高阶统计量地震子波估计建模
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摘要
本文在反射系数序列为非高斯、平稳和统计独立的随机过程,地震子波为非因果、混合相位的假设条件下,分别应用滑动平均(MA)和自回归滑动平均(ARMA)模型对地震记录进行建模,并采用运算代价较小的基于高阶累积量的线性化求解方法——累积量矩阵方程法进行了子波提取和模型适应性的研究。数值模拟结果和实际地震数据处理结果表明:自回归滑动平均(ARMA)模型比滑动平均(MA)模型具有参数节省、模型更为高效的特点;累积量矩阵方程法可以有效地压制加性高斯噪声,但对累积量样本估计的准确性要求较高;如果累积量样本估计的误差和方差适度,结合自回归滑动平均(ARMA)模型描述的累积量矩阵方程法可以高效、准确地估计出地震子波。
Under the hypothetical condition that the stochastic process is non-Gauss, stationary and statistic independence and seismic wavelet is non-causal and mixed phase, the paper carried out the study of wavelet pickup and model adaptability by application of moving average (MA) and autoregressive moving average (ARMA) models to create the models of seismic records respectively and using high-order-cumulants-based linear solution approach—cumulants matrix equation approach that is small operational efforts. The results of numeric simulation and real seismic data processing showed that the ARMA model was characterized by parameter-economic and high efficiency in comparison with MA model; the cumulants matrix equation approach can more effectively suppress the addictive Gauss colored noise but requires the estimation of cumulants samples to have high accuracy; if the errors of estimation of cumulants samples and variance are appropriate, the described cumulants matrix equation approach combing with ARMA model can high-efficiently and accurately estimate the seismic wavelet.
Under the hypothetical condition that the stochastic process is non-Gauss, stationary and statistic independence and seismic wavelet is non-causal and mixed phase, the paper carried out the study of wavelet pickup and model adaptability by application of moving average (MA) and autoregressive moving average (ARMA) models to create the models of seismic records respectively and using high-order-cumulants-based linear solution approach—cumulants matrix equation approach that is small operational efforts. The results of numeric simulation and real seismic data processing showed that the ARMA model was characterized by parameter-economic and high efficiency in comparison with MA model; the cumulants matrix equation approach can more effectively suppress the addictive Gauss colored noise but requires the estimation of cumulants samples to have high accuracy; if the errors of estimation of cumulants samples and variance are appropriate, the described cumulants matrix equation approach combing with ARMA model can high-efficiently and accurately estimate the seismic wavelet.
引文
[1]Lazear G D.Mixed-phase wavelet esti mation using fourth-order cumulants.Geophysics,1993,58(7):1042~1051
[2]Velis D Rand Ulrych TJ.Si mulated annealing wave-let esti mation via fourth-order cumulant matching.Geophysics,1996,61(6):1939~1948
[3]尹成等.基于综合的混沌优化算法估计地震子波.物探化探计算技术,2001,23(2):97~100
[4]石殿祥,李岩.基于高阶累积量的非最小相位地震子波提取.石油地球物理勘探,1999,34(5):491~499
[5]Zhang X Det al.FIRsystemidentification using high-er-order cumulants alone.IEEE Trans on Signal Processing,1994,42(10):2854~2858
[6]Tugnait J K.Fitting non-causal autoregressive signal plus noise model to noisy non-Gaussian linear proces-ses.IEEE Trans on Automatic Control,1987,32(6):547~552
[7]Giannakis G B and Swami A.On esti mating non-caus-al non-mini mumphase ARMA models of non-Gaussi-an process.IEEE Trans on ASSP,1990,38(3):478~495
[8]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.电子学报,1996,24(4):24~28
[9]Cadzow J A.Spectral esti mation:An overdetermined rational model equation approach.Proceedings of the IEEE,1982,70(9):907~939
[10]Zhang X D et al.Singular value decomposition-based MA order determination of non-Gaussian ARMA models.IEEE Trans on Signal Processing,1993,41:2657~2664
[2]Velis D Rand Ulrych TJ.Si mulated annealing wave-let esti mation via fourth-order cumulant matching.Geophysics,1996,61(6):1939~1948
[3]尹成等.基于综合的混沌优化算法估计地震子波.物探化探计算技术,2001,23(2):97~100
[4]石殿祥,李岩.基于高阶累积量的非最小相位地震子波提取.石油地球物理勘探,1999,34(5):491~499
[5]Zhang X Det al.FIRsystemidentification using high-er-order cumulants alone.IEEE Trans on Signal Processing,1994,42(10):2854~2858
[6]Tugnait J K.Fitting non-causal autoregressive signal plus noise model to noisy non-Gaussian linear proces-ses.IEEE Trans on Automatic Control,1987,32(6):547~552
[7]Giannakis G B and Swami A.On esti mating non-caus-al non-mini mumphase ARMA models of non-Gaussi-an process.IEEE Trans on ASSP,1990,38(3):478~495
[8]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.电子学报,1996,24(4):24~28
[9]Cadzow J A.Spectral esti mation:An overdetermined rational model equation approach.Proceedings of the IEEE,1982,70(9):907~939
[10]Zhang X D et al.Singular value decomposition-based MA order determination of non-Gaussian ARMA models.IEEE Trans on Signal Processing,1993,41:2657~2664
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