三维地震数据复小波频谱分析技术
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摘要
经过几十年的勘探开发，我国陆上东部油区勘探开发程度渐高，油气勘探已进入复杂油气储层领域，已投入开发的大型老油田也多已进入高含水期；勘探程度相对较低的中西部复杂地表区油气藏已逐渐成为未来主要勘探目标。新的勘探开发形势对传统的地球物理技术提出了严峻的挑战。
我国陆上复杂油气储层包括薄互层砂岩储层、碳酸盐岩储层以及各类特殊岩性体储集层。复杂储层油气藏是今后重要的勘探领域之一。薄互层砂岩储层的特点是分布面积大、丰度低、渗透率差。这类油气藏主要有松辽盆地长垣两侧和松南地区岩性油藏、鄂尔多斯中生界岩性油藏和上古生界岩性气藏、川西北浅层岩性气藏等，需要采用高新技术，识别主砂带、裂缝发育区，查明岩性圈闭。碳酸盐岩油气藏主要分布在四川盆地、鄂尔多斯盆地下古生界以及塔里木盆地台盆区。这类油气藏的特点是储集空间为碳酸盐岩缝洞和孔隙，非均质性强。勘探的关键是确定碳酸盐岩溶洞型储层内幕及风化壳孔、洞、缝系统的空间展布。复杂储层预测技术具有广阔的应用前景。
频谱分析技术在理论上主要是依据薄层反射的调谐原理。根据该原理，对于厚度小于四分之一波长的薄层而言，在时间域，随着薄层厚度的增加，地震反射振幅逐渐增加。当薄层厚度增加至四分之一波长的调谐厚度时，反射振幅达到最大值，随着薄层厚度的增加反射振幅逐渐减小。时间域的最大反射振幅值，对应着频率域的最大振幅能量值。由薄层调谐引起的振幅谱的干涉特征取决于薄层的声学特征及其厚度。
频谱分析技术是一项基于频率的储层解释技术，它展现给我们的是一种全新的地震解释方法。通过离散傅里叶变换或复小波变换将地震数据由时间域转换到频率域，转换后计算得到振幅谱，解释人员不但能从剖面上，而且能从平面上看到薄层干涉特征。这种特殊的处理技术，我们定义为三维地震资料的频谱分析处理技术。
2006年下半年发表的文章中仍然大多采用短时傅里叶变换的方法进行频谱分析，但是，若原始地震记录主频太低，识别地层的时间厚度是一个等效厚度，即多个薄层的总体效应。并且，只能定位准确到时窗时间位置，而无法确定时窗中任一时间的时间位置。
作者提出了复小波频谱分析方法，经过该方法得到的3D地震分频数据体，可进行全3D解释(包括水平切片的解释)。可以识别岩性圈闭和地层圈闭，并检测小的不连续体。该方法即具备离散频率能量体(频谱分解技术)特点，又有时间定位准确(而传统频谱分解技术只能做到小时窗时间定位准确)。
复小波变换可以突出小波变换的局部化特性，避免窗口傅里叶变换过程中面临的窗函数选择，窗口大小选择的繁复问题，且复小波变换克服了窗口傅里叶由于窗口滑动造成的计算量过大的问题。结果表明复小波变换频谱分析技术相对窗口傅里叶变换有更高的分辨率，对有利储层的频谱特征有更好的反映。
本文首先分析了希尔伯特变换求取地震剖面瞬时特征的方法，进而介绍了用窗口傅里叶变换及复小波变换方法进行频谱分析的原理及算法实现，着重对比窗口傅里叶变换及复小波变换的频谱分析技术。
(1)介绍了复地震道分析法，希尔伯特变换的原理以及用希尔伯特变换进行复地震道分析，计算地震剖面瞬时特征。
(2)介绍了傅里叶变换，窗口傅里叶变换的原理，及基于窗口傅里叶变换方法的三维地震数据地震频谱分析技术，详细介绍了这种方法的算法及实现过程，分析计算结果，寻找改进方法。
(3)介绍了小波变换、复小波变换的原理，给出复小波的阐述定义，介绍了基于复小波变换方法的三维地震数据地震频谱分析技术，详细介绍了这种方法的算法及实现过程，分析对比该方法与傅里叶变换频谱分析的区别。
在分析傅里叶变换频谱分析技术的原理及实现算法的过程中，认识到了该方法存在的局限性，因为估算的地震振幅谱的重要特征是所选时窗函数的长度。如果所选时窗过短，振幅谱会与变换窗函数褶积，使其失去频率的局部化特征。另一方面，过短的时窗会使子波的旁瓣呈现为单一反射的假象。增加时窗长度，会改善频率的分辨率，但是，如果所选时窗过长，时窗内的多个反射会使振幅谱以槽痕为特征，很难分清单个反射的振幅谱特征。以傅里叶变换相关算法的时窗问题，会使振幅谱的估算产生偏差。由于在实际运用中，难以选择时窗的长度，而且无法定量分析时窗长度产生的偏差，以小波变换为基础的频谱分析技术成为了地震解释及储层预测的重要工具，在很多实际应用中发挥更大的作用。
本文采用复小波分析方法进行对地震信号频谱分析，选择morlet复小波，对地震信号进行复小波变换，并将尺度域转换到频率域，获得不同频率的频谱特征水平切片。并用理论模型说明了复小波频谱分析精度明显高于傅里叶变换的频谱分析，最后对新疆某油田及江汉盆地谢凤桥地区的三维地震实际资料进行了处理，结果表明复小波频谱分析能细致地反映储层的分布、位置及形态。
After decades of exploration and exploitation of land in eastern China, oil exploration anddevelopment degree grows gradually. Hydrocarbon exploration has entered the complexreservoir area, large oil fields which have been put into the development have almost entered thehigh water content period. Since exploration of the central and western complex surface area isin a relatively low level, reservoir has gradually become the main exploration targets. Newsituation in the exploration and development presented a serious challenge to the traditionalgeophysical technology.
China's land-based oil and gas complex reservoir includes thin interbedded sandstonereservoir, carbonate lithology reservoir and a variety of special lithology reservoir. Complexreservoir is now important for the exploration area. Thin interbedded sandstone reservoir ischaracterized by large area distribution, low abundance and worse permeability. Such reservoirsare the main sides of Songliao Basin Placanticline, Songnan area lithology reservoir, OrdosMesozoic lithology reservoir and Upper Paleozoic lithology gas reservoir, northwest Sichuanshallow gas reservoir. High technology is needed for the identification of the main belt andfracture zones, identifying stratigraphic trap, looking for confections in low-grade reserior.Carbonate reservoirs are mainly distributed in Sichuan, the Ordos Basin and Tarim Basin. Suchreservoirs are characterized that reservoir space for carbonate fracture-hole and porosity and thepowerful inhomogeneity. The key to exploration is to determine carbonate reservoir insider caveand the weathering crust hole, cave, slit the spatial distribution. Complex reservoir predictiontechnology has broad application prospects.
Spectrum analysis technology in theory is mainly based on the thin-layer reflection tuningprinciple. According to the theory, for the thin layer whose thickness is less than one fourth ofthe wavelength, in the time domain, with growth of the thickness of the thin, seismic reflectionamplitude gradually increases. When the thickness increases to a quarter wavelength tunablethickness, the amplitude of reflection come to the maximum value. With the increase in thethickness of thin, reflection amplitude decreased gradually. Time domain reflection amplitude ofthe greatest value, which corresponds to the frequency domain amplitude of the largest energyvalue. Thin tuning caused by the amplitude spectrum interference depends on the characteristicsof the acoustic characteristics of thin and its thickness.
Spectrum analysis is an interpretation of reservoir technology which based on the frequency. It demonstrated to us a new seismic interpretation methods. Discrete Fourier transform orcomplex wavelet transform seismic data from the time domain into the frequency domain.Conversion calculated amplitude spectrum. The staff can see thin interference characteristics notonly from explained profile, but also from the plane. Such special treatment technology, wedefined as three-dimensional seismic data spectrum analysis techniques. Papers published in thesecond half of 2006 still mostly use short-time Fourier transform method for spectrum analysis.However, if the main frequency of the original seismic record is low, identifying stratigraphicthickness of the time is an equivalent thickness, which is the effects of overall number of thins.Moreover, with this method, the accurate positioning is only the time of window,but it can notestablish the accurate positioning in the window. The author presented a method of complexwavelet spectrum analysis, the result of the method of 3D seismic data in different frequency,full 3D explanation (including horizontal slice explanation)become possible. It can identifylithology and stratigraphic trap, and detect small incontinuity. The methods that have discretefrequency energy body (spectral decomposition techniques) characteristics, have timepositioning accuracy (traditional spectral decomposition technology can only get the timepositioning of the window). Complex wavelet transform highlightings local characteristics ofwavelet transform, which can avoid facing the process of selecting the window function and thesizes of time window when using WFT. Complex wavelet transform overcome the calculationoverload problem caused by sliding window in WFT. The results showed the complex wavelettransform spectrum analysis techniques have higher resolution than WFT. The spectrum offavorable reservoir characteristics is better reflected.
This paper begins with complex seismic data transformation based on Hilbert transform toget seismic instantaneous features, then introduces the principle and algorithm of both the WFTand complex wavelet transform method for spectrum analysis, especially Contrasts WFT andcomplex wavelet transform spectrum analysis techniques.
(1) It introduced a complex seismic analysis, the principle of Hiibert transform. Complexseismic analysis Using Hilbert transform to compute seismic instantaneous features.
(2) It introduced the Fourier transform and window Fourier transform theory. It introduced3D seismic data spectrum analysis technology based on the window Fourier transform method.Details of algorithm and implementation process of this method was given. Through analyzingthe results, try to look for ways to improve this method.
(3) It introduced the wavelet transform and complex wavelet transform theory. Definition ofcomplex wavelet is given. It introduced 3D seismic data spectrum analysis technology based onthe complex wavelet transform. Details of algorithm and implementation process of this methodwas given. This method was compared with the window Fourier transform spectrum analysis toshow the difference.
During researching the principle and algorithm of Fourier transform spectrum analysis,we realized the limitations of the method, because the important feature of the estimate ofseismic amplitude spectrum is the length of selected time window function. If the selected timewindow is too short, the amplitude spectrum will proceed deconvolution with window function, which made this method lose local frequency characteristics. The other hand, too short a timewindow will make wavelet Sidelobe show for the illusion of a single reflection. Increasing thelength of time window will improve the frequency resolution, but if the time window is too long,flute marks for the features will show on the several reflection in the time window on theamplitude spectrum, so it is difficult to distinguish individual reflection amplitude spectrumcharacteristics. The time window problem of Fourier transform algorithm will make theamplitude spectrum deviate from the estimates. In practical application, it is difficult todetermine the length of the window, and it is impossible to get the quantitative analysis of thedeviation caused by the window length. Wavelet-based spectral analysis technology isbecoming the important tools of the seismic interpretation and reservoir prediction, In manypractical applications which play a greater role.
In this paper, we used complex wavelet method for seismic signal spectrum analysis, morletwavelet transforms. We transform the scale domain into the frequency domain and get thespectrum characteristics of different frequency. And the theoretical model to illustrate thecomplex wavelet analysis of spectrum has higher accuracy than the Fourier transform. Finally,the actual 3-D seismic data in the Xinjiang Oilfield and Jianghan Basin Xiefengqiao area wereproceeded with complex wavelet transform spectrum analysis. The results showed complexwavelet this method can reflect reservoir distribution, location and morphology.
我国陆上复杂油气储层包括薄互层砂岩储层、碳酸盐岩储层以及各类特殊岩性体储集层。复杂储层油气藏是今后重要的勘探领域之一。薄互层砂岩储层的特点是分布面积大、丰度低、渗透率差。这类油气藏主要有松辽盆地长垣两侧和松南地区岩性油藏、鄂尔多斯中生界岩性油藏和上古生界岩性气藏、川西北浅层岩性气藏等，需要采用高新技术，识别主砂带、裂缝发育区，查明岩性圈闭。碳酸盐岩油气藏主要分布在四川盆地、鄂尔多斯盆地下古生界以及塔里木盆地台盆区。这类油气藏的特点是储集空间为碳酸盐岩缝洞和孔隙，非均质性强。勘探的关键是确定碳酸盐岩溶洞型储层内幕及风化壳孔、洞、缝系统的空间展布。复杂储层预测技术具有广阔的应用前景。
频谱分析技术在理论上主要是依据薄层反射的调谐原理。根据该原理，对于厚度小于四分之一波长的薄层而言，在时间域，随着薄层厚度的增加，地震反射振幅逐渐增加。当薄层厚度增加至四分之一波长的调谐厚度时，反射振幅达到最大值，随着薄层厚度的增加反射振幅逐渐减小。时间域的最大反射振幅值，对应着频率域的最大振幅能量值。由薄层调谐引起的振幅谱的干涉特征取决于薄层的声学特征及其厚度。
频谱分析技术是一项基于频率的储层解释技术，它展现给我们的是一种全新的地震解释方法。通过离散傅里叶变换或复小波变换将地震数据由时间域转换到频率域，转换后计算得到振幅谱，解释人员不但能从剖面上，而且能从平面上看到薄层干涉特征。这种特殊的处理技术，我们定义为三维地震资料的频谱分析处理技术。
2006年下半年发表的文章中仍然大多采用短时傅里叶变换的方法进行频谱分析，但是，若原始地震记录主频太低，识别地层的时间厚度是一个等效厚度，即多个薄层的总体效应。并且，只能定位准确到时窗时间位置，而无法确定时窗中任一时间的时间位置。
作者提出了复小波频谱分析方法，经过该方法得到的3D地震分频数据体，可进行全3D解释(包括水平切片的解释)。可以识别岩性圈闭和地层圈闭，并检测小的不连续体。该方法即具备离散频率能量体(频谱分解技术)特点，又有时间定位准确(而传统频谱分解技术只能做到小时窗时间定位准确)。
复小波变换可以突出小波变换的局部化特性，避免窗口傅里叶变换过程中面临的窗函数选择，窗口大小选择的繁复问题，且复小波变换克服了窗口傅里叶由于窗口滑动造成的计算量过大的问题。结果表明复小波变换频谱分析技术相对窗口傅里叶变换有更高的分辨率，对有利储层的频谱特征有更好的反映。
本文首先分析了希尔伯特变换求取地震剖面瞬时特征的方法，进而介绍了用窗口傅里叶变换及复小波变换方法进行频谱分析的原理及算法实现，着重对比窗口傅里叶变换及复小波变换的频谱分析技术。
(1)介绍了复地震道分析法，希尔伯特变换的原理以及用希尔伯特变换进行复地震道分析，计算地震剖面瞬时特征。
(2)介绍了傅里叶变换，窗口傅里叶变换的原理，及基于窗口傅里叶变换方法的三维地震数据地震频谱分析技术，详细介绍了这种方法的算法及实现过程，分析计算结果，寻找改进方法。
(3)介绍了小波变换、复小波变换的原理，给出复小波的阐述定义，介绍了基于复小波变换方法的三维地震数据地震频谱分析技术，详细介绍了这种方法的算法及实现过程，分析对比该方法与傅里叶变换频谱分析的区别。
在分析傅里叶变换频谱分析技术的原理及实现算法的过程中，认识到了该方法存在的局限性，因为估算的地震振幅谱的重要特征是所选时窗函数的长度。如果所选时窗过短，振幅谱会与变换窗函数褶积，使其失去频率的局部化特征。另一方面，过短的时窗会使子波的旁瓣呈现为单一反射的假象。增加时窗长度，会改善频率的分辨率，但是，如果所选时窗过长，时窗内的多个反射会使振幅谱以槽痕为特征，很难分清单个反射的振幅谱特征。以傅里叶变换相关算法的时窗问题，会使振幅谱的估算产生偏差。由于在实际运用中，难以选择时窗的长度，而且无法定量分析时窗长度产生的偏差，以小波变换为基础的频谱分析技术成为了地震解释及储层预测的重要工具，在很多实际应用中发挥更大的作用。
本文采用复小波分析方法进行对地震信号频谱分析，选择morlet复小波，对地震信号进行复小波变换，并将尺度域转换到频率域，获得不同频率的频谱特征水平切片。并用理论模型说明了复小波频谱分析精度明显高于傅里叶变换的频谱分析，最后对新疆某油田及江汉盆地谢凤桥地区的三维地震实际资料进行了处理，结果表明复小波频谱分析能细致地反映储层的分布、位置及形态。
After decades of exploration and exploitation of land in eastern China, oil exploration anddevelopment degree grows gradually. Hydrocarbon exploration has entered the complexreservoir area, large oil fields which have been put into the development have almost entered thehigh water content period. Since exploration of the central and western complex surface area isin a relatively low level, reservoir has gradually become the main exploration targets. Newsituation in the exploration and development presented a serious challenge to the traditionalgeophysical technology.
China's land-based oil and gas complex reservoir includes thin interbedded sandstonereservoir, carbonate lithology reservoir and a variety of special lithology reservoir. Complexreservoir is now important for the exploration area. Thin interbedded sandstone reservoir ischaracterized by large area distribution, low abundance and worse permeability. Such reservoirsare the main sides of Songliao Basin Placanticline, Songnan area lithology reservoir, OrdosMesozoic lithology reservoir and Upper Paleozoic lithology gas reservoir, northwest Sichuanshallow gas reservoir. High technology is needed for the identification of the main belt andfracture zones, identifying stratigraphic trap, looking for confections in low-grade reserior.Carbonate reservoirs are mainly distributed in Sichuan, the Ordos Basin and Tarim Basin. Suchreservoirs are characterized that reservoir space for carbonate fracture-hole and porosity and thepowerful inhomogeneity. The key to exploration is to determine carbonate reservoir insider caveand the weathering crust hole, cave, slit the spatial distribution. Complex reservoir predictiontechnology has broad application prospects.
Spectrum analysis technology in theory is mainly based on the thin-layer reflection tuningprinciple. According to the theory, for the thin layer whose thickness is less than one fourth ofthe wavelength, in the time domain, with growth of the thickness of the thin, seismic reflectionamplitude gradually increases. When the thickness increases to a quarter wavelength tunablethickness, the amplitude of reflection come to the maximum value. With the increase in thethickness of thin, reflection amplitude decreased gradually. Time domain reflection amplitude ofthe greatest value, which corresponds to the frequency domain amplitude of the largest energyvalue. Thin tuning caused by the amplitude spectrum interference depends on the characteristicsof the acoustic characteristics of thin and its thickness.
Spectrum analysis is an interpretation of reservoir technology which based on the frequency. It demonstrated to us a new seismic interpretation methods. Discrete Fourier transform orcomplex wavelet transform seismic data from the time domain into the frequency domain.Conversion calculated amplitude spectrum. The staff can see thin interference characteristics notonly from explained profile, but also from the plane. Such special treatment technology, wedefined as three-dimensional seismic data spectrum analysis techniques. Papers published in thesecond half of 2006 still mostly use short-time Fourier transform method for spectrum analysis.However, if the main frequency of the original seismic record is low, identifying stratigraphicthickness of the time is an equivalent thickness, which is the effects of overall number of thins.Moreover, with this method, the accurate positioning is only the time of window,but it can notestablish the accurate positioning in the window. The author presented a method of complexwavelet spectrum analysis, the result of the method of 3D seismic data in different frequency,full 3D explanation (including horizontal slice explanation)become possible. It can identifylithology and stratigraphic trap, and detect small incontinuity. The methods that have discretefrequency energy body (spectral decomposition techniques) characteristics, have timepositioning accuracy (traditional spectral decomposition technology can only get the timepositioning of the window). Complex wavelet transform highlightings local characteristics ofwavelet transform, which can avoid facing the process of selecting the window function and thesizes of time window when using WFT. Complex wavelet transform overcome the calculationoverload problem caused by sliding window in WFT. The results showed the complex wavelettransform spectrum analysis techniques have higher resolution than WFT. The spectrum offavorable reservoir characteristics is better reflected.
This paper begins with complex seismic data transformation based on Hilbert transform toget seismic instantaneous features, then introduces the principle and algorithm of both the WFTand complex wavelet transform method for spectrum analysis, especially Contrasts WFT andcomplex wavelet transform spectrum analysis techniques.
(1) It introduced a complex seismic analysis, the principle of Hiibert transform. Complexseismic analysis Using Hilbert transform to compute seismic instantaneous features.
(2) It introduced the Fourier transform and window Fourier transform theory. It introduced3D seismic data spectrum analysis technology based on the window Fourier transform method.Details of algorithm and implementation process of this method was given. Through analyzingthe results, try to look for ways to improve this method.
(3) It introduced the wavelet transform and complex wavelet transform theory. Definition ofcomplex wavelet is given. It introduced 3D seismic data spectrum analysis technology based onthe complex wavelet transform. Details of algorithm and implementation process of this methodwas given. This method was compared with the window Fourier transform spectrum analysis toshow the difference.
During researching the principle and algorithm of Fourier transform spectrum analysis,we realized the limitations of the method, because the important feature of the estimate ofseismic amplitude spectrum is the length of selected time window function. If the selected timewindow is too short, the amplitude spectrum will proceed deconvolution with window function, which made this method lose local frequency characteristics. The other hand, too short a timewindow will make wavelet Sidelobe show for the illusion of a single reflection. Increasing thelength of time window will improve the frequency resolution, but if the time window is too long,flute marks for the features will show on the several reflection in the time window on theamplitude spectrum, so it is difficult to distinguish individual reflection amplitude spectrumcharacteristics. The time window problem of Fourier transform algorithm will make theamplitude spectrum deviate from the estimates. In practical application, it is difficult todetermine the length of the window, and it is impossible to get the quantitative analysis of thedeviation caused by the window length. Wavelet-based spectral analysis technology isbecoming the important tools of the seismic interpretation and reservoir prediction, In manypractical applications which play a greater role.
In this paper, we used complex wavelet method for seismic signal spectrum analysis, morletwavelet transforms. We transform the scale domain into the frequency domain and get thespectrum characteristics of different frequency. And the theoretical model to illustrate thecomplex wavelet analysis of spectrum has higher accuracy than the Fourier transform. Finally,the actual 3-D seismic data in the Xinjiang Oilfield and Jianghan Basin Xiefengqiao area wereproceeded with complex wavelet transform spectrum analysis. The results showed complexwavelet this method can reflect reservoir distribution, location and morphology.
引文
[1] Partyka G, Gridley J, Lopz J. Interpretational application of sepctral decomposition in reservoir characterization. The Leading Edge, 1999(3): 353～360;
[2] 朱庆荣，张越迁，于兴河．分频解释技术在表征储层中的应用．矿物岩石，2003，23(3)：104～108：
[3] 徐丽英，徐鸣洁，陈振岩．利用谱分解技术进行薄储层预测．石油地球物理勘探，2006，41(3)：299～302；
[4] 田建章，武耀辉．廊固凹陷万庄构造薄砂岩储层预测．石油地球物理勘探，2006，41(2)：177～187；
[5] 王大兴，高静怀，李幼铭．XF地区中生界砂岩储层预测技术及应用．石油地球物理勘探，2004，39(5)：559～564；
[6] 高静怀，汪文秉，朱光明．小波变换与信号瞬时特征分析．地球物理学报，1997，40(6)：821～830；
[7] 王西文，刘全新，李幼铭．地震信号瞬时特征在小波域分频提取的方法和应用．石油地球物理勘探，2000，35(4)：452～478；
[8] 李宏兵，赵文智，曹宏．小波尺度域含气储层地震波衰减特征．地球物理学报，2004，47(5)：892～898；
[9] 李宏兵，赵文智，曹宏．应用小波尺度域地震波衰减属性检测气层．石油地球物理勘探，2005，40(4)：411～416；
[10] Sun Shengjie, John P. Castagna. Examples of wavelet transform time-frequency analysis in direct hydrocarbon detection. SEG Int'l Exposition and 72nd Annual Meeting, 2002;
[11] Jeff P. Grossman, Gary F. Margrave, Michael P. Lamoureux. a robust algorithm for constant-Q wavelet estimation using Gabor analysis. SEG Int'l Exposition and 72nd Annual Meeting, 2002;
[12] Abry, P., P. Goncalves, and P. Flandrin, 1993, Wavelet-based spectral analysis of 1/f processes: International Conference on Acoustic, Speech and Signal Processing, IEEE, Proceedings, 3, 237-240;
[13] Castagna, J. P., S. Sun, and R. W. Seigfried, 2003, Instantaneous spectral analysis: Detection of low-frequency shadows associated with hydrocarbons: The Leading Edge, 22, 120-127;
[14] 崔凤林，管叶君．时频分析—薄护层结构研究的新途径．石油物探，1992，31(2)：1～15；
[15] 黄平，路中侃．川东石炭系气水分布及预测．石油地球物理勘探，1996，31(增刊)12：95～100；
[16] 黄臣强，王军，张金伟．时频分析技术在三角洲层序分析中的应用．断块油气田，2002，9(2)：18～20；
[17] 张奎凤，蓝晖．短时窗地震信号谱分析方法．石油物探，1995，34(2)，94～98：
[18] 邵海龙，贺振华，黄德济．小波变换与最大熵法联合计算薄层厚度．石油地球物理勘探，1998，33(2)：204～213：
[19] 王西文．地震资料处理和解释中的小波分析方法．北京：石油工业出版社，2004；
[20] Satish Sinha, Parthas Routh, Phil D. Anno. Spectral decomposition of seismic data with continuous-wavelet transform. Geophysics,2005,70(6): 19～25;
[21] 王新红．频谱成像技术在稠油热采地震监测中的应用．华北地震科学，2005，23(3)，1～8；
[22] Taner M, Koehler F, Sheriff RE. Complex seismic trace analysis. Geophysics,1979,44(6): 1041～1063;
[23] 卢新城，龚沈光，周骏．基于Morlet小波的高分辨率信号频谱估计．武汉理工大学学报，2002，26(5)：622～635：
[24] 飞思科技产品研发中心．小波分析理论与MATLAB7实现．电子工业出版社，2005：185～218；
[25] 程乾生．信号数字处理的数学原理．北京：石油工业出版社，1977：113～125；
[26] 张炅，陈家兴．利用Hilbert变换提取信号瞬时特征参数的问题研究．电讯技术研究与开发，2003(4)：44～48；
[27] 李世雄，刘家琦．小波变换和反演数学基础．北京：地质出版社，1994；
[28] 崔锦泰．小波分析导论．西安：西安交通大学出版社，1995；
[29] Eugene Lichman,. Unified Approach to Gas and Fluid Detection on Instantaneous Seismic Wavelets, SEG Expanded Abstracts 22, (2003): 1699;
[30] Satish K. Sinha. Time-Frequency Attribute of Seismic Data using Continuous Wavelet Transform, SEG Expanded Abstracts 22, (2003):1481;
[31] D. E. Rivera-Recillas. Calculation of seismic attributes with the discrete wavelet transform, SEG Expanded Abstracts 22, (2003):2028;
[32] Albena Mateeva. Apparent attenuation from short-period multiples and intrinsic absorption in the seismic wavelet model, SEG Expanded Abstracts 21, (2002):2198;
[33] Daubechiea I. Ten Lectures on Wavelet. Capital City Press, 1992;
[34] Daubechiea I. Wavelet transform: Time-Frequency Localization and Signal Analysis, IEEE Trans. on Information Theory, 1990,36 (5),;
[35] Morlet J, Arena G, Giard D., Wave Propagation and Sampling Theory-Party Ⅰ: Complex Signal and Scattering in Multilayered Media, Geophysics, 1982,47(2);
[36] Morlet J, Arena G, Giard D., Wave Propagation and Sampling Theory-Party Ⅱ: Sampling Theory and complex waves, Geophysics, 1982,47 (2):222～236;
[37] Mallat S. A Theory for Multiresolution Signal Decomposition: The Wavelet Reperaentation, IEEE Trans. on Pattern Anal. Machine Intelligence, 1989,11(7):674～693;
[38] Farge M, Guesennee Y. Continuous Wavelet Analysis of Coherent Structures, Center for Turbulence Research Proceedings of the Summer Program, 1990;
[39] Farge M et al. Wavelet Transform to Detect and Analyze Coherent Structures in Two-Dimensional Turbulent flows, Proe. Scaling Fractals and Nonlinear Variability in Geophysics Ⅱ Harceloae,1989;
[40] Wiclrcrhauaer M．Lectures on Wavelet Packet Algorithms,第三次中法小波会议论文集,1992；
[41] Wiclrcrhauaer M．High-resolution Still Picture Compression,第三次中法小波会议论文,1992；
[42] Frisch M, Measer H. The Use of Wavelet Transform in the Detection of Unknown Transient Signals, IEEE Trans. on Information Theory, 1992,38 (2);
[43] Dutilleux P, Grossmann A. Application of the Wavelet Transform to the Analysis, Transformation and Synthesis of Musical Sounds, Preprint, 85th Aes Convention;
[44] Bames A. Instantaneous Spectral bandwidth and dominant frequency with applications to seismic reflection data, Geophysics, 1993,58,419～428;
[45] Voogd J, Rooijen N,. Thin-layer response and spectral bandwidth,Geophsics, 1983,48,12～18;
[46] Boashash B,White L. Instantaneous frequency estimation and automatic time-varying filtering. Proc. IEEE ICASSP'90,1990:1221～1224;
[47] Roessgen M, Boashash B. Time-frequency peak filtering applied to FSK signals. Proc. IEEE ICASSP'94,1994:516～519;
[48] Pitton J, Kuansan Wang. Time-frequency analysis and auditory modeling for automatic recognition of speech. Proc. IEEE, 1996, 84 (9): 1199～1215;
[49] Gaunaurd C, Strifors H. Signal analysis by means of time-frequency (Wigner-type) distribution-applications to sonar and radar echoes. Proc. IEEE, 1996, 84(9):1231～1234;
[50] Andria G et al. Application of Wigner-Ville distribution to measurements on transient signals. IEEE trans. Instrumentation and Measurement, 1994,43 (2):187～193;
[51] Atlas L, Bernard D. Applications of time-frequency analysis to signals from manufacturing and machine monitoring sensors. Proc. IEEE, 1996, 84(9): 1319～1329;
[52] Luuis R et al. The application of two-dimensional signal transformations to the analysis and synthesis of structural excitations observed in acoustic scattering. Proc. IEEE, 1996,84(9): 1249～1266;
[53] Koenig R Dunn K. The sound spectrograph. Acoust, 1946,18:19～49;
[54] Grossmann A, Morlet J. Decomposion of Hardy function into square integrable wavelets of constant shape. SIAM J.Math, 1984,15(4):723～736;
[55] Mallet S. Multifrequency channel decomposition of image and wavelet models. IEEE traps. ASSP, 1989,37(12):2091～2110;
[56] Daubechies I. The wavelet transform, time-frequency localization and signal analysis.IEEE trans.Information Theory, 1990,(36):961～1005;
[57] Vetterli M, Herley C. Wavelet and filter banks: theory and design. IEEE trans. Signal Processing, 1992,40(9):2207～2232.
[2] 朱庆荣，张越迁，于兴河．分频解释技术在表征储层中的应用．矿物岩石，2003，23(3)：104～108：
[3] 徐丽英，徐鸣洁，陈振岩．利用谱分解技术进行薄储层预测．石油地球物理勘探，2006，41(3)：299～302；
[4] 田建章，武耀辉．廊固凹陷万庄构造薄砂岩储层预测．石油地球物理勘探，2006，41(2)：177～187；
[5] 王大兴，高静怀，李幼铭．XF地区中生界砂岩储层预测技术及应用．石油地球物理勘探，2004，39(5)：559～564；
[6] 高静怀，汪文秉，朱光明．小波变换与信号瞬时特征分析．地球物理学报，1997，40(6)：821～830；
[7] 王西文，刘全新，李幼铭．地震信号瞬时特征在小波域分频提取的方法和应用．石油地球物理勘探，2000，35(4)：452～478；
[8] 李宏兵，赵文智，曹宏．小波尺度域含气储层地震波衰减特征．地球物理学报，2004，47(5)：892～898；
[9] 李宏兵，赵文智，曹宏．应用小波尺度域地震波衰减属性检测气层．石油地球物理勘探，2005，40(4)：411～416；
[10] Sun Shengjie, John P. Castagna. Examples of wavelet transform time-frequency analysis in direct hydrocarbon detection. SEG Int'l Exposition and 72nd Annual Meeting, 2002;
[11] Jeff P. Grossman, Gary F. Margrave, Michael P. Lamoureux. a robust algorithm for constant-Q wavelet estimation using Gabor analysis. SEG Int'l Exposition and 72nd Annual Meeting, 2002;
[12] Abry, P., P. Goncalves, and P. Flandrin, 1993, Wavelet-based spectral analysis of 1/f processes: International Conference on Acoustic, Speech and Signal Processing, IEEE, Proceedings, 3, 237-240;
[13] Castagna, J. P., S. Sun, and R. W. Seigfried, 2003, Instantaneous spectral analysis: Detection of low-frequency shadows associated with hydrocarbons: The Leading Edge, 22, 120-127;
[14] 崔凤林，管叶君．时频分析—薄护层结构研究的新途径．石油物探，1992，31(2)：1～15；
[15] 黄平，路中侃．川东石炭系气水分布及预测．石油地球物理勘探，1996，31(增刊)12：95～100；
[16] 黄臣强，王军，张金伟．时频分析技术在三角洲层序分析中的应用．断块油气田，2002，9(2)：18～20；
[17] 张奎凤，蓝晖．短时窗地震信号谱分析方法．石油物探，1995，34(2)，94～98：
[18] 邵海龙，贺振华，黄德济．小波变换与最大熵法联合计算薄层厚度．石油地球物理勘探，1998，33(2)：204～213：
[19] 王西文．地震资料处理和解释中的小波分析方法．北京：石油工业出版社，2004；
[20] Satish Sinha, Parthas Routh, Phil D. Anno. Spectral decomposition of seismic data with continuous-wavelet transform. Geophysics,2005,70(6): 19～25;
[21] 王新红．频谱成像技术在稠油热采地震监测中的应用．华北地震科学，2005，23(3)，1～8；
[22] Taner M, Koehler F, Sheriff RE. Complex seismic trace analysis. Geophysics,1979,44(6): 1041～1063;
[23] 卢新城，龚沈光，周骏．基于Morlet小波的高分辨率信号频谱估计．武汉理工大学学报，2002，26(5)：622～635：
[24] 飞思科技产品研发中心．小波分析理论与MATLAB7实现．电子工业出版社，2005：185～218；
[25] 程乾生．信号数字处理的数学原理．北京：石油工业出版社，1977：113～125；
[26] 张炅，陈家兴．利用Hilbert变换提取信号瞬时特征参数的问题研究．电讯技术研究与开发，2003(4)：44～48；
[27] 李世雄，刘家琦．小波变换和反演数学基础．北京：地质出版社，1994；
[28] 崔锦泰．小波分析导论．西安：西安交通大学出版社，1995；
[29] Eugene Lichman,. Unified Approach to Gas and Fluid Detection on Instantaneous Seismic Wavelets, SEG Expanded Abstracts 22, (2003): 1699;
[30] Satish K. Sinha. Time-Frequency Attribute of Seismic Data using Continuous Wavelet Transform, SEG Expanded Abstracts 22, (2003):1481;
[31] D. E. Rivera-Recillas. Calculation of seismic attributes with the discrete wavelet transform, SEG Expanded Abstracts 22, (2003):2028;
[32] Albena Mateeva. Apparent attenuation from short-period multiples and intrinsic absorption in the seismic wavelet model, SEG Expanded Abstracts 21, (2002):2198;
[33] Daubechiea I. Ten Lectures on Wavelet. Capital City Press, 1992;
[34] Daubechiea I. Wavelet transform: Time-Frequency Localization and Signal Analysis, IEEE Trans. on Information Theory, 1990,36 (5),;
[35] Morlet J, Arena G, Giard D., Wave Propagation and Sampling Theory-Party Ⅰ: Complex Signal and Scattering in Multilayered Media, Geophysics, 1982,47(2);
[36] Morlet J, Arena G, Giard D., Wave Propagation and Sampling Theory-Party Ⅱ: Sampling Theory and complex waves, Geophysics, 1982,47 (2):222～236;
[37] Mallat S. A Theory for Multiresolution Signal Decomposition: The Wavelet Reperaentation, IEEE Trans. on Pattern Anal. Machine Intelligence, 1989,11(7):674～693;
[38] Farge M, Guesennee Y. Continuous Wavelet Analysis of Coherent Structures, Center for Turbulence Research Proceedings of the Summer Program, 1990;
[39] Farge M et al. Wavelet Transform to Detect and Analyze Coherent Structures in Two-Dimensional Turbulent flows, Proe. Scaling Fractals and Nonlinear Variability in Geophysics Ⅱ Harceloae,1989;
[40] Wiclrcrhauaer M．Lectures on Wavelet Packet Algorithms,第三次中法小波会议论文集,1992；
[41] Wiclrcrhauaer M．High-resolution Still Picture Compression,第三次中法小波会议论文,1992；
[42] Frisch M, Measer H. The Use of Wavelet Transform in the Detection of Unknown Transient Signals, IEEE Trans. on Information Theory, 1992,38 (2);
[43] Dutilleux P, Grossmann A. Application of the Wavelet Transform to the Analysis, Transformation and Synthesis of Musical Sounds, Preprint, 85th Aes Convention;
[44] Bames A. Instantaneous Spectral bandwidth and dominant frequency with applications to seismic reflection data, Geophysics, 1993,58,419～428;
[45] Voogd J, Rooijen N,. Thin-layer response and spectral bandwidth,Geophsics, 1983,48,12～18;
[46] Boashash B,White L. Instantaneous frequency estimation and automatic time-varying filtering. Proc. IEEE ICASSP'90,1990:1221～1224;
[47] Roessgen M, Boashash B. Time-frequency peak filtering applied to FSK signals. Proc. IEEE ICASSP'94,1994:516～519;
[48] Pitton J, Kuansan Wang. Time-frequency analysis and auditory modeling for automatic recognition of speech. Proc. IEEE, 1996, 84 (9): 1199～1215;
[49] Gaunaurd C, Strifors H. Signal analysis by means of time-frequency (Wigner-type) distribution-applications to sonar and radar echoes. Proc. IEEE, 1996, 84(9):1231～1234;
[50] Andria G et al. Application of Wigner-Ville distribution to measurements on transient signals. IEEE trans. Instrumentation and Measurement, 1994,43 (2):187～193;
[51] Atlas L, Bernard D. Applications of time-frequency analysis to signals from manufacturing and machine monitoring sensors. Proc. IEEE, 1996, 84(9): 1319～1329;
[52] Luuis R et al. The application of two-dimensional signal transformations to the analysis and synthesis of structural excitations observed in acoustic scattering. Proc. IEEE, 1996,84(9): 1249～1266;
[53] Koenig R Dunn K. The sound spectrograph. Acoust, 1946,18:19～49;
[54] Grossmann A, Morlet J. Decomposion of Hardy function into square integrable wavelets of constant shape. SIAM J.Math, 1984,15(4):723～736;
[55] Mallet S. Multifrequency channel decomposition of image and wavelet models. IEEE traps. ASSP, 1989,37(12):2091～2110;
[56] Daubechies I. The wavelet transform, time-frequency localization and signal analysis.IEEE trans.Information Theory, 1990,(36):961～1005;
[57] Vetterli M, Herley C. Wavelet and filter banks: theory and design. IEEE trans. Signal Processing, 1992,40(9):2207～2232.
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