基于F-K偏移和反偏移的地震道插值方法研究
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摘要
野外采集的地震数据经常存在空道或者坏道的情况,为了满足地震数据处理精度的要求,就必须首先进行插值.本文提出了一种新的地震数据插值方法:F-K偏移和反偏移插值法,该方法是通过F-K偏移和反偏移的串联使用来实现的.与其他的插值方法相比,这种插值方法的优点在于计算速度快,没有经过近似处理,精度高.F-K偏移/反偏移能够实现道插值的原理和Kirchhoff偏移/反偏移插值方法类似,也是由于数据是有限带宽的原因引起的.通过对模型的试算,可以看到F-K偏移和反偏移插值方法有着比较好的插值效果,是一种高效、准确、可行的方法.
It should be performed to interpolate missing seismic traces in order to meet the requirement of processing precision because seismic data acquired in the field often have missing traces or bad traces.This paper presents a new interpolation method for seismic data called F-K migration and demigration interpolation that is achieved by cascading F-K migration and demigration.Comparing with other interpolation methods,the virtue of this method lies in higher computation speed,no approximate processing and high precision.The principle of F-K migration and demigration interpolation resembles Kirchhoff migration and demigration interpolation,that is also because of band-limited data.It can be seen that F-K migration and demigration interpolation has good interpolation result and is highly efficient, precise,and feasible as shown by calculations on model data.
It should be performed to interpolate missing seismic traces in order to meet the requirement of processing precision because seismic data acquired in the field often have missing traces or bad traces.This paper presents a new interpolation method for seismic data called F-K migration and demigration interpolation that is achieved by cascading F-K migration and demigration.Comparing with other interpolation methods,the virtue of this method lies in higher computation speed,no approximate processing and high precision.The principle of F-K migration and demigration interpolation resembles Kirchhoff migration and demigration interpolation,that is also because of band-limited data.It can be seen that F-K migration and demigration interpolation has good interpolation result and is highly efficient, precise,and feasible as shown by calculations on model data.
引文
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[9] Hubral P,Schleicher J,Tygel M.A unified approach to 3D seismic reflection imaging,PART Ⅰ:Basic Concepts[J].Geophysics,1996,61(3) :742～758．
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[15] Bleistein N.Cohen J and Jaramillo H.True-amplitude transformation to zero offset of data from curved reflectors.Geophysics,1999,64:112～129,
[16] Herman H.Jaramillo and Norman Bleistein.The link of Kirchhoff migration and demigration to Kirchhoff and Born modeling.Geophysics,1999,64(6) :1793～1805．
[17] Matthias R,Alexander G,Thomas H.Cascaded seismic migration and demigration:SEG 2000 Expanded Abstracts.
[18] Santos L T,Schleicher J,Tygel M,Hubral P.Seismic modeling,migration,and demigration:The Leading Edge,2000,19,scheduled for July.
[19] Santos L T,Schleicher J,Martin T,Peter H.Seismic modeling by demigration[J].Geophysics,2000,65(4) :1281 ～1289．
[20] Christoph J,Thomas H,Peter H.The Unified approach and its applications:wave-equation based trace interpolation:SEG Intl Exposition and 72nd Annual Meeting,2002．
[21] Robert I B,Swavek M D.Demigration to zero offset:SEG 1995 Expanded Abstracts.
[22] Seongbok L,Shu Schung L,Sonny L,John W,Using 3D kirchhoff time demigration as part of a cost effective depth migration Process:SEG Int'l Exposition and 74th Annual Meeting,2004．
[23] 孙建国.Kirchhoff型真振幅偏移与反偏移[J].勘探地球物理进展,2002,6(6) :1～5． Sun J G.Kirchhofftype true-amplitude migration and demigration[J].Progress in Exploration Geophysics,2002,6(6) :1～5．
[24] 孙建国.均匀介质中的F-K反偏移:基本概念、基本公式及其在非均匀介质中的应用[J].吉林大学学学报(地球科学版), 2008,38(1) :135～143． Sun J G.F-K demigration in media with constant velocity: basic concepts,formulas,and applications in inhomogeneous media.Journal of Jilin University Earth Science Edition,2008,38 (1) :135～143．
[25] 杨锴,王毓玮,王华忠,冯闯.基于偏移/反偏移的地震数据映射方法[J].石油地球物理勘探,2008,43(1) :7～16． Yang K,Wang Y W,Wang H Z.Seismic data mapping based migration and demigration[J].Oil Geophysical Prospecting,2008,43 (1) :7 ～ 16．
[26] 贺振华,王才经,何樵登,等.反射地震资料偏移处理与反演方法[M].重庆:重庆大学出版社,1989．
[27] Claerbout J F.Imaging the earth's interior[M].Beijing:Petroleum Industry Press,1991．
[28] Yilmaz O.Seismic data processing[J].Society of Exploration Geophysics,1987．
[2] 常旭,刘伊克,杜向东,李绪宣.深水崎岖海底地震数据成像方法与应用[J].地球物理学报,2008,51(1) :228～234． Chang X,Liu Y K,Du X D,Li X X.Seismic imaging under the irregular deep water bottom[J].Chinese J.Geophys (in Chinese),2008,51(1) :228～234．
[3] Liu Y K,Sun H S,Chang X.Least-squares wave path migration[J].Geophysical Prospecting,2005,53:811～816．
[4] 吕小林, 刘洪.波动方程深度偏移波场延拓算子的快速重建[J].地球物理学进展,2005,20(1) :24～28． Lu X L,Liu H.Fast reconstruction of wave-field propagator in wave-equation depth migration[J].Progress Geophysics,2005,20(1) :24～28．
[5] 刘 洪,王秀闽,曾锐,李幼铭,勾永峰.单程波算子积分解的象征表示[J].地球物理学进展,2007,22(2) :463～471． Liu H,Wang X M,Zeng R,Li Y M,Gou Y F.Symbol description to integral solution of one-way wave operator[J].Progress Geophysics,2007,22 (2) :463 ～471．
[6] 贾晓峰,胡天 跃,王润秋.无单元法用于地震波波动方程模拟与成像[J].地球物理学进展,2006,20(1) :11～17． Jia X F,Hu T Y,Wang R Q.Wave equation modeling and imaging by using element-free method[J].Progress Geophysics,2006,20 (1) :11～17．
[7] 张剑锋,卢宝坤,刘礼农.波动方程深度偏移的频率相关变步长延拓方法[J].地球物理学报,2008,51(1) :221～227． Zhang J F,Lu B K,Liu L N.Frequency2dependent varying2step depth extrapolation scheme for wave equation basedmigration[J].Chinese J.Geophys,2008,51(1) :221～ 227．
[8] 刘洪,袁江华,陈景波,等.大步长波场深度延拓的理论[J].地球物理学报,2006,49(6) :1779～1793． Liu H,Yuan J H,Chen J B,et al.Theory of large step wavefield depth extrapolation[J].Chinese J.Geophys.,2006,49(6) :1779～1793．
[9] Hubral P,Schleicher J,Tygel M.A unified approach to 3D seismic reflection imaging,PART Ⅰ:Basic Concepts[J].Geophysics,1996,61(3) :742～758．
[10] Tygel M,Schleicher J,Hubral P.A unified approach to 3D seismic reflection imaging,PART Ⅱ:Theory[J].Geophysics,1996,61(3) :759～775．
[11] W hitcombe D N.Fast and accurate model building using demigration and single-step ray-trace migration:1991,61st Ann.Internat.Mtg.,Soc.Expl.Geophys[J].Expanded Abstracts,1175～1178．
[12] WhitcombeD N.Fast model building using demigration and single-step ray migration[J].Geophysics,1994,59(3) :439 ～449．
[13] Feber R G.Migration to multiple offsets and velocity analysis[J].Geophysical Prospecting,1994,42(2) :99～112．
[14] 陈必远,金胜汶,马在田.反偏移法波动方程正演[J].石油地球物理勘探,1994,29(1) :23～29． Cheng B Y,Jin S W,Ma Z T.3-D wave equation forward modeling by inverse migration[J].Oil Geophysical Prospecting,1994,29(1) :23～29．
[15] Bleistein N.Cohen J and Jaramillo H.True-amplitude transformation to zero offset of data from curved reflectors.Geophysics,1999,64:112～129,
[16] Herman H.Jaramillo and Norman Bleistein.The link of Kirchhoff migration and demigration to Kirchhoff and Born modeling.Geophysics,1999,64(6) :1793～1805．
[17] Matthias R,Alexander G,Thomas H.Cascaded seismic migration and demigration:SEG 2000 Expanded Abstracts.
[18] Santos L T,Schleicher J,Tygel M,Hubral P.Seismic modeling,migration,and demigration:The Leading Edge,2000,19,scheduled for July.
[19] Santos L T,Schleicher J,Martin T,Peter H.Seismic modeling by demigration[J].Geophysics,2000,65(4) :1281 ～1289．
[20] Christoph J,Thomas H,Peter H.The Unified approach and its applications:wave-equation based trace interpolation:SEG Intl Exposition and 72nd Annual Meeting,2002．
[21] Robert I B,Swavek M D.Demigration to zero offset:SEG 1995 Expanded Abstracts.
[22] Seongbok L,Shu Schung L,Sonny L,John W,Using 3D kirchhoff time demigration as part of a cost effective depth migration Process:SEG Int'l Exposition and 74th Annual Meeting,2004．
[23] 孙建国.Kirchhoff型真振幅偏移与反偏移[J].勘探地球物理进展,2002,6(6) :1～5． Sun J G.Kirchhofftype true-amplitude migration and demigration[J].Progress in Exploration Geophysics,2002,6(6) :1～5．
[24] 孙建国.均匀介质中的F-K反偏移:基本概念、基本公式及其在非均匀介质中的应用[J].吉林大学学学报(地球科学版), 2008,38(1) :135～143． Sun J G.F-K demigration in media with constant velocity: basic concepts,formulas,and applications in inhomogeneous media.Journal of Jilin University Earth Science Edition,2008,38 (1) :135～143．
[25] 杨锴,王毓玮,王华忠,冯闯.基于偏移/反偏移的地震数据映射方法[J].石油地球物理勘探,2008,43(1) :7～16． Yang K,Wang Y W,Wang H Z.Seismic data mapping based migration and demigration[J].Oil Geophysical Prospecting,2008,43 (1) :7 ～ 16．
[26] 贺振华,王才经,何樵登,等.反射地震资料偏移处理与反演方法[M].重庆:重庆大学出版社,1989．
[27] Claerbout J F.Imaging the earth's interior[M].Beijing:Petroleum Industry Press,1991．
[28] Yilmaz O.Seismic data processing[J].Society of Exploration Geophysics,1987．
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