自适应Kalman滤波反褶积的快速实现方法
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摘要
提出了以二进小波变换为基础的自适应Kalman滤波反褶积 (AKFD)新方法 ,针对该方法的计算复杂程度 ,提出了一种快速实现方法 .二进小波变换的AKFD抛弃了传统预测反褶积对信号平稳性的假设 ,克服了提高分辨率而信噪比明显降低的问题 ,具有很好的抗噪性能 .在小波域进行的AKFD在压制假反射以及提高分辨率方面比时间域的AKFD好 ,克服了在时域内进行AKFD抬升低频成分的缺陷 .利用二维地震数据的局部平稳性的假设提出了快速实现方法 ,通过分段求取自适应预测算子 ,分别于横向及纵向采用样条插值的方法进行插值 ,来减少求取自适应预测算子的计算量 ,达到快速实现的目的 .经过大量实验表明计算速度提高数百倍 ,仍能保持原来的计算效果 .
A new approach of adaptive Kalman filtering deconvolution (AKFD) via dyadic wavelet transform is proposed. To the computing complexity of the approach, a fast implementation technique is proposed. The AKFD via dyadic wavelet transform discards the assumption of stationarity of signals in predictive deconvolution, and solves the problem of improving resolution at the price of decreasing signal to noise rate (SNR) obviously, consequently it has a better ability of resistance noise. Suppressing false reflections and improving resolution in dyadic wavelet transform domain is better than that in time domain. At the same time, the approach also overcomes the drawback of increasing the low frequency component of AKFD in time domain. The fast implementation technique makes use of the assumption of local stationary for 2D seismic data. The technique reduces the calculation amount of the adaptive predictive operators by calculating an adaptive predictive operator in each segment, and then applying the algorithm of spline interpolation to interpolate in transverse and in portrait. A great deal of experiments indicates that the computing speed can be increased hundreds times, and the original calculation effect is still maintained.
A new approach of adaptive Kalman filtering deconvolution (AKFD) via dyadic wavelet transform is proposed. To the computing complexity of the approach, a fast implementation technique is proposed. The AKFD via dyadic wavelet transform discards the assumption of stationarity of signals in predictive deconvolution, and solves the problem of improving resolution at the price of decreasing signal to noise rate (SNR) obviously, consequently it has a better ability of resistance noise. Suppressing false reflections and improving resolution in dyadic wavelet transform domain is better than that in time domain. At the same time, the approach also overcomes the drawback of increasing the low frequency component of AKFD in time domain. The fast implementation technique makes use of the assumption of local stationary for 2D seismic data. The technique reduces the calculation amount of the adaptive predictive operators by calculating an adaptive predictive operator in each segment, and then applying the algorithm of spline interpolation to interpolate in transverse and in portrait. A great deal of experiments indicates that the computing speed can be increased hundreds times, and the original calculation effect is still maintained.
引文
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[1 4 ] 孟鸿鹰 ,刘贵忠 .小波变换多尺度地震波形反演 .地球物理学报 ,1 999,4 2 ( 2 ) :2 4 1— 2 4 8.MENGHong Ying ,LIUGui Zhong .MultiscaleSeismicWaveformInversionbyWaveletTransform .ChineseJ.Geophys.(inChinese) ,1 999,4 2 ( 2 ) :2 4 1— 2 4 8.
[1 5] 李世雄 ,汪继文 .信号的瞬时参数与正交小波基 .地球物理学报 ,2 0 0 0 ,4 3 ( 1 ) :97— 1 0 4 .LIShi Xiong ,WANGJi Wen.InstantaneousParametersofSignalsandOrthogonalBasesofWavelets.ChineseJGeophys.(inChinese) ,2 0 0 0 ,4 3 ( 1 ) :97— 1 0 4 .
[1 6] BrownRG ,HwangPYC .IntroductiontoRandomSignalsandAppliedKalmanFilteringwithMatlabExercisesandSolutions,NewYork :Wiley ,1 997.
[1 7] PrasadS ,MahalanabisAK .AdaptiveFilterStructuresforDeconvolutionofSeismicSignals.IEEETranscationsonGeoscienceandRemoteSensing ,1 980 ,GE 1 8( 3 ) :2 67— 2 73 .
[1 8] GriffithsLJ.,SmolkaFR .andTremblyLD .Adaptivedeconvolution :Anewtechniquefortime varingseismicda ta .Geophysics,1 977,4 2 :74 2— 759.
[1 9] WidrowB ,McCoolJM ,LarimoreMGandJohnsonCRJ.StationaryandnonstationarylearningcharacteristicsoftheLMSadaptivefilter.Proc.IEEE ,1 976,64 :1 1 51— 1 1 62 .
[2 ] UlrychTJ,MatsuokaT .Outputofpredictivedeconvolution .Geophysics,1 991 ,56( 3 ) :3 71— 3 77.
[3 ] SchoenbergerM ,HoustonLM .Stationaritytransformationofmultiplestoimprovetheperformanceofpredictivede convolution.Geophysics,1 998,63 ( 2 ) :72 3— 73 7.
[4 ] GriffithsLJ .Asimpleadaptivealgorithmforrealtimeprocessinginantennaarrays.Proc.IEEE ,1 969,57:1 696— 1 70 4 .
[5] ClarkeGKC .Time varyingdeconvolutionfilters.Geophysics,1 968,3 9:1— 1 3 .
[6] FrostIIIOL .Analgorithmforlinearlyconstraintedadaptivearrayprocessing.Proc.IEEE ,1 975,63 :1 692—1 71 6.
[7] WidrowB ,GloverJRJ,McCoolJM .etal.Adaptivenoisecanceling:PrinciplesandApplications.Proc.IEEE ,1 975,63 :1 692— 1 71 6.
[8] 黄绪德 .反褶积与地震道反演 .北京 :石油工业出版社 ,1 992 .HUANGXu De.DeconvolutionandSeismicTraceInversion(inChinese) .Beijing :PetroleumIndustryPress,1 992 .
[9] 马振兴 .卡尔曼滤波在地震数据处理中的应用 .石油地球物理勘探 ,1 984 ,4 ( 2 ) :1 4 0— 1 4 7.MAZhen Xing .ApplicationofKalmanfilteringtheorytothedeconvolutionofseismicdata.OilGeophysicalProspecting(inChinese) ,1 984 ,4 :1 4 0— 1 4 7.
[1 0 ] MallatS ,ZhongS .CharacterizationofSignalfromMultiscaleEdges.IEEETransactiononPAMI ,1 992 ,1 4 ( 7) :71 0— 73 2 .
[1 1 ] MallatS ,HwangWL .SingularityDetectionandProcessingwithWavelet.IEEETrans.onInformationTheory,1 992 ,3 8( 2 ) :61 7— 64 3 .
[1 2 ] MallatS .AWaveletTourofSignalProcessing .NewYork :AcademicPress,1 998.
[1 3 ] ZHANGKe ,LIUGui Zhong ,ZOUDa Wenetal.SeismicDataDenoisingintheTime FrequencyDomainBasedontheDyadicWaveletTransform .ChineseJ.Geophys.1 996,3 9( 2 ) :2 95— 3 0 2 .
[1 4 ] 孟鸿鹰 ,刘贵忠 .小波变换多尺度地震波形反演 .地球物理学报 ,1 999,4 2 ( 2 ) :2 4 1— 2 4 8.MENGHong Ying ,LIUGui Zhong .MultiscaleSeismicWaveformInversionbyWaveletTransform .ChineseJ.Geophys.(inChinese) ,1 999,4 2 ( 2 ) :2 4 1— 2 4 8.
[1 5] 李世雄 ,汪继文 .信号的瞬时参数与正交小波基 .地球物理学报 ,2 0 0 0 ,4 3 ( 1 ) :97— 1 0 4 .LIShi Xiong ,WANGJi Wen.InstantaneousParametersofSignalsandOrthogonalBasesofWavelets.ChineseJGeophys.(inChinese) ,2 0 0 0 ,4 3 ( 1 ) :97— 1 0 4 .
[1 6] BrownRG ,HwangPYC .IntroductiontoRandomSignalsandAppliedKalmanFilteringwithMatlabExercisesandSolutions,NewYork :Wiley ,1 997.
[1 7] PrasadS ,MahalanabisAK .AdaptiveFilterStructuresforDeconvolutionofSeismicSignals.IEEETranscationsonGeoscienceandRemoteSensing ,1 980 ,GE 1 8( 3 ) :2 67— 2 73 .
[1 8] GriffithsLJ.,SmolkaFR .andTremblyLD .Adaptivedeconvolution :Anewtechniquefortime varingseismicda ta .Geophysics,1 977,4 2 :74 2— 759.
[1 9] WidrowB ,McCoolJM ,LarimoreMGandJohnsonCRJ.StationaryandnonstationarylearningcharacteristicsoftheLMSadaptivefilter.Proc.IEEE ,1 976,64 :1 1 51— 1 1 62 .
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