非线性地震属性关联维的研究与应用
摘要
目前,从地震道提取属性参数是地震资料处理中的一种主要的技术方法。地震道从本质上讲是一个典型的非线性时间序列,用非线性的技术方法进行地震道属性参数提取才会对地震信息的合理利用更有利。
本文是在非线性理论的基础上对非线性地震属性参数关联维的研究。首先对动力学非线性系统的混沌、分形特征以及地震信号非线性特征等理论进行了分析。表明地震信号是混沌的时间序列,具有混沌与分形的特征。其次在分析了地震属性,包括属性的分类,属性的提取之后,利用非线性的理论对地震数据进行非线性地震属性提取。以分形技术为基础,文章主要研究了地震道的分维数关联维的求取原理与过程。由于地震道是一个时间序列,一般时间序列主要是在时间域或变换域中进行研究,而在混沌时间序列处理中,各种不变量的计算都是在相空间中进行,因此相空间重构是混沌时间序列处理中非常重要的第一步。所以文章对相空间重构理论以及对相空间重构的参数的计算方法进行了分析。为分形维数关联维的求解提供了理论基础。在对实际的地震资料处理求取关联维时,一方面针对地震数据本身的特点,文中分析确定了计算中各个参数的取值情况。另一方面由于地震数据量非常大,利用传统的计算方法,时间太久。基于这个问题,分析了在误差允许的范围内,采用人机结合的方式以及对关联积分的计算进行改进以求取地震道的关联维数。在算法中我们采取了加窗与不加窗两种计算方式。
文中首先运用该方法针对不同的理论模型进行数值试验。目的是分析这个非线性地震属性参数关联维在不同地质状况的响应情况。结果表明参数关联维能明显地反映地质状况。其次文章分析了利用此改进后的算法对实际地震资料求解关联维这个地震属性参数。求取的关联维结果能较好地与测井、地质资料吻合。所以说在地震勘探中,关联维数的研究对地震资料的处理与解释提供了较好的判断依据。
At present, the seismic attribute extraction from the seismic trace is a main technical method in seismic data processing. The seismic trace essentially is a typical nonlinear time series. We use the seismic information reasonably by using the nonlinear method to extract the seismic attribute.
We study the nonlinear seismic attribute correlation dimension based on the theory of nonlinear in this paper. And we first analyze chaotic characteristics and fractal characteristics of the dynamic Nonlinear System and the nonlinear characteristics of seismic signals. It Show that the seismic signal is chaotic time series with chaotic and fractal characteristics. Secondly we extract non-linear seismic attributes from seismic data by using non-linear theory after the analysis of seismic attributes, including the classification of seismic attributes and extraction of seismic attributes. This paper mainly studied the calculation principle and calculation process of seismic correlation dimension based on Fractal Technology. Phase space reconstruction is a very important first step in dealing with the chaotic time series. Because seismic is a time series and the general time-series mostly are studied in the time domain or transform domain; but all non-variable must be counted in phase space in chaotic time series processing. We analyze phase space reconstruction theory and the calculation of the phase space reconstruction parameters in the article. It provides a theoretical basis for solving the correlation dimension. On the one hand we analyze to determine the parameters in the calculation because of the characteristics of the earthquake data itself. On the other hand because of seismic data is very large it takes a long time for using the traditional method in the calculation. When we calculate the correlation dimension in the actual seismic data processing. For this problem we make use of man-machine combination within the permitted error and improve the calculation of correlation integral to obtain the correlation dimension of seismic traces. We adopt the calculation with window and the calculation without window in the algorithm.
In order to analyze the nonlinear seismic attribute correlation dimension response to different geological conditions, we first conduct numerical experiments using this method on different models in the paper. And The results show that the correlation dimension can clearly reflect the geological conditions. Second, we use the improved algorithm to calculate the seismic attribute correlation dimension in the actual seismic data processing. And the correlation dimension results consistent with the logging data and geological data. Therefore, the research of the correlation dimension can provide a better basis to judge in the processing and interpretation of seismic data in seismic exploration.
本文是在非线性理论的基础上对非线性地震属性参数关联维的研究。首先对动力学非线性系统的混沌、分形特征以及地震信号非线性特征等理论进行了分析。表明地震信号是混沌的时间序列,具有混沌与分形的特征。其次在分析了地震属性,包括属性的分类,属性的提取之后,利用非线性的理论对地震数据进行非线性地震属性提取。以分形技术为基础,文章主要研究了地震道的分维数关联维的求取原理与过程。由于地震道是一个时间序列,一般时间序列主要是在时间域或变换域中进行研究,而在混沌时间序列处理中,各种不变量的计算都是在相空间中进行,因此相空间重构是混沌时间序列处理中非常重要的第一步。所以文章对相空间重构理论以及对相空间重构的参数的计算方法进行了分析。为分形维数关联维的求解提供了理论基础。在对实际的地震资料处理求取关联维时,一方面针对地震数据本身的特点,文中分析确定了计算中各个参数的取值情况。另一方面由于地震数据量非常大,利用传统的计算方法,时间太久。基于这个问题,分析了在误差允许的范围内,采用人机结合的方式以及对关联积分的计算进行改进以求取地震道的关联维数。在算法中我们采取了加窗与不加窗两种计算方式。
文中首先运用该方法针对不同的理论模型进行数值试验。目的是分析这个非线性地震属性参数关联维在不同地质状况的响应情况。结果表明参数关联维能明显地反映地质状况。其次文章分析了利用此改进后的算法对实际地震资料求解关联维这个地震属性参数。求取的关联维结果能较好地与测井、地质资料吻合。所以说在地震勘探中,关联维数的研究对地震资料的处理与解释提供了较好的判断依据。
At present, the seismic attribute extraction from the seismic trace is a main technical method in seismic data processing. The seismic trace essentially is a typical nonlinear time series. We use the seismic information reasonably by using the nonlinear method to extract the seismic attribute.
We study the nonlinear seismic attribute correlation dimension based on the theory of nonlinear in this paper. And we first analyze chaotic characteristics and fractal characteristics of the dynamic Nonlinear System and the nonlinear characteristics of seismic signals. It Show that the seismic signal is chaotic time series with chaotic and fractal characteristics. Secondly we extract non-linear seismic attributes from seismic data by using non-linear theory after the analysis of seismic attributes, including the classification of seismic attributes and extraction of seismic attributes. This paper mainly studied the calculation principle and calculation process of seismic correlation dimension based on Fractal Technology. Phase space reconstruction is a very important first step in dealing with the chaotic time series. Because seismic is a time series and the general time-series mostly are studied in the time domain or transform domain; but all non-variable must be counted in phase space in chaotic time series processing. We analyze phase space reconstruction theory and the calculation of the phase space reconstruction parameters in the article. It provides a theoretical basis for solving the correlation dimension. On the one hand we analyze to determine the parameters in the calculation because of the characteristics of the earthquake data itself. On the other hand because of seismic data is very large it takes a long time for using the traditional method in the calculation. When we calculate the correlation dimension in the actual seismic data processing. For this problem we make use of man-machine combination within the permitted error and improve the calculation of correlation integral to obtain the correlation dimension of seismic traces. We adopt the calculation with window and the calculation without window in the algorithm.
In order to analyze the nonlinear seismic attribute correlation dimension response to different geological conditions, we first conduct numerical experiments using this method on different models in the paper. And The results show that the correlation dimension can clearly reflect the geological conditions. Second, we use the improved algorithm to calculate the seismic attribute correlation dimension in the actual seismic data processing. And the correlation dimension results consistent with the logging data and geological data. Therefore, the research of the correlation dimension can provide a better basis to judge in the processing and interpretation of seismic data in seismic exploration.
引文
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[2]王安良,杨春信.评价奇怪吸引子分形特征的Grassberger-Procaccia算法[J].物理学报. 2002, (12): 2719-2728.
[3]李琼.复杂储层地震预测理论及方法研究[D].成都成都理工大学,2007,
[4]安鸿伟.混沌动力学与地震油储信息检测方法[D].成都成都理工学院,2002
[5]蒋加钰,段玉顺.分形理论在油气检测中的应用[J].石油物探,1995,34(1):47-51.
[6]李正文,李琼.油气储集层裂缝非线性预测技术及应用研究「J」.石油地球物理勘探,2003,38(1):48一52.
[7]周越,杨杰.求解关联维数的快速算法研究[J].电子学报. 2002, (10): 1526-1529.
[8]温晓通,孟丽艳,朱劲松.一种非线性时间序列的关联维快速算法[J].北京师范大学学报(自然科学版). 2005, (04): 358-361.
[9]王克斌,彭真明,杨旭明,安鸿伟.地震数据关联维的快速计算方法[J].物探化探计算技术,2000,22(3):225-228.
[10]刘适达、刘适式.地球物理中的混沌[M].长春:东北师范大学出版社,1999年10月.
[11]黄润生,混沌及其应用[M].武汉:武汉大学出版社.2000
[12]陆基孟等,地震勘探原理[M].北京:石油工业出版社.l993
[13]于青.关联维数计算的分析研究[J].天津理工学院学报. 2004, (04): 60-62.
[14]李夕海,刘代志,张斌.基于重采样的混沌时间序列相空间重构研究[J].信号处理. 2006, (02): 248-251.
[15]谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京:科学出版社,1998.
[16]汪富泉,罗朝盛,陈国先.G-P算法的改进及应用[J].计算物理, 1993, 10( 3) : 345
[17]李庆忠.怎样正确对待分形、分维技术[J].石油地球物理勘探,1996,33(1):136一161.
[18]李正文,李琼.岩性储集层的混沌识别技术研究[J].矿物岩石,1999,19(2):81一85
[19]罗朝盛,汪富泉.地震信号的能量维数及其在油气勘探中的应用[J].杭州:杭州应用技术工程学院学报,1999,11(1,2):11一15.
[20]吴大奎.分形、混沌、突变论在油气预测中的应用[D].成都:成都理工学院,1995
[21]刘希强,李红,郑建常等.非线性方法在地球物理研究中的应用综述和展望[J].国际地震动态,2000,(5):5一12.
[22]罗芳琼,吴春梅.时间序列分析的理论与应用综述[J].柳州师专学报,2009,24(3):26-30
[23]韩敏.混沌时间序列预测理论与方法[M].北京:中国水利水电出版社,2007
[24]张雨.时间序列的混沌和符号分析及实践[M].长沙:国防科技大学出版社,2007.3
[25]刘式达,梁福明,刘式适,辛国君。自然科学中的混沌和分形[M].北京:北京大学出版社,2003.11
[26]陈颙等.分形与混沌理论在地球科学中的应用[M].学术出版社,1991
[27]刘式达.地球系统模拟和混沌时间序列[J].地球物理学报,1990,3
[28]何光明等.分形理论在油气检测的尝试[J].石油地球物理勘探,1993,1.27(6):753一756
[29]党建武,黄建国.基于G.P算法的关联维计算中参数取值的研究[J].计算机应用研究. 2004, (01): 48-51.
[30]杨志家,赵光宙.关于关联积分和关联维[J].浙江大学学报[J].2000,34(5):523-526.
[31] Rosenstein M T, Collins J J, De L C, et al. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena. 1993, 65(1-2): 117-134.
[32]李正文.地震勘探资料解释[M].地质出版社,1988。
[33]刘企英.利用地震信息进行油气预测[M].北京:石油工业出版社,1994.
[34]安鸿伟、李正文、许强.非线性地震信息油气检测[J].2000地球物理年会,中国地质大学出版社.
[35]王克斌,彭真明,杨旭明,安鸿伟.地震数据关联维的快速计算方法[J].物化探计算技术.2003,22(3):36-42
[36]洪时中.非线性时间序列分析的最新进展及其在地球科学中的应用前景[J].地球科学进展.1999,12:45-51
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