基于波动方程的自由界面多次波压制
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摘要
勘探地震学中，多次波问题一直是方法理论和应用研究备受关注的热点之一，始终是给予解决而未能很好被解决的问题，特别是海洋油气地震勘探；多次波的存在，干扰有效波的成像，直接导致错误的地质解释。因此，研究和压制多次波，具有重要的现实意义和发展前景。本学位论文依托国家自然科学面上基金(编码：49974028)“TI介质中与自由界面有关多次波的产生和衰减”课题。
基于波动方程理论，压制和利用多次波是20世纪90年代发展起来的一种新思路，也是国外多次波研究的发展趋势。这种思路方法，综合考虑自由界面多次波传播的运动学特性和动力学特性，有效针对多次波产生的机理，避免了各种非波动方程方法解决问题所带来的局限性，使多次波研究发展步入了新的里程，标志着多次波理论与应研究进入了一个新的层次和水平。本人在上述背景下，开展博士学位论文工作。
首先，本文全面系统地论述了多次波压制简况和各种主要技术方法。分别对非波动方程的滤波方法和基于波动方程的多次波压制方法作了全面的论述，对几种具有代表性的多次波压制技术的方法原理作了概要的介绍。其次，深入研究了基于波动方程的多次波压制技术，重点阐述了基于波动方程的自由界面多次波压制(SRMA)方法。论文从声波波场理论出发，研究了在不考虑自由界面反射的情况下有效波波场的传播及反射规律；在考虑自由界面反射的情况下，详尽推导验证了自由界面多次波产生的数学模型；用程序实现了自由界面多次波波场的模拟；更进一步，详尽推导验证了作为自由界面多次波产生的逆过程----自由界面多次波消除----的数学模型，给出了推导过程中的必要的、关键的细节步骤；用程序实现了自由界面多次波的消除。从物理本质上对自由界面多次波的产生和消除作了深入的剖析，以达到数学原理与物理解释的完全一致。针对SRMA方法的原理及特殊性，对进行实际勘探时的观测系统设计提出了改进措施。然后，为了验证算法及程序的正确性和有效性，对三个典型的理论模型进行试算和分析，得到了正确的结果，取得了较好的效果。针对一条实际的海洋地震测线，进行了实际资料的试算，并和其它消除多次波的技术方法(预测反褶积、抛物Radon变换消除多次波、二维滤波压制多次波)处理的结果进行了对比分析。最后，对全文的研究成果进行了总结，并提出了进一步开展研究工作的建议。
本文在消化吸收A．J．Berkhout提出的基于波动方程的自由界面多次波压制技术的思想理论体系的基础上，在以下方面作了创新和突破：在国内，本文的研究工作，基于波动方程的自由界面多次波压制的理论方法和实际应用研究，具有一定的系统性和完整性。在国内，首次采用波动方程方法实现了任意阶自由界面多次波波场的模拟及消除；首次明确给出了自由界面多次波波场模拟的迭代形式；首次提出了自适应滤波中的快速多道维纳滤波算法；在国内，首次应用基于波动方程的自由界面多次波压制方法技术，进行了理论模型和实际资料试算研究工作。
In seismic data processing the interference of multiple reflections is still a large problem, especially for marine dataset. Strong multiples can lead to fault seismic interpretation and finally lead to dry-well. So it is very important and necessary for multiple suppression. The research of this dissertation is financed by the Chinese National Natural Science Foundation (49974028).
Over the years the SRMA (surface-related multiple attenuation) has proved to be very useful and powerful because all types of surface-related multiples are removed, without the need of a subsurface model, using the data itself as a multiple predictor. A review has been given first for the multiple attenuation techniques. A comprehensive study has been done on the wave equation-based demultiple techniques, especially on SRMA.
Starting from the acoustic wave field theory, using the second type of Riley integral, we have obtained wave field extrapolation formula in the frequency-space domain. Regardless of surface reflection, the primary propagates downward, reflects at the subsurface reflector, and then propagates upward. Taking account into the reflection of the free surface, the so-called surface-related multiple has been generated. As the inverse procedure of surface-related multiple generation, surface-related multiple can be removed using the data itself as a multiple predictor. Algorithms, formulas, program flowcharts for surface-related multiple generation and attenuation have been given in detail in this dissertation. From the physical insight, we have explained why surface-related multiple can be predicted and how it is predicted. The surface-related multiple attenuation method can be formulated in an iterative procedure: the output of one iteration step is used as input for the next iteration step. This technique is illu
strated with some numerical experiments as well as field data examples. The results show that our SRMA method is very effective and robust. SRMA method seems to be very attractive with the following advantages: completely independent to the velocity, requiring no information about the subsurface, almost automatically running. At last some conclusions has been made and some advice for further research has been given.
Based on A.J. Berkhout's pioneering work, this dissertation has made the following innovations: The iterative form for surface-related multiple modeling is presented, which is equivalent to the series form but make the surface-multiple modeling formula more concise and make easier to transfer the algorithm to the practical programming. Fast multi-channel Wiener filter is used for adaptive filtering, which take the horizontal variety into account and has a fast computational speed. Comprehensive and deep discussion for SRMA has been given. Massive work from theory research, algorithm deducing, and program implementing to practical application has been done for this research.
基于波动方程理论，压制和利用多次波是20世纪90年代发展起来的一种新思路，也是国外多次波研究的发展趋势。这种思路方法，综合考虑自由界面多次波传播的运动学特性和动力学特性，有效针对多次波产生的机理，避免了各种非波动方程方法解决问题所带来的局限性，使多次波研究发展步入了新的里程，标志着多次波理论与应研究进入了一个新的层次和水平。本人在上述背景下，开展博士学位论文工作。
首先，本文全面系统地论述了多次波压制简况和各种主要技术方法。分别对非波动方程的滤波方法和基于波动方程的多次波压制方法作了全面的论述，对几种具有代表性的多次波压制技术的方法原理作了概要的介绍。其次，深入研究了基于波动方程的多次波压制技术，重点阐述了基于波动方程的自由界面多次波压制(SRMA)方法。论文从声波波场理论出发，研究了在不考虑自由界面反射的情况下有效波波场的传播及反射规律；在考虑自由界面反射的情况下，详尽推导验证了自由界面多次波产生的数学模型；用程序实现了自由界面多次波波场的模拟；更进一步，详尽推导验证了作为自由界面多次波产生的逆过程----自由界面多次波消除----的数学模型，给出了推导过程中的必要的、关键的细节步骤；用程序实现了自由界面多次波的消除。从物理本质上对自由界面多次波的产生和消除作了深入的剖析，以达到数学原理与物理解释的完全一致。针对SRMA方法的原理及特殊性，对进行实际勘探时的观测系统设计提出了改进措施。然后，为了验证算法及程序的正确性和有效性，对三个典型的理论模型进行试算和分析，得到了正确的结果，取得了较好的效果。针对一条实际的海洋地震测线，进行了实际资料的试算，并和其它消除多次波的技术方法(预测反褶积、抛物Radon变换消除多次波、二维滤波压制多次波)处理的结果进行了对比分析。最后，对全文的研究成果进行了总结，并提出了进一步开展研究工作的建议。
本文在消化吸收A．J．Berkhout提出的基于波动方程的自由界面多次波压制技术的思想理论体系的基础上，在以下方面作了创新和突破：在国内，本文的研究工作，基于波动方程的自由界面多次波压制的理论方法和实际应用研究，具有一定的系统性和完整性。在国内，首次采用波动方程方法实现了任意阶自由界面多次波波场的模拟及消除；首次明确给出了自由界面多次波波场模拟的迭代形式；首次提出了自适应滤波中的快速多道维纳滤波算法；在国内，首次应用基于波动方程的自由界面多次波压制方法技术，进行了理论模型和实际资料试算研究工作。
In seismic data processing the interference of multiple reflections is still a large problem, especially for marine dataset. Strong multiples can lead to fault seismic interpretation and finally lead to dry-well. So it is very important and necessary for multiple suppression. The research of this dissertation is financed by the Chinese National Natural Science Foundation (49974028).
Over the years the SRMA (surface-related multiple attenuation) has proved to be very useful and powerful because all types of surface-related multiples are removed, without the need of a subsurface model, using the data itself as a multiple predictor. A review has been given first for the multiple attenuation techniques. A comprehensive study has been done on the wave equation-based demultiple techniques, especially on SRMA.
Starting from the acoustic wave field theory, using the second type of Riley integral, we have obtained wave field extrapolation formula in the frequency-space domain. Regardless of surface reflection, the primary propagates downward, reflects at the subsurface reflector, and then propagates upward. Taking account into the reflection of the free surface, the so-called surface-related multiple has been generated. As the inverse procedure of surface-related multiple generation, surface-related multiple can be removed using the data itself as a multiple predictor. Algorithms, formulas, program flowcharts for surface-related multiple generation and attenuation have been given in detail in this dissertation. From the physical insight, we have explained why surface-related multiple can be predicted and how it is predicted. The surface-related multiple attenuation method can be formulated in an iterative procedure: the output of one iteration step is used as input for the next iteration step. This technique is illu
strated with some numerical experiments as well as field data examples. The results show that our SRMA method is very effective and robust. SRMA method seems to be very attractive with the following advantages: completely independent to the velocity, requiring no information about the subsurface, almost automatically running. At last some conclusions has been made and some advice for further research has been given.
Based on A.J. Berkhout's pioneering work, this dissertation has made the following innovations: The iterative form for surface-related multiple modeling is presented, which is equivalent to the series form but make the surface-multiple modeling formula more concise and make easier to transfer the algorithm to the practical programming. Fast multi-channel Wiener filter is used for adaptive filtering, which take the horizontal variety into account and has a fast computational speed. Comprehensive and deep discussion for SRMA has been given. Massive work from theory research, algorithm deducing, and program implementing to practical application has been done for this research.
引文
[1] 渥·伊尔马兹，地震数据处理[M]，石油工业出版，1993：379-389．
[2] Berkhout, A. J., Seismic migration: Imaging of acoustic energy by wavefield extrapolation[M], Elsevier Science Publ. Co., Inc., 1982．
[3] R．E．谢里夫，勘探地震学[M]，石油工业出版，1999：215-219
[4] Arthur B. Weglein, Multiple attenuation: an overview of recent advances and the road ahead (1999) [J], The Leading Edge, 1999, Vol. 18, No. 1, 40-44．
[5] Berkhout, A. J., Verschuur, D. J., Estimation of multiple scattering by iterative inversion, Part 1: Theoretical considerations[J], Geophysics, 62,1997,1586~1595．
[6] Verschuur, D. J., Berkhout, A. J., Estimation of multiple scattering by iterative inversion, Part 2: Practical aspects and examples [J], Geophysics, 62, 1997,1596-1611．
[7] Verschuur, D. J., Berkhout, A. J., Wapenaar, C. P. A. Adaptive surface-related multiple elimination[J], Geophysics, 57, No. 9, 1992, 1166-1177．
[8] Berkhout, A. J., Multiple removal based on the feedback model[J], The Leading Edge, Vol. 18, No. 1, 1999, 127-131．
[9] Arthur B. Weglein, Fernanda Araujo Gasparotto, An inverse-scattering series method for attenuation multiples in seismic reflection data: Geophysics, 1997, 62, No. 6, 1975-1989．
[2] Berkhout, A. J., Seismic migration: Imaging of acoustic energy by wavefield extrapolation[M], Elsevier Science Publ. Co., Inc., 1982．
[3] R．E．谢里夫，勘探地震学[M]，石油工业出版，1999：215-219
[4] Arthur B. Weglein, Multiple attenuation: an overview of recent advances and the road ahead (1999) [J], The Leading Edge, 1999, Vol. 18, No. 1, 40-44．
[5] Berkhout, A. J., Verschuur, D. J., Estimation of multiple scattering by iterative inversion, Part 1: Theoretical considerations[J], Geophysics, 62,1997,1586~1595．
[6] Verschuur, D. J., Berkhout, A. J., Estimation of multiple scattering by iterative inversion, Part 2: Practical aspects and examples [J], Geophysics, 62, 1997,1596-1611．
[7] Verschuur, D. J., Berkhout, A. J., Wapenaar, C. P. A. Adaptive surface-related multiple elimination[J], Geophysics, 57, No. 9, 1992, 1166-1177．
[8] Berkhout, A. J., Multiple removal based on the feedback model[J], The Leading Edge, Vol. 18, No. 1, 1999, 127-131．
[9] Arthur B. Weglein, Fernanda Araujo Gasparotto, An inverse-scattering series method for attenuation multiples in seismic reflection data: Geophysics, 1997, 62, No. 6, 1975-1989．