非线性/非高斯叠前地震反演理论及应用
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摘要
α稳定分布是一种比高斯分布适用性更广泛的统计分布。在近二十的时间里,α稳定分布吸引了大量信号处理领域专家学者的注意,人们开始尝试从非高斯的视角来重新审视信号处理方法。另一方面,叠前地震反演是信号处理的一个重要的应用领域,反演的目的就是希望从地面采集到的地震记录以及测井信息,推演出人们感兴趣的深地层地质岩性参数。精确的地质岩性参数信息是储层识别和油气检测的基础。随着人类对隐蔽油气藏的开发,对反演结果精确度和准确率的提出了更高的要求。从信号处理角度来看,要想有效地解决这些问题,必须对传统的反演理论进行适当的改进,寻找新的精确反演方法。
首先,本文从研究非高斯α稳定分布的理论基础、性质、关键参数对分布的影响以及重要的数字特征等出发,找出了非高斯α稳定分布与高斯分布在理论上的不同之处;然后,在叠前反演理论基础上,研究了叠前基本弹性阻抗、扩展弹性阻抗和广义弹性阻抗的特点,确立了叠前地震反演的步骤和关键环节;最后,建立适合数字信号处理的地震反演模型,并将α稳定分布理论应用到叠前地震反演当中,提出了基于分数低阶矩统计量的叠前地震反演算法。通过对实际叠前地震数据反演实验,验证了本文提出的反演方法的正确性和有效性。
本文大胆地打破传统的地震信号服从高斯分布的假设,尝试将非高斯α稳定分布理论应用到地震反演中,取得了较好的效果。本文的突出成果表现在:
(1)提出了利用地震数据的动态样本方差曲线判别地震数据是服从高斯分布还是非高斯α稳定分布的新办法。利用非高斯α稳定分布随机数据没有有限的动态样本方差的特点,通过分别比较理论上的高斯分布随机数据的动态样本方差曲线和理论的非高斯α稳定分布随机数据的动态样本方差曲线与实际的地震数据动态样本反差曲线变化的异同,估计实际地震数据的分布。实例数据的仿真结果表明,实际的地震数据基本服从非高斯的α稳定分布,用α稳定分布来描述地震数据的分布比用高斯分布描述更合适。
(2)提出了基于非高斯α稳定分布的叠前地震反演算法。由于非高斯α稳定分布没有有限的二阶矩,基于传统的高斯分布假设下的最小二乘等方法不再适用。本文在非高斯α稳定分布的分数低阶矩理论的基础上,建立了以反演误差的最小平均l p范数作为目标函数的地震反演模型。在此基础上,结合非高斯α稳定分布下的信号处理方法,提出了适合计算机编程的地震反演算法,并给出了具体的实施步骤。
通过实际的叠前地震资料反演的实例,验证了本文提出基于非高斯α稳定分布的叠前地震低阶矩反演方法的正确性和有效性。
Alpha stable distribution processes which has greater applicability than the ideal Gaussian distribution attracts a great deal of attention of signal processing experts and scholars in the past less than twenty years’time. And now, people begin to try to re-examine and improve signal processing methods in the new perspective of non-Gaussian. While pre-stack seismic inversion is an important application in the field of signal processing, and the purpose of seismic inversion is to deduce the required deep geological information and lithology parameters from seismic records and a small amount of available logging information. As it is known, accurate geological information and lithology parameters are of vital importance for the reservoir identification and hydrocarbon detection, especially, on the hidden reservoir exploitation, requiring more precise and accurate inversion result than general application. To address the issue with signal processing methods, effectively inversion theory must be improved.
First of all, the dissertation studies suchαstable distribution characteristic as theoretical basis, property, influence of key parameters on the distribution and some important numerical characteristic, and then, differences between non-Gaussianαstable distribution processing and the ideal Gaussian distribution are extracted.
After that, pre-stack inversion theory as well as basic elastic impedance inversion, extended elastic impedance inversion and generalized elastic impedance inversion are studied, pre-stack seismic inversion steps are established.
In the last part of this dissertation,αstable distribution signal processing theory is applied to pre-stack seismic inversion, and a new pre-stack seismic inversion algorithm based on fractional lower order statistics theory is proposed. The algorithm proposed in the dissertation was performed in practical pre-stack seismic inversion application successfully, which demonstrat the algorithm is practical and effective in pre-stack seismic inversion.
The dissertation abandoned the traditional assumption that seismic signal obeys the ideal Gaussian distribution, and successfully appliedαstable distribution to pre-stack seismic inversion. The main achievements of the dissertation can be summarized as follows:
⑴Proposed a method of observing dynamic sample variance curve to determine whether the seismic signal obeys Gaussian distribution or non-Gaussianαstable distribution. As non-Gaussianαstable distribution signal does not own limited dynamic sample variance value theoretically, comparing the the dynamic sample variance curves of Gaussian distribution and non-Gaussianαstable distribution is a convenient way to distinguish them. In fact, real seismic data subjects to non-Gaussian stable distribution rather Gaussian distribution.
⑵Proposed a new pre-stack seismic inversion algorithm based on the assumption that seismic signal subjects to non-Gaussianαstable distribution. Different from Gaussian distribution, non-Gaussianαstable distribution does not have a second order moment, the classic signal processing methods such as least sequares algorithm do not work at all. Combining fractional lower order statistic theory and the convolution theory, this dissertation established a new objective function with least average l p norm of the inversion error, on this basis, proposed non-Gaussian stable distribution inversion algorithm and implementation steps.
首先,本文从研究非高斯α稳定分布的理论基础、性质、关键参数对分布的影响以及重要的数字特征等出发,找出了非高斯α稳定分布与高斯分布在理论上的不同之处;然后,在叠前反演理论基础上,研究了叠前基本弹性阻抗、扩展弹性阻抗和广义弹性阻抗的特点,确立了叠前地震反演的步骤和关键环节;最后,建立适合数字信号处理的地震反演模型,并将α稳定分布理论应用到叠前地震反演当中,提出了基于分数低阶矩统计量的叠前地震反演算法。通过对实际叠前地震数据反演实验,验证了本文提出的反演方法的正确性和有效性。
本文大胆地打破传统的地震信号服从高斯分布的假设,尝试将非高斯α稳定分布理论应用到地震反演中,取得了较好的效果。本文的突出成果表现在:
(1)提出了利用地震数据的动态样本方差曲线判别地震数据是服从高斯分布还是非高斯α稳定分布的新办法。利用非高斯α稳定分布随机数据没有有限的动态样本方差的特点,通过分别比较理论上的高斯分布随机数据的动态样本方差曲线和理论的非高斯α稳定分布随机数据的动态样本方差曲线与实际的地震数据动态样本反差曲线变化的异同,估计实际地震数据的分布。实例数据的仿真结果表明,实际的地震数据基本服从非高斯的α稳定分布,用α稳定分布来描述地震数据的分布比用高斯分布描述更合适。
(2)提出了基于非高斯α稳定分布的叠前地震反演算法。由于非高斯α稳定分布没有有限的二阶矩,基于传统的高斯分布假设下的最小二乘等方法不再适用。本文在非高斯α稳定分布的分数低阶矩理论的基础上,建立了以反演误差的最小平均l p范数作为目标函数的地震反演模型。在此基础上,结合非高斯α稳定分布下的信号处理方法,提出了适合计算机编程的地震反演算法,并给出了具体的实施步骤。
通过实际的叠前地震资料反演的实例,验证了本文提出基于非高斯α稳定分布的叠前地震低阶矩反演方法的正确性和有效性。
Alpha stable distribution processes which has greater applicability than the ideal Gaussian distribution attracts a great deal of attention of signal processing experts and scholars in the past less than twenty years’time. And now, people begin to try to re-examine and improve signal processing methods in the new perspective of non-Gaussian. While pre-stack seismic inversion is an important application in the field of signal processing, and the purpose of seismic inversion is to deduce the required deep geological information and lithology parameters from seismic records and a small amount of available logging information. As it is known, accurate geological information and lithology parameters are of vital importance for the reservoir identification and hydrocarbon detection, especially, on the hidden reservoir exploitation, requiring more precise and accurate inversion result than general application. To address the issue with signal processing methods, effectively inversion theory must be improved.
First of all, the dissertation studies suchαstable distribution characteristic as theoretical basis, property, influence of key parameters on the distribution and some important numerical characteristic, and then, differences between non-Gaussianαstable distribution processing and the ideal Gaussian distribution are extracted.
After that, pre-stack inversion theory as well as basic elastic impedance inversion, extended elastic impedance inversion and generalized elastic impedance inversion are studied, pre-stack seismic inversion steps are established.
In the last part of this dissertation,αstable distribution signal processing theory is applied to pre-stack seismic inversion, and a new pre-stack seismic inversion algorithm based on fractional lower order statistics theory is proposed. The algorithm proposed in the dissertation was performed in practical pre-stack seismic inversion application successfully, which demonstrat the algorithm is practical and effective in pre-stack seismic inversion.
The dissertation abandoned the traditional assumption that seismic signal obeys the ideal Gaussian distribution, and successfully appliedαstable distribution to pre-stack seismic inversion. The main achievements of the dissertation can be summarized as follows:
⑴Proposed a method of observing dynamic sample variance curve to determine whether the seismic signal obeys Gaussian distribution or non-Gaussianαstable distribution. As non-Gaussianαstable distribution signal does not own limited dynamic sample variance value theoretically, comparing the the dynamic sample variance curves of Gaussian distribution and non-Gaussianαstable distribution is a convenient way to distinguish them. In fact, real seismic data subjects to non-Gaussian stable distribution rather Gaussian distribution.
⑵Proposed a new pre-stack seismic inversion algorithm based on the assumption that seismic signal subjects to non-Gaussianαstable distribution. Different from Gaussian distribution, non-Gaussianαstable distribution does not have a second order moment, the classic signal processing methods such as least sequares algorithm do not work at all. Combining fractional lower order statistic theory and the convolution theory, this dissertation established a new objective function with least average l p norm of the inversion error, on this basis, proposed non-Gaussian stable distribution inversion algorithm and implementation steps.
引文
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[2]陈建江. AVO三参数反演方法研究:[博士学位论文].青岛:中国石油大学,2007
[3]岳碧波,彭真明,洪余刚等.基于粒子群优化算法的叠前角道集子波反演.地球物理学报, 2009, 52(12):3116-3123
[4]彭真明,李亚林,魏文阁等.粒子滤波非线性AVO反演方法.地球物理学报,2008, 51(4):1218-122
[5] K. I. Aki, P. G. Richards. Quantitative Seismology. New York: W. H. Freeman and Co., 1980. 226-308
[6] R. T. Shuey. A simplification of the Zoeppritz equations. Geophysics, 1985, 50(3): 609-614
[7] Whitcombe D.N. Elastic impedance normalization. Geophysics, 2002, 67(1), 60-62
[8] Whitcomble D.N, Connolly P.A, Reagan R.L, et al. Extended elastic impedance for fluid and lithology prediction. Geophysics, 2002, 67(1):63-67
[9]彭真明,肖慈珣,杨斌等.利用地震非线性参数重建声波测井曲线.石油物探,2000, 39(2):72-76
[10]彭真明,张启衡,龚奇.波阻抗反演中的全局寻优策略.物探化探计算技术,2003,25(2):151-156
[11]王克斌,彭真明,安鸿伟等.地震数据关联维的快速计算方法.物探化探计算技术,2000,22(3):225-228
[12]孙永梅,邱天爽.α稳定分布噪声下自适应信号处理的研究进展.信号处理,2004, 20(6):618-622
[13] Mittink S, Doganoglu T, Chenyao D. Computing the probability density function of the stable Paretion distribution, Mathematical and Computer Modelling, 1999, 29: 235-240
[14] M. Shao, C L. Nikias. Signal processing with fractional lower order moments: stable processes and their applications. Proceeding of the IEEE, July 1993, 81(7):986-1010
[15] A. Weron. Stable processes and measures: A Survey. in Probability Theory on Vector SpacesⅢ(S.Cambanis, ed.),Berlin: Springer, 1983, 306-364
[16] E. E .Kuruoglu. Signal Processing with fractional lower order moments: stable processes and their applications. Proceeding of the IEEE, 1993, 81(7): 987-1010
[17] Kidmose P. Methods for Blind Seqaration of Linear Mixtures of Signals with Heavy Tail Distributions. [Ph. D dissertion]. Denmark: technical University of Denmark,2001
[18]陈良均,朱庆棠.随机过程及其应用.北京:高等教育出版社,2006,47-48
[19]郭文强.稳定分布噪声下的盲信号处理方法及应用研究:[博士学位论文].大连:大连理工大学,2007
[20] J. G. Gonzalez, J. L. Paredes, G. R. Arce. Zero-order statistics: a mathematical framework for the processing and characterization of very impulsive signals. IEEE Transactions on Signal Processing, 2006, 54(10):3939-3851
[21] L.T. Joon. System Identification Using Novel Adaptive Filter Structures.[Ph.D dissertion]. Cambridge: University of Cambridge, 1995
[22] L. Devrorye. Random variate generation for unimodal and monotone desities. Computing, 1984, 32(1):43-68
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