基于高阶累积量的线性化子波提取方法研究
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摘要
在地震子波非因果、混合相位的假设下,分别应用滑动平均(MA)和自回归滑动平均(ARMA)模型对地震记录建模,并采用基于高阶累积量的线性方程法对子波提取和模型适应性进行了研究。数值仿真结果表明,ARMA模型比MA模型在描述地震记录时具有参数节俭、模型更为高效的特点;基于高阶累积量的线性方程法对加性高斯色噪声有较好的压制效果,却强烈依赖于累积量样本估计的准确性。如果累积量样本估计的误差和方差适度,结合AR-MA模型描述的累积量线性方程法适用于非因果、混合相位的子波提取,其有效性通过实际地震数据的处理得到了验证。
Based on the assumption that the wavelet is non-causal and mixed phase,both the moving average(MA) and autoregressive moving average(ARMA) models were introduced to fit the seismic record.A linear equation approach based on higher-order cumulant was employed to extract the wavelet and evaluate the adaptability of each model.Numerical simulations demonstrate that the ARMA model provides a parsimonious,more efficient signal model for fitting seismic trace than the MA model does.The cumulant-based linear equations approach is not sensitive to Gaussian colored noise,but strongly relies upon the accuracy of the trace cumulant estimates.If the estimated error and variance of trace cumulants are moderate,the cumulant-based linear equations approach combined with the ARMA model description of the seismic record is appropriate for non-causal,mixed phase wavelet extraction.The real seismic data examples demonstrate possible uses of the method.
Based on the assumption that the wavelet is non-causal and mixed phase,both the moving average(MA) and autoregressive moving average(ARMA) models were introduced to fit the seismic record.A linear equation approach based on higher-order cumulant was employed to extract the wavelet and evaluate the adaptability of each model.Numerical simulations demonstrate that the ARMA model provides a parsimonious,more efficient signal model for fitting seismic trace than the MA model does.The cumulant-based linear equations approach is not sensitive to Gaussian colored noise,but strongly relies upon the accuracy of the trace cumulant estimates.If the estimated error and variance of trace cumulants are moderate,the cumulant-based linear equations approach combined with the ARMA model description of the seismic record is appropriate for non-causal,mixed phase wavelet extraction.The real seismic data examples demonstrate possible uses of the method.
引文
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[12]CADZOW J A.Spectral estimation:an overdeterminedrational model equation approach[J].Proceedings of theIEEE,1982,70(9):907-939.
[2]VELIS D R,ULRYCH T J.Simulated annealing waveletestimation via fourth-order cumulant matching[J].Geo-physics,1996,61(6):1 939-1 948.
[3]尹成,周翼,谢桂生,等.基于综合的混沌优化算法估计地震子波[J].物探化探计算技术,2001,23(2):97-100.YIN Cheng,ZHOU Yi,XIE Gui-sheng,et al.Seismicwavelet estimation using hybrid chaos optimization algo-rithm[J].Computing Techniques for Geophysical andGeochemical Exploration,2001,23(2):97-100.
[4]DAI Yong-shou,ZHENG De-ling,LI Yuan-yuan,et al.Immune algorithm seismic wavelet estimation using fourth-order cumulant[C]//QI Ji-ming.Proceedings of the Sev-enth International Conference on Electronic Measurement&Instruments(ICEMI 2005).Beijing:International Academ-ic Publishers/World Publishing Corporation,2005:241-244.
[5]石殿祥,李岩.基于高阶累积量的非最小相位地震子波提取[J].石油地球物理勘探,1999,34(5):491-499.SHI Dian-xiang,LI Yan.Non-minimum phase waveletobtainment based on high-order accumulated amount[J].Oil Geophysical Prospecting,1999,34(5):491-499.
[6]ZHANG Xian-da,ZHENG Yuan-sheng.FIR system identi-fication using higher-order cumulants alone[J].IEEE Trans-actions on Signal Processing,1994,42:2 854-2 858.
[7]TUGNAIT J K.Fitting non-causal autoregressive signalplus noise model to noisy non-Gaussian linear processes[J].IEEE Transactions on Automatic Control,1987,32(6):547-552.
[8]GIANNAKIS G B,SWAMI A.On estimating non-causalnon-minimum phase ARMA models of non-Gaussian process[J].IEEE Transactions on Acoustics,Speech,and SignalProcessing,1990,38(3):478-495.
[9]陈滨宁,张贤达.高斯ARMA噪声中非因果非最小相位系统的辨识[J].电子学报,1996,24(4):24-28.CHEN Bin-ning,ZHANG Xian-da.Identification of anon-causal non-minimum phase system in a Gaussian AR-MA noise[J].Acta Electronica Sinica,1996,24(4):24-28.
[10]梁光河.地震子波提取方法研究[J].石油物探,1998,37(1):31-39.LIANG Guang-he.On the method of seismic waveletextraction[J].Geophysical Prospecting for Petroleum,1998,37(1):31-39.
[11]ZHANG Xian-da,ZHENG Yuan-sheng.Singular valuedecomposition-based MA order determination of non-Gaussian ARMA models[J].IEEE Transactions on Sig-nal Processing,1993,41:2 657-2 664.
[12]CADZOW J A.Spectral estimation:an overdeterminedrational model equation approach[J].Proceedings of theIEEE,1982,70(9):907-939.
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