基于双曲Radon变换表面多次波衰减方法研究
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摘要
根据地震资料共中心点道集（CMP道集）同相轴经由部分动校正（NMO）后，多次波剩余时差同相轴更接近双曲线形式。本文给出了时不变双曲Radon变换表面多次波衰减的原理和方法。
表面多次波是一种能量很强的相干干扰，在海洋地震勘探中，这种问题尤为突出。首先，文中介绍了多次波衰减方法大致可分为两大类：基于波动方程预测的衰减方法（预测减去法）和利用地震波时距曲线特征的滤波衰减法（简称滤波法），然后简要介绍了两种多次波衰减方法的研究现状和发展，并着重介绍了几种Radon变换方法的理论和公式。
本文所采用的时不变双曲Radon变换表面多次波衰减方法是一种滤波法，并结合波动方程粗略预测，采用GPU/CPU协同并行加速计算技术，提高计算效率。并通过对比分析的方式，分别对几种Radon变换方法和基于波动方程理论的反馈迭代法进行了试算分析，验证了时不变双曲Radon变换表面多次波衰减方法的优点。
本文通过时不变双曲Radon变换表面多次波衰减方法对简单的模拟地震记录和实际地震记录的处理和分析，该方法具有较强的实用性。
Based on the partial normal moveout of CMP gather events, the residualmoveout events is more close to hyperbola. This paper presents the principle andmethod of surface-related multiple attenuation by the time invariant hyperbolic Radontransform.
Surface-related multiple is a kind of coherent noise with strong energy in seismicdata. In marine seismic prospecting, this kind of problem is particularly outstanding.First of all, the paper introduces the multiple attenuation can be roughly divided intotwo categories: prediction and subtraction approach based on the wave theory(prediction attenuation approach) and the filter approach based on the difference innormal moveout (NMO) velocity of the multiple and primary(filter approach), andthen briefly presents the research status and development of two kinds of multipleattenuation, and emphasizes on the theories and formulas on some Radon transform.
Surface-related multiple attenuation by time invariant hyperbolic Radontransform is a kind of filter approach, and this paper combines with the roughprediction of wave equation, using GPU/CPU collaborative parallel computing toaccelerate the technology to improve the computational efficiency. Throughcomparative analysis of several Radon transform and feedback iterative method basedon the theory of wave equation, verified the advantages of the time invarianthyperbolic Radon transform surface multiple attenuation method.
In this paper, according to the processing and analysis for the simple analogseismic records and practical seismic records using the time invariant hyperbolicRadon transform surface-related multiple attenuation method, this method has verystrong practicability.
表面多次波是一种能量很强的相干干扰，在海洋地震勘探中，这种问题尤为突出。首先，文中介绍了多次波衰减方法大致可分为两大类：基于波动方程预测的衰减方法（预测减去法）和利用地震波时距曲线特征的滤波衰减法（简称滤波法），然后简要介绍了两种多次波衰减方法的研究现状和发展，并着重介绍了几种Radon变换方法的理论和公式。
本文所采用的时不变双曲Radon变换表面多次波衰减方法是一种滤波法，并结合波动方程粗略预测，采用GPU/CPU协同并行加速计算技术，提高计算效率。并通过对比分析的方式，分别对几种Radon变换方法和基于波动方程理论的反馈迭代法进行了试算分析，验证了时不变双曲Radon变换表面多次波衰减方法的优点。
本文通过时不变双曲Radon变换表面多次波衰减方法对简单的模拟地震记录和实际地震记录的处理和分析，该方法具有较强的实用性。
Based on the partial normal moveout of CMP gather events, the residualmoveout events is more close to hyperbola. This paper presents the principle andmethod of surface-related multiple attenuation by the time invariant hyperbolic Radontransform.
Surface-related multiple is a kind of coherent noise with strong energy in seismicdata. In marine seismic prospecting, this kind of problem is particularly outstanding.First of all, the paper introduces the multiple attenuation can be roughly divided intotwo categories: prediction and subtraction approach based on the wave theory(prediction attenuation approach) and the filter approach based on the difference innormal moveout (NMO) velocity of the multiple and primary(filter approach), andthen briefly presents the research status and development of two kinds of multipleattenuation, and emphasizes on the theories and formulas on some Radon transform.
Surface-related multiple attenuation by time invariant hyperbolic Radontransform is a kind of filter approach, and this paper combines with the roughprediction of wave equation, using GPU/CPU collaborative parallel computing toaccelerate the technology to improve the computational efficiency. Throughcomparative analysis of several Radon transform and feedback iterative method basedon the theory of wave equation, verified the advantages of the time invarianthyperbolic Radon transform surface multiple attenuation method.
In this paper, according to the processing and analysis for the simple analogseismic records and practical seismic records using the time invariant hyperbolicRadon transform surface-related multiple attenuation method, this method has verystrong practicability.
引文
[1]刘光鼎．1997．服务经济建设——地球物理的使命．中国地质，(12)：9~11．
[2]刘光鼎，李幼铭，吴永刚．陆相油储地球物理学导论[M]．北京：科学出版社，1998．11~15．
[3]刘光鼎，陈洁．中国海域残留盆地油气勘探潜力分析[J]．地球物理学进展，2005，20(4)：881~888．
[4]胡天跃．多次波问题的研究进展[J]．地球物理学进展，2006，21(3)：888~897．
[5]王汝芬．多次波识别与衰减[J]．勘探地球物理进展，2003，26(5-6)：423~432．
[6]牛滨华，沈操，黄新武．波动方程多次波压制技术的进展[J]．地球物理学进展，2002，17(3)：480~485．
[7] Wiggins J W, Abma R. Using the parabolic Radon transform as a moveout filter[J].52nd Ann. International Mtg., European Assoc. Expl. Geophysics,1990.Abstracts.
[8] Schneider W A, Pince E R, Giles B F. A new data-processing technique formultiple attenuation exploiting differential normal moveout [J]. Geophysics,1965,30:348~362.
[9] Wang Y. Multiple attenuation: coping with the spatial truncation effect in theRadon transform domain [J]. Geophysical Prospecting,2003,51:75~87.
[11] Wang Y. Multiple subtraction using an expanded multichannel matching filter[J]. Geophysics,2003,68:346~354.
[10] Hargreaves N, Cooper N. High-resolution Radon demulitple [J].71st SEGInternational Ann. Mtg., Expanded Abstracts, MS:2~7.
[11] Foster D J. and Mosher C C. Suppression of multiple reflections using theRadon transform [J]. Geophysics,1992,57(3):386~395.
[12] Kabir M M N, Marfurt K J. Toward true amplitude multiple removal [J]. TheLeading Edge,1999,18:66~73.
[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]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.
[15] Taner M T. Long period sea-floor multiples and their suppression [J].Geophysical Prospecting,1980,8:30~48.
[16]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．
[17]王维红，首皓，刘洪，孙兆海．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．
[18]洪菲，胡天跃．用优化聚束域滤波方法消除低信噪比地震资料中的多次波[J]．地球物理学报，2004，47(6)：1106~1110．
[19] Alam A, Austin J. Suppression of multiples using slant stacks [J].51st Ann.International. Mtg., Soc. of Expl. Geophys., Expanded Abstracts,1981.
[20] Hampson D. Inverse velocity stacking for multiple elimination [J]. Journal ofthe Canadian Society of Exploration Geophysicists,1986,22:44~55.
[21]朱生旺，魏修成，李锋，等．用抛物Radon变换稀疏解分离和压制多次波[J]．石油地球物理勘探，2002，37(2)：110~115．
[22] Backus, M M. Water reverberations: their nature and elimination [J].Geophysics,1959,24,233~261.
[23] Peacock K L, Treital S. Predictive deconvolution theory and practice [J].Geophysics,1969,34:155~169
[24] Robinson E A, Treitel S. Geophysical signal analysis [M]. Englewood Cliffs:Prentice-Hall, Inc.,1980,238~250.
[25] Berry hill J R, Kim Y C. Deep-water peg-legs and multiples: simulation andsuppression [J]. Geophysics,1986,51:2177~2184.
[26] Wiggins J W. Attenuation of complex water-bottom multiples by wave equationbased prediction and subtraction [J]. Geophysics,1988,53:1527~1539.
[27] Carvalho P M, Weglein A B, Stolt R H. Non-linear inverse scattering formultiple attenuation: Applications to real data, Part I [J]. Society of ExplorationGeophysicists International Exposition and62nd Annual Meeting,1992,1093~1095.
[28] Araujo F V, Weglein A B, Carvalho P M, Stolt R H. Inverse scattering series formultiple attenuation: an example with surface and internal multiples [J]. Societyof Exploration Geophysicists International Exposition and64th Annual Meeting,1994,1039~1041.
[29] Weglein A B, Gasparotto F A, Carvalho P M, Stolt R H. An inverse scatteringseries method for attenuating multiples in seismic reflection data [J].Geophysics,1997,62,1975~1989.
[30] Verschuur D J, Berkhout A J, Kelamis P G. Estimation of multiple scattering byiterative inversion, part II: Examples on marine and land data [J].65th Ann.International. Mtg: Soc.of Expl. Geophysics,1995,1470~1473.
[31] Verschuur D J, Berkhout A J. Estimation of multiple scattering by iterative inversion, part2: practical aspects and examples [J]. Geophysics,1997,62:1596~1611.
[32] Verschuur D J, Berkhout A J, Matson K H, Weglein A B, Young C Y. Comparingthe interface and point scatter methods for attenuating internal multiples: a studywith synthetic data Part I [J]. Society of Exploration Geophysicist InternationalExposition and68th Annual Meeting,1998,1519~1522.
[33]李学聪．表面多次波衰减方法与应用研究[D]．北京：中国科学院地质与地球物理研究所，2009．11~22．
[34] Riley D C, Claerbout J F.2D multiple reflections [J]. Geophysics,1976,41(4):592~620.
[35] Morley L. Predictive deconvolution in shot-receiver space [J]. Geophysics,1983,48(5):515~531.
[36] Verschuur D J. Seismic multiple removal techniques. Past, present and future
[M]. HOUSTEN: EAEG Publications,2006,16~18.
[37] Verschuur D J, Berkhout A J, and Wapenarr P A. Adaptive surface-relatedmultiple elimination [J]. Geophysics,1992,57(9):1166~1177.
[38] Berkhout A J, Verschuur D J. Estimation of multiple scattering by iterative inversion [J]. Geophysics,1997,62(5):1586~1611.
[39] Dragoset W H, Jericevic Z. Some remarks on surface multiples attenuation [J].Geophysics,1998,63(2):772~789.
[40] Wapenaar C P A, Herrmann P, Verschuur D J, etal. Decomposition ofmulti-component seismic data into primary P-wave and S-wave responses [J].Geophysical Prospecting,1990,38:633~661.
[41]牛滨华，沈操，黄新武，等．波动方程压制多次波的技术方法[J]．地学前缘，2002，9（2）：511~517．
[42] Borselen R G V, Schonewille M A, Hegge R F.3D surface-related multipleelimination: Acquisition and processing solutions [J]. The Leading Edge,2005,March:260~268.
[43] Pica A, Poulain G, David B, etal.3D surface-related multiple modeling. Theleading edge,2005, March:292~296.
[44] Kelamis P G, Verschuur D J. Surface-related multiple elimination on landseismic data-Strategies via case studies [J]. Geophysics,2000,65(3):719~734.
[45] Wang Y. Multiple prediction through inversion: a fully data driven concept forsurface-related multiple attenuation [J]. Geophysics,2004,69(2):547~553.
[46] Wang Y. Multiple prediction through inversion: Theoretical advancements andreal data application [J]. Geophysics,2007,72(2): V33~V39.
[47] Van Groenestjin G J A, Verschuur D J. Estimation primaries by sparse inversionnear-offset reconstruction: Marine data applications [J]. Geophysics,2009a,74(6): R119~R128.
[48] Van Groenestjin G J A, Verschuur D J. Estimation of primaries and near-offsetreconstruction by sparse inversion: Marine data applications [J]. Geophysics,2009b,74(6): R119~R128.
[49] Berkhout A J, Verschuur D J. Seismic processing in the inverse data space [J].Geophysics,2006,71(4):29~33.
[50] Carvalho P M, Weglein A B and Stolt R H. Examples of a nonlinear inversionmethod based on the T matrix of scattering theory: application on multiplesuppression [J].61st Ann. International. Mtg., Soc. of Expl. Geophys.,Expanded Abstracts,1991,1319~1322.
[51]金德刚，常旭，刘伊克．逆散射级数法预测层间多次波的算法改进及其策略[J]．地球物理学报，2008，51(4)：1209~1217．
[52] Dragoset B, Verschuur E, Moore L and Bisley R. A perspective on3Dsurface-related multiple elimination [J]. Geophysics,2010,75(5):245~261.
[53] Zhou B, Stewart G. Multiple suppression by2D filtering in the parabolic domain:a wave equation based method [J]. Geophysical Prospecting,1996,44:375~401.
[54] Landa E, Belfer I, Keydar S. Multiple attenuation in the parabolic domain usingwave front characters of multiple generating primaries [J]. Geophysics,64:1806~1815.
[55] Sava P, Guitton A. Multiple attenuation in the image space [J]. Geophysics,2005,70:10~20.
[56]王维红．叠前地震数据重建和多次波衰减：加权和结合多次波预测的Radon变换方法[D]．北京：中国科学院地质与地球物理研究所，2005，46~54．
[57] Dedem E, Verschuur D J.3D surface multiple prediction using sparse inversion[J].71st Annual International Meeting, SEG, Expanded Abstracts,2001,1285~1288.
[58]吴律，武克奋，孙力．τ-p变换方法及其在地震资料处理中的应用[J]．石油物探，1986，25(1)：37~52．
[59]王维红，崔宝文．双曲Radon变换法多次波衰减[J]．新疆石油地质，2007，28(3)：363~365．
[60]赵秀莲，陈茂根，等．SRME技术在澳大利亚Timer Sea地区的应用[J]．海洋石油，2009，48(5)：48~52．
[61]田继强，胡天跃．反馈迭代法在自由表面多次波压制中的应用[J]．石油物探，2008，47(5)：449~454．
[2]刘光鼎，李幼铭，吴永刚．陆相油储地球物理学导论[M]．北京：科学出版社，1998．11~15．
[3]刘光鼎，陈洁．中国海域残留盆地油气勘探潜力分析[J]．地球物理学进展，2005，20(4)：881~888．
[4]胡天跃．多次波问题的研究进展[J]．地球物理学进展，2006，21(3)：888~897．
[5]王汝芬．多次波识别与衰减[J]．勘探地球物理进展，2003，26(5-6)：423~432．
[6]牛滨华，沈操，黄新武．波动方程多次波压制技术的进展[J]．地球物理学进展，2002，17(3)：480~485．
[7] Wiggins J W, Abma R. Using the parabolic Radon transform as a moveout filter[J].52nd Ann. International Mtg., European Assoc. Expl. Geophysics,1990.Abstracts.
[8] Schneider W A, Pince E R, Giles B F. A new data-processing technique formultiple attenuation exploiting differential normal moveout [J]. Geophysics,1965,30:348~362.
[9] Wang Y. Multiple attenuation: coping with the spatial truncation effect in theRadon transform domain [J]. Geophysical Prospecting,2003,51:75~87.
[11] Wang Y. Multiple subtraction using an expanded multichannel matching filter[J]. Geophysics,2003,68:346~354.
[10] Hargreaves N, Cooper N. High-resolution Radon demulitple [J].71st SEGInternational Ann. Mtg., Expanded Abstracts, MS:2~7.
[11] Foster D J. and Mosher C C. Suppression of multiple reflections using theRadon transform [J]. Geophysics,1992,57(3):386~395.
[12] Kabir M M N, Marfurt K J. Toward true amplitude multiple removal [J]. TheLeading Edge,1999,18:66~73.
[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]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.
[15] Taner M T. Long period sea-floor multiples and their suppression [J].Geophysical Prospecting,1980,8:30~48.
[16]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．
[17]王维红，首皓，刘洪，孙兆海．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．
[18]洪菲，胡天跃．用优化聚束域滤波方法消除低信噪比地震资料中的多次波[J]．地球物理学报，2004，47(6)：1106~1110．
[19] Alam A, Austin J. Suppression of multiples using slant stacks [J].51st Ann.International. Mtg., Soc. of Expl. Geophys., Expanded Abstracts,1981.
[20] Hampson D. Inverse velocity stacking for multiple elimination [J]. Journal ofthe Canadian Society of Exploration Geophysicists,1986,22:44~55.
[21]朱生旺，魏修成，李锋，等．用抛物Radon变换稀疏解分离和压制多次波[J]．石油地球物理勘探，2002，37(2)：110~115．
[22] Backus, M M. Water reverberations: their nature and elimination [J].Geophysics,1959,24,233~261.
[23] Peacock K L, Treital S. Predictive deconvolution theory and practice [J].Geophysics,1969,34:155~169
[24] Robinson E A, Treitel S. Geophysical signal analysis [M]. Englewood Cliffs:Prentice-Hall, Inc.,1980,238~250.
[25] Berry hill J R, Kim Y C. Deep-water peg-legs and multiples: simulation andsuppression [J]. Geophysics,1986,51:2177~2184.
[26] Wiggins J W. Attenuation of complex water-bottom multiples by wave equationbased prediction and subtraction [J]. Geophysics,1988,53:1527~1539.
[27] Carvalho P M, Weglein A B, Stolt R H. Non-linear inverse scattering formultiple attenuation: Applications to real data, Part I [J]. Society of ExplorationGeophysicists International Exposition and62nd Annual Meeting,1992,1093~1095.
[28] Araujo F V, Weglein A B, Carvalho P M, Stolt R H. Inverse scattering series formultiple attenuation: an example with surface and internal multiples [J]. Societyof Exploration Geophysicists International Exposition and64th Annual Meeting,1994,1039~1041.
[29] Weglein A B, Gasparotto F A, Carvalho P M, Stolt R H. An inverse scatteringseries method for attenuating multiples in seismic reflection data [J].Geophysics,1997,62,1975~1989.
[30] Verschuur D J, Berkhout A J, Kelamis P G. Estimation of multiple scattering byiterative inversion, part II: Examples on marine and land data [J].65th Ann.International. Mtg: Soc.of Expl. Geophysics,1995,1470~1473.
[31] Verschuur D J, Berkhout A J. Estimation of multiple scattering by iterative inversion, part2: practical aspects and examples [J]. Geophysics,1997,62:1596~1611.
[32] Verschuur D J, Berkhout A J, Matson K H, Weglein A B, Young C Y. Comparingthe interface and point scatter methods for attenuating internal multiples: a studywith synthetic data Part I [J]. Society of Exploration Geophysicist InternationalExposition and68th Annual Meeting,1998,1519~1522.
[33]李学聪．表面多次波衰减方法与应用研究[D]．北京：中国科学院地质与地球物理研究所，2009．11~22．
[34] Riley D C, Claerbout J F.2D multiple reflections [J]. Geophysics,1976,41(4):592~620.
[35] Morley L. Predictive deconvolution in shot-receiver space [J]. Geophysics,1983,48(5):515~531.
[36] Verschuur D J. Seismic multiple removal techniques. Past, present and future
[M]. HOUSTEN: EAEG Publications,2006,16~18.
[37] Verschuur D J, Berkhout A J, and Wapenarr P A. Adaptive surface-relatedmultiple elimination [J]. Geophysics,1992,57(9):1166~1177.
[38] Berkhout A J, Verschuur D J. Estimation of multiple scattering by iterative inversion [J]. Geophysics,1997,62(5):1586~1611.
[39] Dragoset W H, Jericevic Z. Some remarks on surface multiples attenuation [J].Geophysics,1998,63(2):772~789.
[40] Wapenaar C P A, Herrmann P, Verschuur D J, etal. Decomposition ofmulti-component seismic data into primary P-wave and S-wave responses [J].Geophysical Prospecting,1990,38:633~661.
[41]牛滨华，沈操，黄新武，等．波动方程压制多次波的技术方法[J]．地学前缘，2002，9（2）：511~517．
[42] Borselen R G V, Schonewille M A, Hegge R F.3D surface-related multipleelimination: Acquisition and processing solutions [J]. The Leading Edge,2005,March:260~268.
[43] Pica A, Poulain G, David B, etal.3D surface-related multiple modeling. Theleading edge,2005, March:292~296.
[44] Kelamis P G, Verschuur D J. Surface-related multiple elimination on landseismic data-Strategies via case studies [J]. Geophysics,2000,65(3):719~734.
[45] Wang Y. Multiple prediction through inversion: a fully data driven concept forsurface-related multiple attenuation [J]. Geophysics,2004,69(2):547~553.
[46] Wang Y. Multiple prediction through inversion: Theoretical advancements andreal data application [J]. Geophysics,2007,72(2): V33~V39.
[47] Van Groenestjin G J A, Verschuur D J. Estimation primaries by sparse inversionnear-offset reconstruction: Marine data applications [J]. Geophysics,2009a,74(6): R119~R128.
[48] Van Groenestjin G J A, Verschuur D J. Estimation of primaries and near-offsetreconstruction by sparse inversion: Marine data applications [J]. Geophysics,2009b,74(6): R119~R128.
[49] Berkhout A J, Verschuur D J. Seismic processing in the inverse data space [J].Geophysics,2006,71(4):29~33.
[50] Carvalho P M, Weglein A B and Stolt R H. Examples of a nonlinear inversionmethod based on the T matrix of scattering theory: application on multiplesuppression [J].61st Ann. International. Mtg., Soc. of Expl. Geophys.,Expanded Abstracts,1991,1319~1322.
[51]金德刚，常旭，刘伊克．逆散射级数法预测层间多次波的算法改进及其策略[J]．地球物理学报，2008，51(4)：1209~1217．
[52] Dragoset B, Verschuur E, Moore L and Bisley R. A perspective on3Dsurface-related multiple elimination [J]. Geophysics,2010,75(5):245~261.
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