单程波动方程偏移算法浅析
|
摘要
本文的研究工作主要有两个方面:分析了传统单程波动方程偏移中,采用不同方法近似相移算子进行偏移,其偏移像场能量变化的特点;在Kirchhoff真振幅理论的基础上,总结性的介绍了真振幅单程波动方程偏移方法,以克服传统单程波动方程偏移成像缺乏波场振幅信息的缺点。
在研究传统单程波动方程偏移算法时,通过对比分析不同近似相移算子相位特点,叠后偏移单位脉冲响应、子波拉伸以及频谱等相关动力学特性。得出由不同近似相移算子计算后的偏移像场能量变化特点。通过在均匀介质条件下的研究,可为生产实践提供方法选择的依据。
在总结学习前人提出的Kirchhoff真振幅理论的基础上,由拟微分算子的象征意义、定理以及单程波动方程组的耦合性,在二维条件下推导出真振幅条件下的上下行波方程组。并总结性的说明了其与全程波动方程具有相同的程函方程和运输方程。说明改造后的单程波动方程组具有保幅特性是真振幅偏移,能够提供更加可靠的地震成像信息。根据二维情况下真振幅单程波动方程组的特点,对传统单程波动方程偏移中的傅立叶有限差分法(FFD)进行改进。
One-way wave equation migration is an extremely effective seismic migration imaging algorithm, with the method of classic Kirchhoff integral migration, it avoid the hypothesis of the asymptotic wave equation. Compared with reverse-time migration, one-way wave equation is efficient, and saves the computer memory space. One-way wave equation migration is mainly about the equation of square root operator (i.e. phase-shift operator), use different methods of singularities, fit differential phase shift operators are approaching, in order to improve the calculation precision of one-way wave equation, and enhance the ability to complex geological conditions. This article is mainly aimed at the method of different transmission shift operator and impulse responses of one-way equation, and analysis a series of related dynamic properties of migration imaging. According to the phase shift operator of one-way wave equation methods, we can divide it into three different methods: the frequency domain (ω-kdomain), time - space domains (t-xdomain) and mixed domains (ω-xdomain). The algorithm ofω-kdomain is simpler, we can directly recursive calculation according to the extrapolating. Extrapolating of t-xdomain algorithm contains 2D convolution computation, we can use FFT to manage in theω-xdomain, only use one convolution. Nowωplays a part of parameter. In theω-xdomain we also use FFT conversion,ω-x domain and t-x domain method is a relatively simple extrapolation, only consider for smooth surface that it is independent on time. Whenω-xfield changes toω-kdomain, although simplified calculation, but lost flexibility, and lateral velocity variation cannot handle. The biggest advantage in theω-xdomain is aimed at that different frequency components can use different effective, in addition, the wavelet is calculated, has a good flexibility and adaptability.
Under the condition of uneven medium, impulse response analysis method, different direction due to the t-xdomain of wave propagation, its velocity different wave field rays not perpendicular to face, including from Persia array of semicircle arc shape closed curve which areas for development, this area was invalid part. Disperse phenomenon is in phase shift operator due to the t-xdomain of solving the approximate expansion. Considering the resolution of the wavelet controlled by three factors, through the comparison between the mixed domain and t-xdomain finite difference method,ω-kdomain has a high resolution of wavelet, but t-xdomain finite difference method of oscillation amplitudes tail in the initial sampling points bigger error, so the mixed domain has an advantage in improving the resolution of wavelet. Through the spectrum analysis, it shows that the one-way wave operators applicationω-kdomain to earthquake has advantages of lighting, but because of the calculation principle , its speed limit is only in the case without change of lateral velocity. Mixed domain operator can reserve energy though relatively weak, but its complex geological conditions for earthquake lighting has good effect. t-xdomain can complex medium environment, and maintain relatively mixed domain method more energy, but this kind of method is limited, only can use in some of the application of geological model said illumination analysis.
By understanding the different algorithms of adaptive, can provide a reference basis for practical production, also provide information for further improved algorithm. Due to the accuracy of the migration imaging decision in actual geological conditions and taking the compensation method is also selected processing method. Under the principle of classical significance on the migration technology can simply to spread effect is relatively wave propagation lag compensation, accurately reflect the phase information, but did not consider wave field amplitude adjustment problems. Aim at one-way wave, geophysicists raise that we can use the theory of true amplitude improving traditional one-way equation method. This paper introduces the theory of one-way wave equation under the algorithms and process improvements based on true amplitude. It sufficiently shows that, true amplitude one-way equation is exact, rotate, and enough to provide more accurate and more meaningful data for seismic exploration.
在研究传统单程波动方程偏移算法时,通过对比分析不同近似相移算子相位特点,叠后偏移单位脉冲响应、子波拉伸以及频谱等相关动力学特性。得出由不同近似相移算子计算后的偏移像场能量变化特点。通过在均匀介质条件下的研究,可为生产实践提供方法选择的依据。
在总结学习前人提出的Kirchhoff真振幅理论的基础上,由拟微分算子的象征意义、定理以及单程波动方程组的耦合性,在二维条件下推导出真振幅条件下的上下行波方程组。并总结性的说明了其与全程波动方程具有相同的程函方程和运输方程。说明改造后的单程波动方程组具有保幅特性是真振幅偏移,能够提供更加可靠的地震成像信息。根据二维情况下真振幅单程波动方程组的特点,对传统单程波动方程偏移中的傅立叶有限差分法(FFD)进行改进。
One-way wave equation migration is an extremely effective seismic migration imaging algorithm, with the method of classic Kirchhoff integral migration, it avoid the hypothesis of the asymptotic wave equation. Compared with reverse-time migration, one-way wave equation is efficient, and saves the computer memory space. One-way wave equation migration is mainly about the equation of square root operator (i.e. phase-shift operator), use different methods of singularities, fit differential phase shift operators are approaching, in order to improve the calculation precision of one-way wave equation, and enhance the ability to complex geological conditions. This article is mainly aimed at the method of different transmission shift operator and impulse responses of one-way equation, and analysis a series of related dynamic properties of migration imaging. According to the phase shift operator of one-way wave equation methods, we can divide it into three different methods: the frequency domain (ω-kdomain), time - space domains (t-xdomain) and mixed domains (ω-xdomain). The algorithm ofω-kdomain is simpler, we can directly recursive calculation according to the extrapolating. Extrapolating of t-xdomain algorithm contains 2D convolution computation, we can use FFT to manage in theω-xdomain, only use one convolution. Nowωplays a part of parameter. In theω-xdomain we also use FFT conversion,ω-x domain and t-x domain method is a relatively simple extrapolation, only consider for smooth surface that it is independent on time. Whenω-xfield changes toω-kdomain, although simplified calculation, but lost flexibility, and lateral velocity variation cannot handle. The biggest advantage in theω-xdomain is aimed at that different frequency components can use different effective, in addition, the wavelet is calculated, has a good flexibility and adaptability.
Under the condition of uneven medium, impulse response analysis method, different direction due to the t-xdomain of wave propagation, its velocity different wave field rays not perpendicular to face, including from Persia array of semicircle arc shape closed curve which areas for development, this area was invalid part. Disperse phenomenon is in phase shift operator due to the t-xdomain of solving the approximate expansion. Considering the resolution of the wavelet controlled by three factors, through the comparison between the mixed domain and t-xdomain finite difference method,ω-kdomain has a high resolution of wavelet, but t-xdomain finite difference method of oscillation amplitudes tail in the initial sampling points bigger error, so the mixed domain has an advantage in improving the resolution of wavelet. Through the spectrum analysis, it shows that the one-way wave operators applicationω-kdomain to earthquake has advantages of lighting, but because of the calculation principle , its speed limit is only in the case without change of lateral velocity. Mixed domain operator can reserve energy though relatively weak, but its complex geological conditions for earthquake lighting has good effect. t-xdomain can complex medium environment, and maintain relatively mixed domain method more energy, but this kind of method is limited, only can use in some of the application of geological model said illumination analysis.
By understanding the different algorithms of adaptive, can provide a reference basis for practical production, also provide information for further improved algorithm. Due to the accuracy of the migration imaging decision in actual geological conditions and taking the compensation method is also selected processing method. Under the principle of classical significance on the migration technology can simply to spread effect is relatively wave propagation lag compensation, accurately reflect the phase information, but did not consider wave field amplitude adjustment problems. Aim at one-way wave, geophysicists raise that we can use the theory of true amplitude improving traditional one-way equation method. This paper introduces the theory of one-way wave equation under the algorithms and process improvements based on true amplitude. It sufficiently shows that, true amplitude one-way equation is exact, rotate, and enough to provide more accurate and more meaningful data for seismic exploration.
引文
[1]张宇.真振幅全倾角单程波动方程偏移方法[J].石油物探,2007,46(6)
[2]刘喜武,刘洪.波动方程地震偏移成像方法的现状与进展[J].地球物理学进展, 2002,17(4):582~591
[3]郑海山.地震偏移技术研究进展[J].世界地质,2000,19(4):392~395.
[4]张关泉.波动方程的上行波和下行波耦合方程组[J].应用数学学报, 1993,16(2):251~263
[5]孙建国.复杂地表条件下地球物理场数值模拟方法评述.[J].世界地质,2007, 26(3):345~362
[6]王雪秋.中国西部复杂地表地震波响应特征研究[D].2009
[7]马在田.高阶方程偏移的分裂算法[J].地球物理学报.1983,26 (4): 377~388
[8]吴如山,金胜汉,谢小碧.广义屏传播子及其在地震波偏移成像方面的应用[J].石油地球物理勘,2001, 36 (6): 655~654
[9]杨辉,刘洪,李幼铭.单程波方程偏移算子高阶辛格式[J].地球物理学报,2003,46: 533~538
[10]李冰,刘洪,李幼铭.波场延拓短算子构造方法[J].地球物理学报,2003, 46(2):246-251
[11]王华忠.最小二乘叠前偏移成像的数学物理含义及在FK域中的一种实现[J].国际地球物理会议(北京).2009.
[12]Sun J. On the limited aperture migration in two dimensions[J]. Geophysics, 1998,63(4):984~994
[13]李振春,朱绪峰,韩文功.真振幅偏移方法综述[J].勘探地球物体进展,2008,31(1):10~15
[14]刘定进,印兴耀.傅立叶有限差分法保幅叠前深度偏移方法[J].地球物理学报, 2007,42(1):11~16
[15]谢立.波场地震成像方法概述和分类[J].石油科技动态,2009,284(6).12~26
[16]A.J.Berkhou著.马在田,张叔伦译.地震偏移波场外推法声波成像[M].北京,石油工业出版社.1983
[17]Claerbout J F.Imaging the earth’s interior[M]. Blackwell Scientific publications, 1985.
[18]马在田.论反射地震偏移成像[J].勘探地球物理进展,2002,3(25)
[19]马在田.地震成像技术有限差分法偏移[M].北京,石油工业出版社,1989
[20]贺振华.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
[21]陈生昌等.地震成像中的Born近似与Rytov近似比较[J].天然气工业,2007,27 (1) :37~40
[22]Gazdag J. Wave-equation migration with the phase-shift method [J]. Geophysics, 1978, 43(7):1342~1351.
[23]Stolt R H. Migration by Fourier transform [J] .Geophysics, 1978, 43(1):23~48.
[24]李振春.地震成像理论与方法[M].北京,石油大学研究生院,2007
[25]陈生昌,曹进忠,马在田.混合域单程波传播算子及其在偏移成像中的应用[J]地球物理学进展,2003,18(2):210~217.
[26]Stoffa P L, Fokkema J T, Luna F , et al .Split-step Fourier migration [J] . Geophysics.1990 ,55(4) :410~421
[27]Ristow D, Ruhl T. Fourier Finite-Difference Migration[J].Geophysics, 1994 ,59(12) :1882~1893
[28]李世雄.波动方程的高频近似与辛几何[M].北京,科学出版社,2001
[29] Berkhout A J. Ware field extrapolation techniques in seismic migration [J]. Geophysics,1981,46(12):1638~1656.
[30]Myung W Lee, Sang Y Suh. Optimization of one-way wave equations[J]. Geophysics,1985,50(10):1634~1637
[31]罗明秋.地震波传播的哈密顿表述及辛几何算法[J].地球物理学报,2001,44 : 120～128
[32]刘军,侯平,魏茂林.地震波动力学参数在砂体预测中的应用[J].世界地质,2002,21(2):185-188
[33]谢忠求.浅层地震探测技术应用中的分辨率问题[J].矿产与地质,1999.
[34]云美厚,丁伟.地震子波频率浅析[J].石油物探,2005,44(5)
[35]皮红梅.双程波动方程数值模拟和照明分析方法研究[D].吉林大学,2009
[36]张宇.振幅保真的单程波方程偏移理论[J].地球物理学报,2006.49(5):1410-1430
[37]Berkhout A J. Seismic migration: Imaging of acoustic energy by wave field extrapolation:Theoretical aspects[M]. America: The Journal of the Acoustical Society of America,1986.1558
[38]Bleistein N. On the imaging of reflectors in the earth[J]. Geophysics, 1988, 53(12):1540~1546
[39]Tygel M.,Schleicher J. and Hubral P.Pulse distortion in depth migration[J]. Geophysics, 1994, 59(10):1561～156
[40]Gray S.True-amplitude seismic migration: A comparison of three approaches[J]. Geophysics, 1997, 62(2): 629~638
[41]孙建国.Kirchhoff型真振幅偏移与反偏移[J].勘探地球物理进展,2002,25(6)
[42]杨红霞等.真振幅地震偏移三种方法的比较[J].石油物探译丛,1998,2
[43]孙建国.论基于波场延拓的真振幅偏移[C].地球物理年会,2002
[44]Yu Zhang. Towards accurate amplitudes for one-way wavefiled extrapolation of 3-D common shot records[J].Geophysics.
[45]ZhangY,Zhang G Q,Norman B. True amplitude wave equation migration arising from true amplitude one-way wave equations [J].Institute Of Physics Publishing, 2003,19(3):1113~1138
[46]齐民友.仿微分算子导论[M].超星阅读电子文献.
[47]Zhang Y,Zhang G, Bleistein N. Theory of true amplitude one-way wave equations and true amplitude common-shot migration [J].Geophysics ,2005 , 70(3)
[48]Yu Zhang. Theory of true amplitude one-way wave equation and true amplitude common-shot migration[J].Geophysics.
[49]Wapenaar. Representation of the seismic sources in one-way wave equations. Geophysics. 1990.55:786~790.
[50]孙建国.成像原理、成像过程及偏移像场的动力学特性[C].中国地球物理年会,2004,59
[51]孙建国.深度偏移中的振幅畸变[C]. CPS/SEG 2004国际地球物理会议2004
[52]朱绪峰.单程波方程的保幅偏移及其角度域成像[D].中国石油大学,2008
[53]Fomel S.Theory of 3-D angle gathers in wave-equation imaging[J]. Expanded Abstracts of 74th Annual Internat SEG Mtg,2004,1053~1056
[54]徐琴,李振春.波动方程偏移中的成像条件研究进展[J].勘探地球物理进展,2008,31(4):1~6
[55]Yu Zhang. True-amplitude common-offset,common-azimuth v(z) migration[J]. Geophysics,2007,72(1):49~58
[56]刘定进.波动方程保幅地震偏移成像方法研究[D].中国石油大学,2007
[2]刘喜武,刘洪.波动方程地震偏移成像方法的现状与进展[J].地球物理学进展, 2002,17(4):582~591
[3]郑海山.地震偏移技术研究进展[J].世界地质,2000,19(4):392~395.
[4]张关泉.波动方程的上行波和下行波耦合方程组[J].应用数学学报, 1993,16(2):251~263
[5]孙建国.复杂地表条件下地球物理场数值模拟方法评述.[J].世界地质,2007, 26(3):345~362
[6]王雪秋.中国西部复杂地表地震波响应特征研究[D].2009
[7]马在田.高阶方程偏移的分裂算法[J].地球物理学报.1983,26 (4): 377~388
[8]吴如山,金胜汉,谢小碧.广义屏传播子及其在地震波偏移成像方面的应用[J].石油地球物理勘,2001, 36 (6): 655~654
[9]杨辉,刘洪,李幼铭.单程波方程偏移算子高阶辛格式[J].地球物理学报,2003,46: 533~538
[10]李冰,刘洪,李幼铭.波场延拓短算子构造方法[J].地球物理学报,2003, 46(2):246-251
[11]王华忠.最小二乘叠前偏移成像的数学物理含义及在FK域中的一种实现[J].国际地球物理会议(北京).2009.
[12]Sun J. On the limited aperture migration in two dimensions[J]. Geophysics, 1998,63(4):984~994
[13]李振春,朱绪峰,韩文功.真振幅偏移方法综述[J].勘探地球物体进展,2008,31(1):10~15
[14]刘定进,印兴耀.傅立叶有限差分法保幅叠前深度偏移方法[J].地球物理学报, 2007,42(1):11~16
[15]谢立.波场地震成像方法概述和分类[J].石油科技动态,2009,284(6).12~26
[16]A.J.Berkhou著.马在田,张叔伦译.地震偏移波场外推法声波成像[M].北京,石油工业出版社.1983
[17]Claerbout J F.Imaging the earth’s interior[M]. Blackwell Scientific publications, 1985.
[18]马在田.论反射地震偏移成像[J].勘探地球物理进展,2002,3(25)
[19]马在田.地震成像技术有限差分法偏移[M].北京,石油工业出版社,1989
[20]贺振华.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
[21]陈生昌等.地震成像中的Born近似与Rytov近似比较[J].天然气工业,2007,27 (1) :37~40
[22]Gazdag J. Wave-equation migration with the phase-shift method [J]. Geophysics, 1978, 43(7):1342~1351.
[23]Stolt R H. Migration by Fourier transform [J] .Geophysics, 1978, 43(1):23~48.
[24]李振春.地震成像理论与方法[M].北京,石油大学研究生院,2007
[25]陈生昌,曹进忠,马在田.混合域单程波传播算子及其在偏移成像中的应用[J]地球物理学进展,2003,18(2):210~217.
[26]Stoffa P L, Fokkema J T, Luna F , et al .Split-step Fourier migration [J] . Geophysics.1990 ,55(4) :410~421
[27]Ristow D, Ruhl T. Fourier Finite-Difference Migration[J].Geophysics, 1994 ,59(12) :1882~1893
[28]李世雄.波动方程的高频近似与辛几何[M].北京,科学出版社,2001
[29] Berkhout A J. Ware field extrapolation techniques in seismic migration [J]. Geophysics,1981,46(12):1638~1656.
[30]Myung W Lee, Sang Y Suh. Optimization of one-way wave equations[J]. Geophysics,1985,50(10):1634~1637
[31]罗明秋.地震波传播的哈密顿表述及辛几何算法[J].地球物理学报,2001,44 : 120～128
[32]刘军,侯平,魏茂林.地震波动力学参数在砂体预测中的应用[J].世界地质,2002,21(2):185-188
[33]谢忠求.浅层地震探测技术应用中的分辨率问题[J].矿产与地质,1999.
[34]云美厚,丁伟.地震子波频率浅析[J].石油物探,2005,44(5)
[35]皮红梅.双程波动方程数值模拟和照明分析方法研究[D].吉林大学,2009
[36]张宇.振幅保真的单程波方程偏移理论[J].地球物理学报,2006.49(5):1410-1430
[37]Berkhout A J. Seismic migration: Imaging of acoustic energy by wave field extrapolation:Theoretical aspects[M]. America: The Journal of the Acoustical Society of America,1986.1558
[38]Bleistein N. On the imaging of reflectors in the earth[J]. Geophysics, 1988, 53(12):1540~1546
[39]Tygel M.,Schleicher J. and Hubral P.Pulse distortion in depth migration[J]. Geophysics, 1994, 59(10):1561～156
[40]Gray S.True-amplitude seismic migration: A comparison of three approaches[J]. Geophysics, 1997, 62(2): 629~638
[41]孙建国.Kirchhoff型真振幅偏移与反偏移[J].勘探地球物理进展,2002,25(6)
[42]杨红霞等.真振幅地震偏移三种方法的比较[J].石油物探译丛,1998,2
[43]孙建国.论基于波场延拓的真振幅偏移[C].地球物理年会,2002
[44]Yu Zhang. Towards accurate amplitudes for one-way wavefiled extrapolation of 3-D common shot records[J].Geophysics.
[45]ZhangY,Zhang G Q,Norman B. True amplitude wave equation migration arising from true amplitude one-way wave equations [J].Institute Of Physics Publishing, 2003,19(3):1113~1138
[46]齐民友.仿微分算子导论[M].超星阅读电子文献.
[47]Zhang Y,Zhang G, Bleistein N. Theory of true amplitude one-way wave equations and true amplitude common-shot migration [J].Geophysics ,2005 , 70(3)
[48]Yu Zhang. Theory of true amplitude one-way wave equation and true amplitude common-shot migration[J].Geophysics.
[49]Wapenaar. Representation of the seismic sources in one-way wave equations. Geophysics. 1990.55:786~790.
[50]孙建国.成像原理、成像过程及偏移像场的动力学特性[C].中国地球物理年会,2004,59
[51]孙建国.深度偏移中的振幅畸变[C]. CPS/SEG 2004国际地球物理会议2004
[52]朱绪峰.单程波方程的保幅偏移及其角度域成像[D].中国石油大学,2008
[53]Fomel S.Theory of 3-D angle gathers in wave-equation imaging[J]. Expanded Abstracts of 74th Annual Internat SEG Mtg,2004,1053~1056
[54]徐琴,李振春.波动方程偏移中的成像条件研究进展[J].勘探地球物理进展,2008,31(4):1~6
[55]Yu Zhang. True-amplitude common-offset,common-azimuth v(z) migration[J]. Geophysics,2007,72(1):49~58
[56]刘定进.波动方程保幅地震偏移成像方法研究[D].中国石油大学,2007