常规测井曲线的小波和希尔伯特—黄变换滤波效果分析
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摘要
为了明晰常规测井曲线小波与希尔伯特—黄变换(Hilbert-Huang Transform,HHT)滤波方法效果差异,本文在文献调研基础上,梳理了小波滤波、小波包滤波及HHT滤波的基本思想和方法特点,针对含噪强度为10倍于高斯白噪的自然伽马测井曲线开展了小波阈值滤波、小波包阈值滤波、HHT减性滤波、HHT-WT联合滤波及滤波后信号HHT 3D谱特征分析,并对含有不同噪声强度的自然伽马测井曲线进行了四种滤波结果的均方差、信噪比和相似度对比分析,厘定了滤波效果与噪声强度的关系。研究结果表明:均方差、信噪比、相似度等参数及HHT 3D谱特征均指示四种方法的常规测井曲线滤波效果存在差异;当噪声强度增大时,四种滤波方法效果均下降;噪声强度为中等时,四种滤波方法效果较接近;噪声强度较弱或较强时,小波阈值滤波应为首选滤波去噪方法;HHT-WT联合滤波效果好于HHT减性滤波。
To make clear effect differences among wavelet transform(WT),wavelet package transform(WPT),and Hilbert-Huang transform(HHT)on logging data,we review fundamental idea and approach feature of WT filters, WPT filters,and HHT filters based on published documents.First gamma ray logging data with noise whose intensity is 10 times to Gauss white noise is filtered by WT filters,WPT filters,HHT reducing filters,and HHT-WT associating filters.Then HHT three dimensions spectrum characteristics, root-meansquare(rms)error,signal to noise ratio(S/N),and similar degree(SD)are analyzed on this filtered GR data.Finally the relation between filtering effect and noise intensity is studied.The following observations are found out based on our work:A.There is some difference of rms error,S/N,SD and HHT 3D spectrum features with the four filters;B.Filtering effects will be decreasing when noise intensity is high,filtering effect is similar when noise intensity is between 5 times and 17 times to Gauss white noise;C.WT filters should be the first choice when the noise intensity is relatively weak or strong;D.HHT-WT filters is better than HHT reducing filters.
To make clear effect differences among wavelet transform(WT),wavelet package transform(WPT),and Hilbert-Huang transform(HHT)on logging data,we review fundamental idea and approach feature of WT filters, WPT filters,and HHT filters based on published documents.First gamma ray logging data with noise whose intensity is 10 times to Gauss white noise is filtered by WT filters,WPT filters,HHT reducing filters,and HHT-WT associating filters.Then HHT three dimensions spectrum characteristics, root-meansquare(rms)error,signal to noise ratio(S/N),and similar degree(SD)are analyzed on this filtered GR data.Finally the relation between filtering effect and noise intensity is studied.The following observations are found out based on our work:A.There is some difference of rms error,S/N,SD and HHT 3D spectrum features with the four filters;B.Filtering effects will be decreasing when noise intensity is high,filtering effect is similar when noise intensity is between 5 times and 17 times to Gauss white noise;C.WT filters should be the first choice when the noise intensity is relatively weak or strong;D.HHT-WT filters is better than HHT reducing filters.
引文
[1]潘泉,张磊,孟晋丽等.小波滤波方法及应用.北京:清华大学出版社,2005,1-5.
[2]孙延奎.小波变换与图像、图形处理技术.北京:清华大学出版社,2012,1-2.
[3]朱光明,李庆春,胡建平.数字信号分析与处理.陕西西安:陕西人民教育出版社,2003,442-443.
[4]陈一贤.HHT方法分析[学位论文].浙江杭州:浙江大学,2007.
[5]段希涛.Hilbert-Huang变换的研究与应用[学位论文].河南郑州:解放军信息工程大学,2005,2-3.
[6]刘欢.分频Hilbert-Huang变换对非平稳信号的分析应用[学位论文].湖南长沙:湖南大学,2007,4-6.
[7]安怀志.希尔伯特黄变换理论与应用的研究[学位论文].黑龙江哈尔滨:哈尔滨工程大学,2008,7-9.
[8]王振国,周熙襄,李晶.基于小波变换的最小光滑滤波去噪.石油地球物理勘探,2002,37(6):594-600.Wang Zhenguo,Zhou Xixiang,Li Jing.Noise attenuation using minimum smooth filter based on wavelet transform.OGP,2002,37(6):594-600.
[9]董小刚,秦喜文.信号消噪的小波处理方法及其应用.吉林师范大学学报(自然科学版),2003,24(2):14-17.Dong Xiaogang,Qin Xiwen.Wavelet analysis eliminate the noise and demonstrate the consequence by applying matlab.Journal of Jilin Normal University(Natural Science Edition),2003,24(2):14-17.
[10]赵军龙,谭成仟,焦积田等.小波域阈值滤波在测井信号去噪中的应用.西安科技大学学报,2007,17(2):263-267.Zhao Junlong,Tan Chengqian,Jiao Jitian et al.Application of wavelet analysis in logging signal filtering.Journal of Xi'an University of Science and Technology,2007,17(2):263-267.
[11]杨培杰,印兴耀,张广智.希尔伯特—黄变换地震信号时频分析与属性提取.地球物理学进展,2007,22(5):1585-1590.Yang Peijie,Yin Xingyao,Zhang Guangzhi.Seismic signal time-frequency analysis and attributes extraction based on HHT.Progress in Geophysics,2007,22(5):1585-1590.
[12]刘庆敏,杨午阳,田连玉等.希尔伯特—黄变换在地震资料去噪中的应用.新疆石油地质,2009,30(3):333-336.Liu Qingmin,Yang Wuyang,Tian Lianyu et al.Application of Hilbert-Huang transformation to noise elimination of seismic data.Xinjiang Petroleum Geology,2009,30(3):333-336.
[13]曹思远,邴萍萍,路交通等.利用改进希尔伯特-黄变换进行地震资料时频分析.石油地球物理勘探,2013,48(2):246-254.Cao Siyuan,Bing Pingping,Lu Jiaotong et al.Seismic data time-frequency analysis by the improved HilbertHuang transform.OGP,2013,48(2):246-254.
[14]Wang Zhuwen,Liu Jinghua,Yue Chongwang et al.The filtering characteristics of HHT and its application in acoustic log waveform signal processing.Applied Geophysics,2009,6(1):8-16.
[15]戴前伟,王安飞,杨晓辉.基于经验模态分解的电测井信号去噪研究.工程勘察,2014,5:80-84.Dai Qianwei,Wang Anfei,Yang Xiaohui.Resistivity logging signal denoising based on empirical mode decomposition.Geotechnical Investigation&Surveying,2014,5:80-84.
[16]周伟,周林,张家祥等.MATLAB小波分析高级技术.陕西西安:西安电子科技大学出版社,2006,105-111.
[17]MATLAB技术联盟,孔玲军.MATLAB小波分析超级学习手册.北京:人民邮电出版社,2014,297-303.
[18]黄诚惕.希尔伯特—黄变换及其应用研究[学位论文].四川成都:西南交通大学,2006:36-42.
[19]雍世和.用平滑滤波法消除放射性测井曲线上的统计起伏变化.测井技术,1983,7(4):1-8.Yong Shihe.Elimination of statistical fluctuations in radioactive logging curves by smoothing filtering method.Well Logging Technology,1983,7(4):1-8.
[2]孙延奎.小波变换与图像、图形处理技术.北京:清华大学出版社,2012,1-2.
[3]朱光明,李庆春,胡建平.数字信号分析与处理.陕西西安:陕西人民教育出版社,2003,442-443.
[4]陈一贤.HHT方法分析[学位论文].浙江杭州:浙江大学,2007.
[5]段希涛.Hilbert-Huang变换的研究与应用[学位论文].河南郑州:解放军信息工程大学,2005,2-3.
[6]刘欢.分频Hilbert-Huang变换对非平稳信号的分析应用[学位论文].湖南长沙:湖南大学,2007,4-6.
[7]安怀志.希尔伯特黄变换理论与应用的研究[学位论文].黑龙江哈尔滨:哈尔滨工程大学,2008,7-9.
[8]王振国,周熙襄,李晶.基于小波变换的最小光滑滤波去噪.石油地球物理勘探,2002,37(6):594-600.Wang Zhenguo,Zhou Xixiang,Li Jing.Noise attenuation using minimum smooth filter based on wavelet transform.OGP,2002,37(6):594-600.
[9]董小刚,秦喜文.信号消噪的小波处理方法及其应用.吉林师范大学学报(自然科学版),2003,24(2):14-17.Dong Xiaogang,Qin Xiwen.Wavelet analysis eliminate the noise and demonstrate the consequence by applying matlab.Journal of Jilin Normal University(Natural Science Edition),2003,24(2):14-17.
[10]赵军龙,谭成仟,焦积田等.小波域阈值滤波在测井信号去噪中的应用.西安科技大学学报,2007,17(2):263-267.Zhao Junlong,Tan Chengqian,Jiao Jitian et al.Application of wavelet analysis in logging signal filtering.Journal of Xi'an University of Science and Technology,2007,17(2):263-267.
[11]杨培杰,印兴耀,张广智.希尔伯特—黄变换地震信号时频分析与属性提取.地球物理学进展,2007,22(5):1585-1590.Yang Peijie,Yin Xingyao,Zhang Guangzhi.Seismic signal time-frequency analysis and attributes extraction based on HHT.Progress in Geophysics,2007,22(5):1585-1590.
[12]刘庆敏,杨午阳,田连玉等.希尔伯特—黄变换在地震资料去噪中的应用.新疆石油地质,2009,30(3):333-336.Liu Qingmin,Yang Wuyang,Tian Lianyu et al.Application of Hilbert-Huang transformation to noise elimination of seismic data.Xinjiang Petroleum Geology,2009,30(3):333-336.
[13]曹思远,邴萍萍,路交通等.利用改进希尔伯特-黄变换进行地震资料时频分析.石油地球物理勘探,2013,48(2):246-254.Cao Siyuan,Bing Pingping,Lu Jiaotong et al.Seismic data time-frequency analysis by the improved HilbertHuang transform.OGP,2013,48(2):246-254.
[14]Wang Zhuwen,Liu Jinghua,Yue Chongwang et al.The filtering characteristics of HHT and its application in acoustic log waveform signal processing.Applied Geophysics,2009,6(1):8-16.
[15]戴前伟,王安飞,杨晓辉.基于经验模态分解的电测井信号去噪研究.工程勘察,2014,5:80-84.Dai Qianwei,Wang Anfei,Yang Xiaohui.Resistivity logging signal denoising based on empirical mode decomposition.Geotechnical Investigation&Surveying,2014,5:80-84.
[16]周伟,周林,张家祥等.MATLAB小波分析高级技术.陕西西安:西安电子科技大学出版社,2006,105-111.
[17]MATLAB技术联盟,孔玲军.MATLAB小波分析超级学习手册.北京:人民邮电出版社,2014,297-303.
[18]黄诚惕.希尔伯特—黄变换及其应用研究[学位论文].四川成都:西南交通大学,2006:36-42.
[19]雍世和.用平滑滤波法消除放射性测井曲线上的统计起伏变化.测井技术,1983,7(4):1-8.Yong Shihe.Elimination of statistical fluctuations in radioactive logging curves by smoothing filtering method.Well Logging Technology,1983,7(4):1-8.