基于频谱分析技术的频散AVO反演研究
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摘要
地震波在含流体弹性孔隙介质中的传播可以用Gassmann模型来描述,基于Gassmann理论的流体替换是多数地震流体检测技术的基础。但是近年来实验室模拟和理论研究均表明含流体填充介质常常导致地震波发生不同程度的频散和衰减,实际地震资料也可能在某一频率范围内存在频散特征。Gassmann理论忽略了这一现象,目前的AVO分析也没有考虑这一点。利用含烃储层导致地震波的频散,引起反射系数随频率变化这一性质可以区分不同流体填充情况下的地震响应。论文利用地震波的频散属性,研究了不同的频谱分析方法,并将频谱分析技术与AVO反演相结合,扩展Smith & Gidlow (1987)两项AVO反演近似式到频率域,研究基于频谱分析技术的地震波频散AVO反演,从叠前反射地震资料中提取地震波的频散属性。
在岩石物理模拟方面,论文综述了地震波在含流体介质中的传播理论,包括Gassmann理论、Biot理论和BISQ理论等,重点介绍了Chapman et al. (2003)提出的多尺度频散介质岩石物理模型(Chapman model)及其数值模拟。在实际地震资料处理方面,论文介绍了现代频谱分析技术在地震勘探中的发展现状及其在研究与储层有关的地震波频散现象中的应用,比较了短时傅立叶变换(STFT)、连续小波变换(CWT)以及Wigner-Ville分布(WVD)等多种频谱分析技术的优缺点。在此基础上,实现了一种新的与频率有关的地震属性,即对Smith & Gidlow (1987)两项AVO反演公式进行扩展,将反射系数替代为不同频率的振幅谱,视振幅谱为与频率有关的函数,对AVO反演公式在某一频率内进行泰勒级数展开,采用最小二乘方法求导获得频散程度,并用于理论模型和实际地震资料的频散程度的计算。
论文的主要工作和取得的成果有：
(1)分析对比了短时傅立叶变换(STFT)、连续小波变换(CWT)以及Wigner-Ville分布(WVD)等各种不同的频谱分析方法。短时傅立叶变换受到窗函数的制约导致了时间定位和频率分辨率的折中、连续小波变换通过小波函数的伸缩将信号分解到时间-尺度域,在高频时有较高的时间分辨率,但适合地震信号分析的Morlet小波并非正交小波函数,这导致了该方法在低频时时间分辨率并不高；
(2)重点研究和改进了Wigner-Ville分布时频分析。采用时间域和频率域平滑窗函数,即平滑伪Wigner-Ville分布(SPWVD)来消除多分量信号导致的交叉项的影响,探讨了平滑窗函数的选取对分辨率的影响,得出时间域平滑窗函数一般取地震零相位子波两个波谷之间的长度；而频率域窗函数的长度则取为时间域窗函数的两倍,这样在理论模型和实际地震资料的处理中均能得到较高的时频分辨率；
(3)为进一步提高能量聚集性,研究采用了时频重排算法(Reassignment Algorithm),该算法能在抑制交叉项的同时,显著提高了能量的聚集性,并在低频时有较高的时间分辨率,但该算法以时间来换取分辨率,运算速度缓慢,不适合于大量地震数据的处理,而SPWVD则是一种“性价比”较高的方法,不需要非常大的运算量就能获得比STFT和CWT更高的分辨率,适合大量地震数据处理,并将几种时频分析方法应用于川西坳陷含气砂岩导致的叠后地震数据的“低频阴影”检测和大港油田火成岩边界的确定；
(4)提出了一种新的描述地震波频散特征的地震属性。根据Smith和Gidlow(1987)提出的AVO近似公式,将反射系数替代为不同频率的振幅谱,并将振幅谱视为与频率有关的函数,扩展该AVO近似公式到频谱分解的振幅,然后在频率域内进行泰勒级数展开求导,推导出一套基于谱分析技术的频散AVO反演公式,定量的描述地震波频散的程度；
(5)用Aniseis软件包生成第三类AVO弹性和频散情况下的理论模型,将CWT和SPWVD两种频谱分析技术应用到理论模型的频散AVO反演流程。研究了不同时间尺度参数(Timescale),裂缝密度(Crack density)以及流体替换等影响下的频散AVO特征。得到时间尺度τ在5×10-3s到5×10-2s地震波频散较为明显,并且在τ为5×10-3s时,频散程度更强；而在低频(τ=10-6s)和高频(τ=100s)情况下频散现象不明显；对于不同的裂缝密度情况下,裂缝密度越高,频散越明显；
(6)将频散AVO反演方法应用于实际地震资料的处理,计算了北海某油田两条地震剖面的频散程度属性。将SPWVD与频散AVO反演相结合,先对叠后地震资料进行频谱分析,找出频率异常,再抽取频率异常位置的近偏移距叠前CMP道集进行频散AVO反演,通过频散AVO反演得到的结果消除了由于弹性界面波阻抗差异导致的强震幅能量团,只保留了由于储层填充流体导致的频散异常,并且避免了叠后地震资料叠加处理可能导致的虚假“频率异常”,所得到的结果更可靠。
裂缝孔隙型储层对地震波的频散和衰减特性是目前实际地震勘探中研究的热点和难点。目前虽然各种岩石物理模型在描述地震波频散特征上取得了较大的进展,但理论预测与实际地震资料所得到的结果仍然存在矛盾,地震波在含流体介质中传播的岩石物理理论仍在不断地完善。论文扩展了流体填充导致地震反射系数随频率变化这一观点,并推导了Smith & Gidlow两项AVO反演近似公式到频率域,以现代频谱分析技术为手段,从实际资料中提取了定量描述储层含流体所导致的地震波频散程度的属性,但还需通过更多的实际地震资料处理来验证并完善该方法及理论。
The transmission of seismic waves in porous elastic media saturated with fluids can be described using Gassmann model. Fluid substitution using Gassmann theory lies at the heart of most seismic fluid-detection methods. While Gassmann has proven to provide an excellent approximation, the elastic behaviour of fluid saturated rocks is often frequency-dependent, Considerable effort has been expended on laboratory studies and theoretical investigations with the goal of understanding this frequency dependence. Real seismic data may have this frequency dependence in certain frequency regime due to fluids saturation. It is attractive to try to use this property to discriminate different fluids with seismic data. But this is not accounted for in Gassmann theory and current AVO analysis. Using this frequency dependent property, I integrate modern spectral decomposition and AVO inversion together. First, I study different kinds of spectral decomposition techniques, and then extend Smith & Gidlow (1987)'s two-term approximate formula to frequency domain for frequency dependent AVO inversion. The purpose is to extract the dispersive property from pre-stack reflection data.
In the respect of rock physics, classical theories on the transmission of seismic waves in fluids saturated media are summarized including Gassmann theory, Biot theory and BISQ theory. Chapman model for the description of dispersive medium and numerical modeling is outlined in detail. In the respect of theoretical models and real seismic data processing, the development of modern spectral decomposition techniques and its application in the research of seismic wave dispersion. Three methods including Short Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT) and Wigner-Ville Distribution (WVD) based methods are carried out and compared with each other. Eventually CWT and SPWVD is used for synthetic model and real seismic data processing because of their high resolution and fast calculating speed. Based on spectral decomposition methods, a new seismic attribute for the description of seismic dispersion is presented by extending Smith & Gidlow's AVO inversion formula using Taylor series expansion in the frequency domain, and then the derivative of change rate of velocities of P wave and S wave, namely the magnitude of dispersions are obtained using least-squares method. At last, this new method is used for synthetic model and real seismic data processing.
The main work and achievement of this thesis contain:
(1)Analyze and compare different kinds of spectral decomposition methods including STFT, CWT, as well as WVD based methods. STFT produces time-frequency spectrum by taking Fourier transform over a chosen time window, which leads to a tradeoff between time localization and frequency resolution. Continuous wavelet transform decomposes signals to time-scale domain through stretch and shrink of wavelet function. It possesses high temporal resolution at high frequencies, but Morlet wavelet for seismic signal analysis is not orthogonal wavelet function, which leads to low temporal resolution at low frequencies;
(2)Focus on the research of Wigner-Ville distribution based methods. Use smoothed functions in time and frequency domain, namely smoothed pseudo Wigner-Ville distribution (SPWVD) to eliminate the cross-terms in multi-component signal. Discuss the impact for resolution at different smoothed window lengths, and find that giving a length of the zero-phase wavelet to time domain smoothed function and a length of twice as long as the time domain smoothed function to the frequency domain smoothed function, I get higher temporal and frequency resolutions for the processing of synthetic model and real seismic data;
(3)Use reassignment algorithm to further enhance the energy concentration in time-frequency domain. This algorithm is able to suppress cross-terms and significantly improve energy concentration simultaneously and has high temporal resolution at low frequencies. But high resolution is at the cost of computational time. It is not suitable for massive seismic data processing. Whereas SPWVD is a "cost-effective" approach, which does not need a large amount of calculation for obtain of higher resolutions than STFT and CWT. Eventually, I use these methods for detection of "low frequency shadow" caused by deep buried gas with post-stack seismic data in west Sichuan Depression and determination of igneous reservoir border in Dagang Oilfield;
(4)Present a new frequency dependent seismic attribute for description of seismic dispersion in fluids saturated reservoir. According to Smith & Gidlow's two-term AVO approximate formula, I replace the reflection coefficient with spectral amplitude at different frequencies, and consider spectral amplitude as a function of frequency dependent. And then expand the AVO approximate formula into Taylor series and use the least square inversion for the calculation of derivatives. I derive a set of frequency dependent AVO inversion formula based on modern spectral decomposition techniques. It can be used for quantitative description of magnitude of dispersion of seismic wave;
(5)Use Aniseis package to generate ClassⅢAVO synthetic models at elastic case and dispersive case, incorporate CWT and SPWVD for the frequency dependent AVO inversion process of synthetic models. I study the frequency dependent AVO characteristics under different timescale parameter, Crack density, as well as fluid substitution and find that time scaleτbetween 5×10-3s and 5×10-2s gives rise to high seismic dispersion. Seismic wave dispersion is more obvious whenτhas a value of 5×10-3s, whereas dispersion is unconspicuous at low-frequency (τ=10-6s) and high-frequency (τ=100s) cases. For different crack density, higher crack density gives rise to higher magnitude of dispersion of seismic wave;
(6)Apply frequency dependent AVO inversion to real seismic data processing; calculate the magnitude of dispersion of two seismic sections in certain oilfield of North Sea. I combine modern spectral analysis techniques with frequency dependent AVO inversion. First, I use SPWVD for post-stack seismic data to find out the frequency anomalies. Then I extract the pre-stack CMP gathers at the location of frequency anomalies for frequency dependent AVO inversion. The result shows that the frequency anomalies caused by elastic interfaces disappear and those caused by dispersive interfaces are reserved. Another advantage of this method is that I get a more reliable result which cannot obtain by only dealing with post-stack seismic data because of the stacking-caused "frequency shadows", rather than the real earth response.
The dispersion and attenuation of seismic wave in fractured porous reservoir is a hot and difficult research area in seismic exploration. At present, considerable progress of rock physics modeling has been achieved in describing the characteristics of seismic dispersion. However, there are still certain contradictions between theoretical predictions and actual observations. The theory of seismic wave transmission in fluids saturated media are still being developed and consummated. Fluid-related dispersion and attenuation gives rise to a frequency-dependent reflection coefficient, this thesis extends this idea and deduces Smith & Gidlow's AVO inversion formula to frequency domain, combines spectral decomposition techniques for quantitative description of magnitude of seismic dispersion in reservoirs. But it needs more practical seismic data processing to validate and refine the method and theory.
在岩石物理模拟方面,论文综述了地震波在含流体介质中的传播理论,包括Gassmann理论、Biot理论和BISQ理论等,重点介绍了Chapman et al. (2003)提出的多尺度频散介质岩石物理模型(Chapman model)及其数值模拟。在实际地震资料处理方面,论文介绍了现代频谱分析技术在地震勘探中的发展现状及其在研究与储层有关的地震波频散现象中的应用,比较了短时傅立叶变换(STFT)、连续小波变换(CWT)以及Wigner-Ville分布(WVD)等多种频谱分析技术的优缺点。在此基础上,实现了一种新的与频率有关的地震属性,即对Smith & Gidlow (1987)两项AVO反演公式进行扩展,将反射系数替代为不同频率的振幅谱,视振幅谱为与频率有关的函数,对AVO反演公式在某一频率内进行泰勒级数展开,采用最小二乘方法求导获得频散程度,并用于理论模型和实际地震资料的频散程度的计算。
论文的主要工作和取得的成果有：
(1)分析对比了短时傅立叶变换(STFT)、连续小波变换(CWT)以及Wigner-Ville分布(WVD)等各种不同的频谱分析方法。短时傅立叶变换受到窗函数的制约导致了时间定位和频率分辨率的折中、连续小波变换通过小波函数的伸缩将信号分解到时间-尺度域,在高频时有较高的时间分辨率,但适合地震信号分析的Morlet小波并非正交小波函数,这导致了该方法在低频时时间分辨率并不高；
(2)重点研究和改进了Wigner-Ville分布时频分析。采用时间域和频率域平滑窗函数,即平滑伪Wigner-Ville分布(SPWVD)来消除多分量信号导致的交叉项的影响,探讨了平滑窗函数的选取对分辨率的影响,得出时间域平滑窗函数一般取地震零相位子波两个波谷之间的长度；而频率域窗函数的长度则取为时间域窗函数的两倍,这样在理论模型和实际地震资料的处理中均能得到较高的时频分辨率；
(3)为进一步提高能量聚集性,研究采用了时频重排算法(Reassignment Algorithm),该算法能在抑制交叉项的同时,显著提高了能量的聚集性,并在低频时有较高的时间分辨率,但该算法以时间来换取分辨率,运算速度缓慢,不适合于大量地震数据的处理,而SPWVD则是一种“性价比”较高的方法,不需要非常大的运算量就能获得比STFT和CWT更高的分辨率,适合大量地震数据处理,并将几种时频分析方法应用于川西坳陷含气砂岩导致的叠后地震数据的“低频阴影”检测和大港油田火成岩边界的确定；
(4)提出了一种新的描述地震波频散特征的地震属性。根据Smith和Gidlow(1987)提出的AVO近似公式,将反射系数替代为不同频率的振幅谱,并将振幅谱视为与频率有关的函数,扩展该AVO近似公式到频谱分解的振幅,然后在频率域内进行泰勒级数展开求导,推导出一套基于谱分析技术的频散AVO反演公式,定量的描述地震波频散的程度；
(5)用Aniseis软件包生成第三类AVO弹性和频散情况下的理论模型,将CWT和SPWVD两种频谱分析技术应用到理论模型的频散AVO反演流程。研究了不同时间尺度参数(Timescale),裂缝密度(Crack density)以及流体替换等影响下的频散AVO特征。得到时间尺度τ在5×10-3s到5×10-2s地震波频散较为明显,并且在τ为5×10-3s时,频散程度更强；而在低频(τ=10-6s)和高频(τ=100s)情况下频散现象不明显；对于不同的裂缝密度情况下,裂缝密度越高,频散越明显；
(6)将频散AVO反演方法应用于实际地震资料的处理,计算了北海某油田两条地震剖面的频散程度属性。将SPWVD与频散AVO反演相结合,先对叠后地震资料进行频谱分析,找出频率异常,再抽取频率异常位置的近偏移距叠前CMP道集进行频散AVO反演,通过频散AVO反演得到的结果消除了由于弹性界面波阻抗差异导致的强震幅能量团,只保留了由于储层填充流体导致的频散异常,并且避免了叠后地震资料叠加处理可能导致的虚假“频率异常”,所得到的结果更可靠。
裂缝孔隙型储层对地震波的频散和衰减特性是目前实际地震勘探中研究的热点和难点。目前虽然各种岩石物理模型在描述地震波频散特征上取得了较大的进展,但理论预测与实际地震资料所得到的结果仍然存在矛盾,地震波在含流体介质中传播的岩石物理理论仍在不断地完善。论文扩展了流体填充导致地震反射系数随频率变化这一观点,并推导了Smith & Gidlow两项AVO反演近似公式到频率域,以现代频谱分析技术为手段,从实际资料中提取了定量描述储层含流体所导致的地震波频散程度的属性,但还需通过更多的实际地震资料处理来验证并完善该方法及理论。
The transmission of seismic waves in porous elastic media saturated with fluids can be described using Gassmann model. Fluid substitution using Gassmann theory lies at the heart of most seismic fluid-detection methods. While Gassmann has proven to provide an excellent approximation, the elastic behaviour of fluid saturated rocks is often frequency-dependent, Considerable effort has been expended on laboratory studies and theoretical investigations with the goal of understanding this frequency dependence. Real seismic data may have this frequency dependence in certain frequency regime due to fluids saturation. It is attractive to try to use this property to discriminate different fluids with seismic data. But this is not accounted for in Gassmann theory and current AVO analysis. Using this frequency dependent property, I integrate modern spectral decomposition and AVO inversion together. First, I study different kinds of spectral decomposition techniques, and then extend Smith & Gidlow (1987)'s two-term approximate formula to frequency domain for frequency dependent AVO inversion. The purpose is to extract the dispersive property from pre-stack reflection data.
In the respect of rock physics, classical theories on the transmission of seismic waves in fluids saturated media are summarized including Gassmann theory, Biot theory and BISQ theory. Chapman model for the description of dispersive medium and numerical modeling is outlined in detail. In the respect of theoretical models and real seismic data processing, the development of modern spectral decomposition techniques and its application in the research of seismic wave dispersion. Three methods including Short Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT) and Wigner-Ville Distribution (WVD) based methods are carried out and compared with each other. Eventually CWT and SPWVD is used for synthetic model and real seismic data processing because of their high resolution and fast calculating speed. Based on spectral decomposition methods, a new seismic attribute for the description of seismic dispersion is presented by extending Smith & Gidlow's AVO inversion formula using Taylor series expansion in the frequency domain, and then the derivative of change rate of velocities of P wave and S wave, namely the magnitude of dispersions are obtained using least-squares method. At last, this new method is used for synthetic model and real seismic data processing.
The main work and achievement of this thesis contain:
(1)Analyze and compare different kinds of spectral decomposition methods including STFT, CWT, as well as WVD based methods. STFT produces time-frequency spectrum by taking Fourier transform over a chosen time window, which leads to a tradeoff between time localization and frequency resolution. Continuous wavelet transform decomposes signals to time-scale domain through stretch and shrink of wavelet function. It possesses high temporal resolution at high frequencies, but Morlet wavelet for seismic signal analysis is not orthogonal wavelet function, which leads to low temporal resolution at low frequencies;
(2)Focus on the research of Wigner-Ville distribution based methods. Use smoothed functions in time and frequency domain, namely smoothed pseudo Wigner-Ville distribution (SPWVD) to eliminate the cross-terms in multi-component signal. Discuss the impact for resolution at different smoothed window lengths, and find that giving a length of the zero-phase wavelet to time domain smoothed function and a length of twice as long as the time domain smoothed function to the frequency domain smoothed function, I get higher temporal and frequency resolutions for the processing of synthetic model and real seismic data;
(3)Use reassignment algorithm to further enhance the energy concentration in time-frequency domain. This algorithm is able to suppress cross-terms and significantly improve energy concentration simultaneously and has high temporal resolution at low frequencies. But high resolution is at the cost of computational time. It is not suitable for massive seismic data processing. Whereas SPWVD is a "cost-effective" approach, which does not need a large amount of calculation for obtain of higher resolutions than STFT and CWT. Eventually, I use these methods for detection of "low frequency shadow" caused by deep buried gas with post-stack seismic data in west Sichuan Depression and determination of igneous reservoir border in Dagang Oilfield;
(4)Present a new frequency dependent seismic attribute for description of seismic dispersion in fluids saturated reservoir. According to Smith & Gidlow's two-term AVO approximate formula, I replace the reflection coefficient with spectral amplitude at different frequencies, and consider spectral amplitude as a function of frequency dependent. And then expand the AVO approximate formula into Taylor series and use the least square inversion for the calculation of derivatives. I derive a set of frequency dependent AVO inversion formula based on modern spectral decomposition techniques. It can be used for quantitative description of magnitude of dispersion of seismic wave;
(5)Use Aniseis package to generate ClassⅢAVO synthetic models at elastic case and dispersive case, incorporate CWT and SPWVD for the frequency dependent AVO inversion process of synthetic models. I study the frequency dependent AVO characteristics under different timescale parameter, Crack density, as well as fluid substitution and find that time scaleτbetween 5×10-3s and 5×10-2s gives rise to high seismic dispersion. Seismic wave dispersion is more obvious whenτhas a value of 5×10-3s, whereas dispersion is unconspicuous at low-frequency (τ=10-6s) and high-frequency (τ=100s) cases. For different crack density, higher crack density gives rise to higher magnitude of dispersion of seismic wave;
(6)Apply frequency dependent AVO inversion to real seismic data processing; calculate the magnitude of dispersion of two seismic sections in certain oilfield of North Sea. I combine modern spectral analysis techniques with frequency dependent AVO inversion. First, I use SPWVD for post-stack seismic data to find out the frequency anomalies. Then I extract the pre-stack CMP gathers at the location of frequency anomalies for frequency dependent AVO inversion. The result shows that the frequency anomalies caused by elastic interfaces disappear and those caused by dispersive interfaces are reserved. Another advantage of this method is that I get a more reliable result which cannot obtain by only dealing with post-stack seismic data because of the stacking-caused "frequency shadows", rather than the real earth response.
The dispersion and attenuation of seismic wave in fractured porous reservoir is a hot and difficult research area in seismic exploration. At present, considerable progress of rock physics modeling has been achieved in describing the characteristics of seismic dispersion. However, there are still certain contradictions between theoretical predictions and actual observations. The theory of seismic wave transmission in fluids saturated media are still being developed and consummated. Fluid-related dispersion and attenuation gives rise to a frequency-dependent reflection coefficient, this thesis extends this idea and deduces Smith & Gidlow's AVO inversion formula to frequency domain, combines spectral decomposition techniques for quantitative description of magnitude of seismic dispersion in reservoirs. But it needs more practical seismic data processing to validate and refine the method and theory.
引文
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[29]Holzner, R., Eschle, P., Zurcher, H., et al., Applying microtremor analysis to identify hydrocarbon reservoirs, First Break,2005,23:41-48.
[30]Bradford, J.H. and Wu, Y, Instantaneous spectral analysis:Time-frequency mapping via wavelet matching with application to contaminated-site characterization by 3D GPR. The Leading Edge,2007,26(8):1018-1023.
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[32]高静怀,陈文超,李幼铭,田芳.广义S变换与薄互层地震响应分析.2003,46(4)：526-532
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[42]Wu X., and Liu T., Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner-Ville distribution, Journal of Applied Geophysics,2009,68(3):386-393.
[43]Wu X., and Liu, T., Analysis of seismic spectral attenuation based on Wigner-Ville distribution for sandstone reservoir characterization——Case Study from West Sichuan Depression, China, Journal of Seismic Exploration,2010,19:69-85.
[44]吴小羊,刘天佑.基于时频重排的地震信号Wigner-Ville分布时频分析.石油地球物理勘探,2009,44(2)：201-205.
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