for attenuating multiples in seismic reflection data.Geophysics,1997,62:1975～1989
[8] Carvalho P M,Weglein A B.Examples of a nonlinear inversion method based on the T matrix of scattering theory:application to multiple suppression.SEG Technical Program Expanded Abstracts,1991,10:1319～1321
[9] Weglein A B,Araujo F V,Carvalho P M,et al.Inverse scattering series and seismic exploration.Inverse Problems,2003,19:R23～R83
[10] Ikelle L T.Using even terms of the scattering series for deghosting and multiple attenuation of ocean bottom cable data.Geophysics,1999,64(2) :579～592
[11] 谢干权,李建华.解三维方程逆散射势问题的新特征迭代 法.中国科学(A辑),1 988,17(4) :359～656 Xie G Q,Li J H.The singular solution of 3 D wave equation.Science in China,Ser.A (in Chinese),1988,17 (4) :359～656
[12] 黄联捷,杨文采.参考波速线性变化时声波方程逆散射反演.地球物理学报,199l,34(1) :89～98 Huang L J,Yang W C.Inversion of the acoustic wave equation by inverse scattering in a medium of linear reference velocity.Chinese J.Geophys.(in Chinese),1991,34(1) :89～98
[13] 杨文采.地震波场反演的BG-逆散射方法.地球物理学报,1995,38(3) :358～366 Yang W C.BG-inverse scattering method for inversion of seismic wavefield.ChineseJ.Geophys.(in Chinese),1995,38(3) :358～366
[14] 刘洪,袁江华,勾永峰等.地震逆散射波场和算子的谱分解.地球物理学报,2007,50(1) :240～247 Liu H,Yuan J H,Gou Y F,et al.Spectral factorization of wavefield and operator in seismic inverse scattering.Chinese J.Geophys.(in Chinese),2007,50(1) :240～247
[15] 丁科,宋守根,谢忠球.逆散射理论的发展及应用前景.地球物理学进展,2005,20(3) :661～666 Ding K,Song S G,Xie Z Q.Development and future application of inverse scattering theory.Progress in Geophysics (in Chinese),2005,20(3) :661～666
[16] 范承亮,丁科,张建贵等.逆散射成像的算法.中南工业大学学报,2001,32(4) :331～335 Fan C L,Ding K,Zhang J G,et al.Algorithm on inverse scattering imaging.Journal of Central South University of Technology (in Chinese),2001,32(4) :331～335
[17] 金德刚,常旭,刘伊克等.逆散射级数法预测层间多次波的算法改进及其策略.地球物理学报,2008,51(4) :1209～121 7 Jin D G,Chang X,Liu Y K.Algorithm improvement and strategy of internal multiples prediction based on inverse scattering series method.Chinese J.Geophys.(in Chinese),2008,51(4) :1209～1217
[18] 金德刚,常旭,刘伊克.逆子波域消除多次波方法研究.地球物理学报,2008,51(1) :250～259 Jin D G,Chang X,Liu Y K.Research of multiple elimination method in inverse wavelet domain.Chinese J.Geophys.(in Chinese),2008,51(1) :250～259
[19] 刘伊克,常旭,卢孟夏等.波路径偏移压制层间多次波的理论与应用.地球物理学报,2008,51(2) :589～595 Liu Y K,Chang X,Lu M X,et al.Internal multiple removal and its application by wavepath migration.Chinese J.Geophys.(in Chinese),2008,51(2) :589～595
[20] 刘伊克,Sun Hongchuan,常 旭.基于波射线路径偏移压制多次波.地球物理学报,2004,47:697～701 Liu Y K,Sun H C,Chang X.Multiple removal by wavepath migration.Chinese J.Geophys.(in Chinese),2004,47:697～701
[21] Verschuur D J,Berkhout A J,Wapenaar C P A.Adaptive surface-related multiple elimination.Geophysics,1992,57 (9) :1166～1177
[22] 牛滨华,沈 操,黄新武.波动方程多次波压制技术的进展.地球物理学进展,2002,17(3) :480～485 Niu B H,Shen C,Huang X W.Progress in multiple attenuation techniques based on wave equation.Progress in Geophysics (in Chinese),2002,17(4) :480～485
[23] 沈操.基于波动方程的自由界面多次波压制[博士论文].北京:中国地质大学(北京),2002 Shen C.Surface-related multiple attenuation based on wave equation [Ph.D.thesis](in Chinese).Beijing:China University of Geosciences (Beijing),2002
[24] Kabir M M,Verschuur D J.Restoration of missing offsets by parabolic Radon transform.Geophysical Prospecting,1995,43:347～368
[25] 王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建.地球物理学报,2007,50(3) :851～859 Wang W H,Pei J Y,Zhang J F.Prestack seismic data reconstruction using weighted parabolic Radon transform.Chinese J.Geophys.(in Chinese),2007,50(3) :851～859
[26] Taylor J R.Scattering Theory.New York:John Wiley&Sons,Inc.,1972
[27] Verschuur D J.Surface-related multiple elimination,an inversion approach [Ph.D.thesis].Delft University of Technology,1991
[2] Bleistein N,Cohen J K,Hagin F G.Computional and asymptotic of velocity inversion.Geophysics,1982,47 (11) :1497～1511
[3] Moses H E.Calculation of scattering potential from reflection coefficients.Phys.Rev.,1956,102:559～567
[4] Prosser R T.Formal solutions of inverse scattering problems.Math.Phys.,1969,10:1819～1822
[5] Stolt R H,Jacobs B.Inversion of seismic data in a laterally heterogeneous medium.SEP Rep.,1980,24:135～152
[6] Weglein A B,Gray S H.The sensitivity of Born inversion to the choice of reference velocity:A simple example.Geophysics,1983,48:36～38
[7] Weglein A B,Gasparotto F A.An inverse scattering series method for attenuating multiples in seismic reflection data.Geophysics,1997,62:1975～1989
[8] Carvalho P M,Weglein A B.Examples of a nonlinear inversion method based on the T matrix of scattering theory:application to multiple suppression.SEG Technical Program Expanded Abstracts,1991,10:1319～1321
[9] Weglein A B,Araujo F V,Carvalho P M,et al.Inverse scattering series and seismic exploration.Inverse Problems,2003,19:R23～R83
[10] Ikelle L T.Using even terms of the scattering series for deghosting and multiple attenuation of ocean bottom cable data.Geophysics,1999,64(2) :579～592
[11] 谢干权,李建华.解三维方程逆散射势问题的新特征迭代 法.中国科学(A辑),1 988,17(4) :359～656 Xie G Q,Li J H.The singular solution of 3 D wave equation.Science in China,Ser.A (in Chinese),1988,17 (4) :359～656
[12] 黄联捷,杨文采.参考波速线性变化时声波方程逆散射反演.地球物理学报,199l,34(1) :89～98 Huang L J,Yang W C.Inversion of the acoustic wave equation by inverse scattering in a medium of linear reference velocity.Chinese J.Geophys.(in Chinese),1991,34(1) :89～98
[13] 杨文采.地震波场反演的BG-逆散射方法.地球物理学报,1995,38(3) :358～366 Yang W C.BG-inverse scattering method for inversion of seismic wavefield.ChineseJ.Geophys.(in Chinese),1995,38(3) :358～366
[14] 刘洪,袁江华,勾永峰等.地震逆散射波场和算子的谱分解.地球物理学报,2007,50(1) :240～247 Liu H,Yuan J H,Gou Y F,et al.Spectral factorization of wavefield and operator in seismic inverse scattering.Chinese J.Geophys.(in Chinese),2007,50(1) :240～247
[15] 丁科,宋守根,谢忠球.逆散射理论的发展及应用前景.地球物理学进展,2005,20(3) :661～666 Ding K,Song S G,Xie Z Q.Development and future application of inverse scattering theory.Progress in Geophysics (in Chinese),2005,20(3) :661～666
[16] 范承亮,丁科,张建贵等.逆散射成像的算法.中南工业大学学报,2001,32(4) :331～335 Fan C L,Ding K,Zhang J G,et al.Algorithm on inverse scattering imaging.Journal of Central South University of Technology (in Chinese),2001,32(4) :331～335
[17] 金德刚,常旭,刘伊克等.逆散射级数法预测层间多次波的算法改进及其策略.地球物理学报,2008,51(4) :1209～121 7 Jin D G,Chang X,Liu Y K.Algorithm improvement and strategy of internal multiples prediction based on inverse scattering series method.Chinese J.Geophys.(in Chinese),2008,51(4) :1209～1217
[18] 金德刚,常旭,刘伊克.逆子波域消除多次波方法研究.地球物理学报,2008,51(1) :250～259 Jin D G,Chang X,Liu Y K.Research of multiple elimination method in inverse wavelet domain.Chinese J.Geophys.(in Chinese),2008,51(1) :250～259
[19] 刘伊克,常旭,卢孟夏等.波路径偏移压制层间多次波的理论与应用.地球物理学报,2008,51(2) :589～595 Liu Y K,Chang X,Lu M X,et al.Internal multiple removal and its application by wavepath migration.Chinese J.Geophys.(in Chinese),2008,51(2) :589～595
[20] 刘伊克,Sun Hongchuan,常 旭.基于波射线路径偏移压制多次波.地球物理学报,2004,47:697～701 Liu Y K,Sun H C,Chang X.Multiple removal by wavepath migration.Chinese J.Geophys.(in Chinese),2004,47:697～701
[21] Verschuur D J,Berkhout A J,Wapenaar C P A.Adaptive surface-related multiple elimination.Geophysics,1992,57 (9) :1166～1177
[22] 牛滨华,沈 操,黄新武.波动方程多次波压制技术的进展.地球物理学进展,2002,17(3) :480～485 Niu B H,Shen C,Huang X W.Progress in multiple attenuation techniques based on wave equation.Progress in Geophysics (in Chinese),2002,17(4) :480～485
[23] 沈操.基于波动方程的自由界面多次波压制[博士论文].北京:中国地质大学(北京),2002 Shen C.Surface-related multiple attenuation based on wave equation [Ph.D.thesis](in Chinese).Beijing:China University of Geosciences (Beijing),2002
[24] Kabir M M,Verschuur D J.Restoration of missing offsets by parabolic Radon transform.Geophysical Prospecting,1995,43:347～368
[25] 王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建.地球物理学报,2007,50(3) :851～859 Wang W H,Pei J Y,Zhang J F.Prestack seismic data reconstruction using weighted parabolic Radon transform.Chinese J.Geophys.(in Chinese),2007,50(3) :851～859
[26] Taylor J R.Scattering Theory.New York:John Wiley&Sons,Inc.,1972
[27] Verschuur D J.Surface-related multiple elimination,an inversion approach [Ph.D.thesis].Delft University of Technology,1991
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