地震信号瞬时频率的估算
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摘要
本文比较了四类计算瞬时频率的方法.基于相位差分的方法对噪声敏感;基于零交叉点的方法是针对周期信号提出的,对非周期信号效果不理想,通过插值改善估算结果;基于FIR微分器的方法有三种,基于两点的FIR方法与标准公式较为接近,但会引入半个采样间隔的时移;基于三点的FIR方法可以消除时移,但计算结果会出现负频尖峰;Claerbout方法不仅会引入半个采样间隔的时移,而且估算的频率值可能超过Nyqusit频率.本文在Claerbout公式的基础上导出了一种估算瞬时频率的公式,该公式消除了时移,且负频尖峰也得到抑制;基于时频表示一阶矩的方法的计算结果较为平滑,同时具有一定的抗噪能力.最后用本文导出的公式和时频表示一阶矩两种方法计算了南海东北部一条地震剖面的瞬时频率,并将其结果与SeismicUnix中相关函数的计算结果做了比较,表明本文导出公式的计算结果较为理想.
We compare four types of methods for estimating instantaneous frequency.The phase difference estimator is susceptible to noise.The zero-crossing estimator is suitable for periodic signal and is not good enough for non-periodic signal.However,the results of the zero-crossing method can be improved by interpolating the signal.There are three FIR differentiator methods.The instantaneous frequency computed with the two-point FIR differentiator resembles the standard instantaneous frequency,but this method introduces a half-sample time shift.This can be avoided by using a three-point FIR differentiator,but the estimating spikes have a tendency to be negative.The Claerbout's method not only can introduce a half-sample time shift,but also can produce results greater than Nyquist frequency.We present a new formula based on the Claerbout's formula.Using this formula,the half-sample time shift can be avoid and the negative spikes can be suppressed.The results calculated with the one-order frequency moment of a time-frequency representation(TFR)are smooth and withstand noise.At last,we calculate the instantaneous frequency section of a seismic post-stack section from the northeastern South China Sea using the new presented formula and the one-order frequency moment of TFR,and compare the results with the instantaneous frequencies which is computed with a related function in Seismic Unix software.The results indicate that the estimations calculated with the new formula are good enough.
We compare four types of methods for estimating instantaneous frequency.The phase difference estimator is susceptible to noise.The zero-crossing estimator is suitable for periodic signal and is not good enough for non-periodic signal.However,the results of the zero-crossing method can be improved by interpolating the signal.There are three FIR differentiator methods.The instantaneous frequency computed with the two-point FIR differentiator resembles the standard instantaneous frequency,but this method introduces a half-sample time shift.This can be avoided by using a three-point FIR differentiator,but the estimating spikes have a tendency to be negative.The Claerbout's method not only can introduce a half-sample time shift,but also can produce results greater than Nyquist frequency.We present a new formula based on the Claerbout's formula.Using this formula,the half-sample time shift can be avoid and the negative spikes can be suppressed.The results calculated with the one-order frequency moment of a time-frequency representation(TFR)are smooth and withstand noise.At last,we calculate the instantaneous frequency section of a seismic post-stack section from the northeastern South China Sea using the new presented formula and the one-order frequency moment of TFR,and compare the results with the instantaneous frequencies which is computed with a related function in Seismic Unix software.The results indicate that the estimations calculated with the new formula are good enough.
引文
[1]Baraniuk R G,Coates M,Steeghs P.Hybrid linear/quadratic time-frequency attributes.IEEE Trans.Signal Processing,2001,49(4):760～766
[2]Boashash B.Estimating andinterpreting the instantaneous of a signal-Part1:algorithms and applications.Proceedings of the IEEE,1992,80(4):520～538
[3]宋海斌,吴时国,江为为.南海东北部973剖面BSR及其热流特征.地球物理学报,2007,50(5):1508～1517Song HB,Wu S G,Jiang W W.The characteristics of BSRs and their derived heat flow on the profile973in the northeastern South China Sea.Chinese J.Geophys.(in Chinese),2007,50(5):1508～1517
[4]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1998Zhang X D,Bao Z.Non-stationary Signal Analysis and Processing(in Chinese).Beijing:National Defence Industry Press,1998
[5]Taner M T,Koehler F,Sheriff R E.Complex seismic trace analysis.Geophysics,1979,44(6):1041～1063
[6]Scheuer T E,Oldenburg D W.Local phase velocity from complex seismic data.Geophysics,1988,53:1503～1511
[7]Matheney M P,Nowack R L.Seismic attenuation values obtained frominstantaneous frequency matching and spectral ratios.Geophys.J.Int.1995,123:1～15
[8]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):821～832Gao J H,Wang W B,Zhu G M.Wavelet transform and instantaneous attributes analysis.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),1997,40(6):821～832
[9]Karsli H,Dondurur D,Cifci G.Application of complex-trace analysis to seismic data for random-noise suppression and temporal resolutionimprovement.Geophysics,2006,71(3):V79～V86
[10]Boashash B.Estimating andinterpreting the instantaneous of a signal-Part2:algorithms and applications.Proceedings of the IEEE,1992,80(4):540～568
[11]程乾生.希尔伯特变换与信号的包络、瞬时相位和瞬时频率.石油地球物理勘探,1979,3:1～14Cheng Q S.Hilbert transform and signal envelope,instantaneous phase and instantaneous frequency.Oil Geophysical Prospecting(in Chinese),1979,3:1～14
[12]贺振华.地震波复数道分析的计算方法.石油物探,1980,4:64～80He Z H.The calculation of complex seismic trace analysis.Geophysical Prospecting for Petroleum(in Chinese),1980,4:64～80
[13]Barnes A E.The calculation of instantaneous frequency and instantaneous bandwidth.Geophysics,1992,57:1520～1524
[14]Barnes A E.Weighted average seismic attributes.Geophysics,2000,65:275～285
[15]陈林.地震时频属性提取及其在海底天然气渗漏识别中的应用[硕士论文].北京:中国科学院地质与地球物理研究所,2007Chen L.The extraction of time-frequency seismic attributes andits application in the detection of submarine natural gas seepage[Master′s thesis](in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2007
[16]Hardy H H,Beier R A,Gaston J D.Frequency estimate of seismic traces.Geophysics,2003,68(1):370～380
[17]Boashash B,O′Shea P,Ristic B.Statistical computation comparison of some estimators for instantaneous frequency.Proc.IEEEICASSP-91,1991.3193～3196
[18]Claerbout J F.Fundamentals of Geophysical Data Processing:with Application to Petroleum Prospecting.New York:McGraw-Hill Book Co.,1976
[19]Steeghs P,Drijkoningen G.Seismic sequence analysis and attribute extraction using quadratic time-frequency representations.Geophysics,2001,66(6):1947～1959
[20]Fleischer P,Orsi T H,Richardson M,et al.Distribution of free gas in marine sediments:a global overview.Geo-Mar.Lett.,2001,21:103～122
[21]Taylor M H,Dillon W P,Pecher I A.Trapping and migration of methane associated withthe gas hydrate stability zone at the Blake Ridge Diapir:new insights from seismic data.Marine Geology,2000,164:79～89
[22]Castagna J P,Sun Shengjie,Siegfried R W.Instantaneous spectral analysis:dectection of low-frequency shadows associated with hydrocarbons.The Leading Edge,2003,22:120～127
[2]Boashash B.Estimating andinterpreting the instantaneous of a signal-Part1:algorithms and applications.Proceedings of the IEEE,1992,80(4):520～538
[3]宋海斌,吴时国,江为为.南海东北部973剖面BSR及其热流特征.地球物理学报,2007,50(5):1508～1517Song HB,Wu S G,Jiang W W.The characteristics of BSRs and their derived heat flow on the profile973in the northeastern South China Sea.Chinese J.Geophys.(in Chinese),2007,50(5):1508～1517
[4]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1998Zhang X D,Bao Z.Non-stationary Signal Analysis and Processing(in Chinese).Beijing:National Defence Industry Press,1998
[5]Taner M T,Koehler F,Sheriff R E.Complex seismic trace analysis.Geophysics,1979,44(6):1041～1063
[6]Scheuer T E,Oldenburg D W.Local phase velocity from complex seismic data.Geophysics,1988,53:1503～1511
[7]Matheney M P,Nowack R L.Seismic attenuation values obtained frominstantaneous frequency matching and spectral ratios.Geophys.J.Int.1995,123:1～15
[8]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):821～832Gao J H,Wang W B,Zhu G M.Wavelet transform and instantaneous attributes analysis.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),1997,40(6):821～832
[9]Karsli H,Dondurur D,Cifci G.Application of complex-trace analysis to seismic data for random-noise suppression and temporal resolutionimprovement.Geophysics,2006,71(3):V79～V86
[10]Boashash B.Estimating andinterpreting the instantaneous of a signal-Part2:algorithms and applications.Proceedings of the IEEE,1992,80(4):540～568
[11]程乾生.希尔伯特变换与信号的包络、瞬时相位和瞬时频率.石油地球物理勘探,1979,3:1～14Cheng Q S.Hilbert transform and signal envelope,instantaneous phase and instantaneous frequency.Oil Geophysical Prospecting(in Chinese),1979,3:1～14
[12]贺振华.地震波复数道分析的计算方法.石油物探,1980,4:64～80He Z H.The calculation of complex seismic trace analysis.Geophysical Prospecting for Petroleum(in Chinese),1980,4:64～80
[13]Barnes A E.The calculation of instantaneous frequency and instantaneous bandwidth.Geophysics,1992,57:1520～1524
[14]Barnes A E.Weighted average seismic attributes.Geophysics,2000,65:275～285
[15]陈林.地震时频属性提取及其在海底天然气渗漏识别中的应用[硕士论文].北京:中国科学院地质与地球物理研究所,2007Chen L.The extraction of time-frequency seismic attributes andits application in the detection of submarine natural gas seepage[Master′s thesis](in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2007
[16]Hardy H H,Beier R A,Gaston J D.Frequency estimate of seismic traces.Geophysics,2003,68(1):370～380
[17]Boashash B,O′Shea P,Ristic B.Statistical computation comparison of some estimators for instantaneous frequency.Proc.IEEEICASSP-91,1991.3193～3196
[18]Claerbout J F.Fundamentals of Geophysical Data Processing:with Application to Petroleum Prospecting.New York:McGraw-Hill Book Co.,1976
[19]Steeghs P,Drijkoningen G.Seismic sequence analysis and attribute extraction using quadratic time-frequency representations.Geophysics,2001,66(6):1947～1959
[20]Fleischer P,Orsi T H,Richardson M,et al.Distribution of free gas in marine sediments:a global overview.Geo-Mar.Lett.,2001,21:103～122
[21]Taylor M H,Dillon W P,Pecher I A.Trapping and migration of methane associated withthe gas hydrate stability zone at the Blake Ridge Diapir:new insights from seismic data.Marine Geology,2000,164:79～89
[22]Castagna J P,Sun Shengjie,Siegfried R W.Instantaneous spectral analysis:dectection of low-frequency shadows associated with hydrocarbons.The Leading Edge,2003,22:120～127
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