频率域拟Born近似偏移成像的研究
摘要
由于地震波动力学属性可以反映地下介质弹性的丰富信息,随着计算机运算能力的提高,基于波动方程的复杂介质的叠前深度偏移成像已成为地球物理学研究领域的一个热点。
而频率域的深度偏移算法,通过快速傅立叶变换大大地提高了运算效率,但是通常的频率域深度偏移算法不能适用横向速度强烈变化的介质。近年来也有许多学者对频率域深度偏移算法进行了改进,使之能适应横向速度变化强烈的介质。但这些改进都是以运算效率的极大降低为代价的。
本论文对拟Born 近似方法提出了改进方案。改进后的频率深度域的偏移方法考虑了高阶扰动,不仅适用于横向速度变化强烈的介质,还可以根据介质横向速度变化的强弱自动调整其计算效率,使效率和精确度之间有一个比较理想的结合点。本文用一系列模型通过正演模拟和偏移进行了理论试算,证明了改进后的理论和方法的有效性和可行性。
When migrating, if we want to keep the amplitude and phase information included in the input, we can’t use Ray-tracing-based migration method. The seismic-wave dynamics attribute can reflect abundant information of the elasticity in the underground structures, so the wave-equation migration method develops quickly. Prestack depth migration imaging in complex structures is a focus in geophysics field. Migration method based on wave-equation becomes mature incessantly and mainstream gradually. But all migration methods in the time field suppose that velocity is constant or changes a little horizontally or that structure doesn’t complex. If this doesn’t right, they can’t make the location of target right. Prestack depth migration without these shortcomings becomes a focus in geophysics field with the powerful ability of computer.
Prestack depth migration in frequency-domain improves efficiency by FFT (Fast Fourier Transform). But the common prestack depth migration in frequency-domain can’t be applied when the velocity of medium isn’t constant horizontally. In order to make prestack depth migration method be applied to the medium with horizontal velocity variety, many scholars improved on it these years, but all these reduce the efficiency of the calculation badly.
In order to make prestack depth migration both image accurately and improve efficiency in complex structure, the thesis analyze some prestack depth migration methods in frequency-domain synthetically and improve the Quasi-Born method. The method improved includes high-level disturbance, can be not only applied in medium with various velocity horizontally, but also adjust the efficiency by the degree of the horizontal velocity variety, which has a better joint between efficiency and exactitude. The thesis proves that the method and theory is effective and feasible by forward modeling and migration of a series of models.
The main idea of the thesis is making use of quasi-born approximation which decomposes the pressure wavefield into two parts, namely, the incident wavefield and scatter wavefield. While in the integrator, the scatter wavefield can be decomposed two terms, namely, the incident wavefield and other summation all terms, which
is similarly to linear relation. This theory is called quasi-liner Born approximation in the theory of electromagnetic wavefield. The thesis extracts the idea of high-level approximation, and improves formula about extrapolate of wavefield based on quasi-born approximation following forerunners. We take into account of high-level disturbance, which accord with the fact of seismic wave’s transmitting in the underground medium. And this also accord with the reality when extrapolating. Comparing to Born approximation, quasi-Born approximation algorithm need much more time in the same medium. So, the efficiency is very low making use of quasi-Born approximation algorithm than the other, especially when the medium isn’t very complex. Born approximation can also get satisfying result. The thesis combines the Born approximation and the quasi-Born approximation algorithm, whose essential is that Born approximation is used when the medium isn’t much complex and quasi-Born approximation is used when the medium is very complex in course of extrapolating. Thus the method combined has a satisfying joint between accuracy and efficiency. The thesis derivate the theory formula of extrapolate and forward algorithm, and applies these extrapolation formulas in forward. And applies formulas improved in wave extrapolation of the prestack depth migration imaging by correlative theory of prestack depth migration. Then, it tests the forward formulas and migration formulas using the numerical technical, and gains the corresponding synthetic seismic records of models. The synthetic records are migrated, and we gain the result of migration of corresponding models. From the maps gained, we see clearly that the maps gained are similar with the corresponding models, which proves that the migration improved can be applied both in poststack depth migration and in prestack depth migration and that the outcome of migration is satisfying. Finally, the migration results of the method before and after improved are written. From them, we can see easily that migration result by migration method improved is more accurate than method before improved, which prove that the migration method are successful. The result is satisfying, but the input data is man-made whose Signal-to-Noise is high. The impact need study more when the
而频率域的深度偏移算法,通过快速傅立叶变换大大地提高了运算效率,但是通常的频率域深度偏移算法不能适用横向速度强烈变化的介质。近年来也有许多学者对频率域深度偏移算法进行了改进,使之能适应横向速度变化强烈的介质。但这些改进都是以运算效率的极大降低为代价的。
本论文对拟Born 近似方法提出了改进方案。改进后的频率深度域的偏移方法考虑了高阶扰动,不仅适用于横向速度变化强烈的介质,还可以根据介质横向速度变化的强弱自动调整其计算效率,使效率和精确度之间有一个比较理想的结合点。本文用一系列模型通过正演模拟和偏移进行了理论试算,证明了改进后的理论和方法的有效性和可行性。
When migrating, if we want to keep the amplitude and phase information included in the input, we can’t use Ray-tracing-based migration method. The seismic-wave dynamics attribute can reflect abundant information of the elasticity in the underground structures, so the wave-equation migration method develops quickly. Prestack depth migration imaging in complex structures is a focus in geophysics field. Migration method based on wave-equation becomes mature incessantly and mainstream gradually. But all migration methods in the time field suppose that velocity is constant or changes a little horizontally or that structure doesn’t complex. If this doesn’t right, they can’t make the location of target right. Prestack depth migration without these shortcomings becomes a focus in geophysics field with the powerful ability of computer.
Prestack depth migration in frequency-domain improves efficiency by FFT (Fast Fourier Transform). But the common prestack depth migration in frequency-domain can’t be applied when the velocity of medium isn’t constant horizontally. In order to make prestack depth migration method be applied to the medium with horizontal velocity variety, many scholars improved on it these years, but all these reduce the efficiency of the calculation badly.
In order to make prestack depth migration both image accurately and improve efficiency in complex structure, the thesis analyze some prestack depth migration methods in frequency-domain synthetically and improve the Quasi-Born method. The method improved includes high-level disturbance, can be not only applied in medium with various velocity horizontally, but also adjust the efficiency by the degree of the horizontal velocity variety, which has a better joint between efficiency and exactitude. The thesis proves that the method and theory is effective and feasible by forward modeling and migration of a series of models.
The main idea of the thesis is making use of quasi-born approximation which decomposes the pressure wavefield into two parts, namely, the incident wavefield and scatter wavefield. While in the integrator, the scatter wavefield can be decomposed two terms, namely, the incident wavefield and other summation all terms, which
is similarly to linear relation. This theory is called quasi-liner Born approximation in the theory of electromagnetic wavefield. The thesis extracts the idea of high-level approximation, and improves formula about extrapolate of wavefield based on quasi-born approximation following forerunners. We take into account of high-level disturbance, which accord with the fact of seismic wave’s transmitting in the underground medium. And this also accord with the reality when extrapolating. Comparing to Born approximation, quasi-Born approximation algorithm need much more time in the same medium. So, the efficiency is very low making use of quasi-Born approximation algorithm than the other, especially when the medium isn’t very complex. Born approximation can also get satisfying result. The thesis combines the Born approximation and the quasi-Born approximation algorithm, whose essential is that Born approximation is used when the medium isn’t much complex and quasi-Born approximation is used when the medium is very complex in course of extrapolating. Thus the method combined has a satisfying joint between accuracy and efficiency. The thesis derivate the theory formula of extrapolate and forward algorithm, and applies these extrapolation formulas in forward. And applies formulas improved in wave extrapolation of the prestack depth migration imaging by correlative theory of prestack depth migration. Then, it tests the forward formulas and migration formulas using the numerical technical, and gains the corresponding synthetic seismic records of models. The synthetic records are migrated, and we gain the result of migration of corresponding models. From the maps gained, we see clearly that the maps gained are similar with the corresponding models, which proves that the migration improved can be applied both in poststack depth migration and in prestack depth migration and that the outcome of migration is satisfying. Finally, the migration results of the method before and after improved are written. From them, we can see easily that migration result by migration method improved is more accurate than method before improved, which prove that the migration method are successful. The result is satisfying, but the input data is man-made whose Signal-to-Noise is high. The impact need study more when the
引文
[1] Lian-jie Huang, Michael C. Fehler, and Ru-Shan Wu; Extended local Born Fourier migration method; Geophysics Vol.64 NO.5(September-October 1999);1524-1534
[2] Lian-jie Huang, MichaelC. Fehler, and Peter M. Roberts, and Charles C. Burch; Extended local Rytov Fourier migration method, Geophysics Vol.64 NO.5(September-October 1999);1535-1545
[3] P.L.Stoffa, J T. Fokkema, R.M. De Luna Freire and W. P. Kessinger, 1990, Split-step Fourier migration, Geophysics vol.55, No.4, 410-412
[4] Huang L.-J. and Wu, R.-S., 1996a, 3-D prestack depth migration with an acoustic pseudo-screen propagators, in Hassanzadeh, S., Ed., Mathematical methods in geophysical imaging IV: Proc. SPIE: The International Society for Optical Engineering, 282, 1-51
[5] Huang,L.-J., and M.C., and Burch, C.C., 1998, a hybrid local Born/Rytov Fourier migration method, in Hassanzadeh, S., Ed., Mathematical methods in geophysical imaging V: Proc. SPIE: The International Society for Optical Engineering, 3453, 14-45.
[6] P.L. Stoffa, J.T. Fokkema, R.M. de Luna Freire, and W.P.Kessinger, 1990, Split-step Fourier migration, Geophysics, Vol.55, NO.4, 410-421.
[7] Zhdanov MS, Fang S. Quasi-linear approximation in 3-D electromagnetic modeling. geophysics, 1996, 61: 646—665
[8] Lian-jie Huang and Michael C. Fehler, 2000, Quasi-Born Fourier migration. Geophysics. J. Int. (2000) Vol.140, 521-534
[9] Zhdanov MS, Fang S. Quasi-linear approximation in 3-D electromagnetic inversion, Radio Sci., 31, 741-754.
[10] Morse, P.M. & Feshbach, H., 1953, Methods of Theoretical Physics, Mc Graw-Hill, New York.
[11] Loewenthal, D. etal, The wave equation applied to migration, Geophysical Prospecting, Vol.24, 1976, 380-390
[12] Rune Mittet, Roger Sollie, and Ketil Hokstad, Prestack depth migration with compensation for absorption and dispersion, Geophysics, Vol.60, 1995, 1485-1494
[13] Jon. F Claerbout, 1971, Toward a unified theory of reflector mapping, Geophysics, Vol.36, 467-481
[14] 贺振华、黄德济、胡光氓等著复杂油气藏地震波场特征方法理论及应用,成都:四川科学技术出版社,1999,1-2
[15] 油气勘探专题资料之十地震资料处理专辑(偏移) 石油工业部科学技术情报研究所,1987,3-7
[16] J.F. 克莱鲍特著,许云译,地震成像理论及方法,石油工业出版社,1991,38
[17] 杨文采、李幼铭等,计算地球物理丛书之一应用地震层析成像,地质出版社,1993,74-75
[18] 陈生昌、曹景忠等,基于拟线性Born 近似的叠前深度偏移方法,地球物理学报,第44 卷第5 期,704-709
[19] 熊小兵、贺振华,相位移加有限差分法波动方程正演模拟,石油物探,1998,37(3),22-28.
[20] 吴清岭、李伟、陈可为等,无反射波动方程正演模型及其应用,石油地球物理勘探,2000,35(2),147-153
[21] 熊高君、贺振华、张琳等,多次反射可控制的波动方程共炮记录正演模拟,石油地球物理勘探,1998,33(5),583-589
[22] 胜利油田,绕射扫描叠加,石油地球物理勘探,1974,No5
[23] 陈玉等译,J. F. Claerbout 著,地球物理数据处理基础,石油化学工业出版社,1983
[24] 杨有发、何樵登等编著,海洋地震勘探,吉林科学技术出版社,1997,87
[25] [日] 酒井英昭编著, 白玉林译,21 世纪工程技术新型教程系列信号处理,科学出版社OHM 社出版,2001,74
[26] 胡光岷,频率波数域地震波变速成像研究,成都理工学院, 2000,19
[27] [美] R.E. 谢里夫,[加] L.P.吉尔达特,初英、李承楚等译,勘探地震学,石油工业出版社,1997,234
[28] 刘馥主编,地震勘探导论,地质出版社,1990,114
[29] 刘馥主编,地震勘探导论,地质出版社,1990,46
[30] 吴律,层析基础及其在井间地震中的应用,石油工业出版社,1997,140
[31] 陆基孟等,地震勘探原理及资料解释,石油工业出版社,1985,44
[32] 刘天放、张爱敏等编,地震勘探原理及方法,煤炭工业出版社,1996,43-48
[33] 范祯详、郑仙种,地震波参数反演与应用技术,河南科学技术出版社,1998,11-13
[34] R.迈斯内尔L、适特格奈著,吴辉译,实用地震勘探技术,地质出版社,1982,12-20
[35] 秦政,石油地球物理勘探下册(地震勘探原理和解释),石油工业出版社,1987,82-84
[36] 任俞,地震勘探的高分辨率技术,石油工业部科学技术情报研究所,1986,39-40
[37] 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,重庆大学出版社,1989,10
[38] 周学亮,地震勘探基础,石油工业出版社,1993,41
[39] 牛毓荃、陈俊生、张淑敏等,反射法地震勘探技术,石油工业出版社,1985,103
[40] [美] K.H.沃特斯著,许云、吴荣祥译,反射地震学能源勘探的工具,石油工业出版社,1983,195
[41] 牟永光, 地震勘探资料数字处理方法, 石油工业出版社,1981,179
[42] 陈丽虹、孙建国、吴燕冈、王忠仁、韩立国、朱建伟等,地球物理反演的拟线性近似方法综述,地球物理学进展,Vol.17,
[2] Lian-jie Huang, MichaelC. Fehler, and Peter M. Roberts, and Charles C. Burch; Extended local Rytov Fourier migration method, Geophysics Vol.64 NO.5(September-October 1999);1535-1545
[3] P.L.Stoffa, J T. Fokkema, R.M. De Luna Freire and W. P. Kessinger, 1990, Split-step Fourier migration, Geophysics vol.55, No.4, 410-412
[4] Huang L.-J. and Wu, R.-S., 1996a, 3-D prestack depth migration with an acoustic pseudo-screen propagators, in Hassanzadeh, S., Ed., Mathematical methods in geophysical imaging IV: Proc. SPIE: The International Society for Optical Engineering, 282, 1-51
[5] Huang,L.-J., and M.C., and Burch, C.C., 1998, a hybrid local Born/Rytov Fourier migration method, in Hassanzadeh, S., Ed., Mathematical methods in geophysical imaging V: Proc. SPIE: The International Society for Optical Engineering, 3453, 14-45.
[6] P.L. Stoffa, J.T. Fokkema, R.M. de Luna Freire, and W.P.Kessinger, 1990, Split-step Fourier migration, Geophysics, Vol.55, NO.4, 410-421.
[7] Zhdanov MS, Fang S. Quasi-linear approximation in 3-D electromagnetic modeling. geophysics, 1996, 61: 646—665
[8] Lian-jie Huang and Michael C. Fehler, 2000, Quasi-Born Fourier migration. Geophysics. J. Int. (2000) Vol.140, 521-534
[9] Zhdanov MS, Fang S. Quasi-linear approximation in 3-D electromagnetic inversion, Radio Sci., 31, 741-754.
[10] Morse, P.M. & Feshbach, H., 1953, Methods of Theoretical Physics, Mc Graw-Hill, New York.
[11] Loewenthal, D. etal, The wave equation applied to migration, Geophysical Prospecting, Vol.24, 1976, 380-390
[12] Rune Mittet, Roger Sollie, and Ketil Hokstad, Prestack depth migration with compensation for absorption and dispersion, Geophysics, Vol.60, 1995, 1485-1494
[13] Jon. F Claerbout, 1971, Toward a unified theory of reflector mapping, Geophysics, Vol.36, 467-481
[14] 贺振华、黄德济、胡光氓等著复杂油气藏地震波场特征方法理论及应用,成都:四川科学技术出版社,1999,1-2
[15] 油气勘探专题资料之十地震资料处理专辑(偏移) 石油工业部科学技术情报研究所,1987,3-7
[16] J.F. 克莱鲍特著,许云译,地震成像理论及方法,石油工业出版社,1991,38
[17] 杨文采、李幼铭等,计算地球物理丛书之一应用地震层析成像,地质出版社,1993,74-75
[18] 陈生昌、曹景忠等,基于拟线性Born 近似的叠前深度偏移方法,地球物理学报,第44 卷第5 期,704-709
[19] 熊小兵、贺振华,相位移加有限差分法波动方程正演模拟,石油物探,1998,37(3),22-28.
[20] 吴清岭、李伟、陈可为等,无反射波动方程正演模型及其应用,石油地球物理勘探,2000,35(2),147-153
[21] 熊高君、贺振华、张琳等,多次反射可控制的波动方程共炮记录正演模拟,石油地球物理勘探,1998,33(5),583-589
[22] 胜利油田,绕射扫描叠加,石油地球物理勘探,1974,No5
[23] 陈玉等译,J. F. Claerbout 著,地球物理数据处理基础,石油化学工业出版社,1983
[24] 杨有发、何樵登等编著,海洋地震勘探,吉林科学技术出版社,1997,87
[25] [日] 酒井英昭编著, 白玉林译,21 世纪工程技术新型教程系列信号处理,科学出版社OHM 社出版,2001,74
[26] 胡光岷,频率波数域地震波变速成像研究,成都理工学院, 2000,19
[27] [美] R.E. 谢里夫,[加] L.P.吉尔达特,初英、李承楚等译,勘探地震学,石油工业出版社,1997,234
[28] 刘馥主编,地震勘探导论,地质出版社,1990,114
[29] 刘馥主编,地震勘探导论,地质出版社,1990,46
[30] 吴律,层析基础及其在井间地震中的应用,石油工业出版社,1997,140
[31] 陆基孟等,地震勘探原理及资料解释,石油工业出版社,1985,44
[32] 刘天放、张爱敏等编,地震勘探原理及方法,煤炭工业出版社,1996,43-48
[33] 范祯详、郑仙种,地震波参数反演与应用技术,河南科学技术出版社,1998,11-13
[34] R.迈斯内尔L、适特格奈著,吴辉译,实用地震勘探技术,地质出版社,1982,12-20
[35] 秦政,石油地球物理勘探下册(地震勘探原理和解释),石油工业出版社,1987,82-84
[36] 任俞,地震勘探的高分辨率技术,石油工业部科学技术情报研究所,1986,39-40
[37] 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,重庆大学出版社,1989,10
[38] 周学亮,地震勘探基础,石油工业出版社,1993,41
[39] 牛毓荃、陈俊生、张淑敏等,反射法地震勘探技术,石油工业出版社,1985,103
[40] [美] K.H.沃特斯著,许云、吴荣祥译,反射地震学能源勘探的工具,石油工业出版社,1983,195
[41] 牟永光, 地震勘探资料数字处理方法, 石油工业出版社,1981,179
[42] 陈丽虹、孙建国、吴燕冈、王忠仁、韩立国、朱建伟等,地球物理反演的拟线性近似方法综述,地球物理学进展,Vol.17,