一种ARMA模型地震子波提取方法研究
|
摘要
在地震子波因果、混合相位的假设下,本文突破突破滑动平均(MA)型假设的地震子波提取技术,提出一种阶数吝啬的自回归滑动平均(ARMA)模型对地震子波进行参数化准确建模的方法.针对地震子波ARMA模型定阶困难,超定阶容易造成计算量大、运算速度慢,欠定阶不能满足精确子波的要求,本文采用基于自相关函数的奇异值分解(SVD)法确定AR模型阶数,同时将信息量准则法与高阶累积量法相结合,提出了一种新的MA模型定阶法.数值仿真和实际地震数据处理结果表明,本文所用方法可以有效地压制加性高斯色噪声,信息量准则法可有效提高MA定阶的准确率,在保证子波精度的同时尽可能降低模型阶数,实现运算高效率.
Seismic wavelets estimated by the current wavelet extraction technology have low resolution and the computing cost is high.Based on seismic record characteristics,assumptions and boundary constraints,we have analyzed various attributes and characteristics of seismic wavelets,broken through the seismic wavelet extraction technology based on Moving Average (MA) model,and proposed a parsimonious parameters Autoregressive Moving Average (ARMA) model which was used to model the parameterized seismic wavelet accurately,and studied the order determination of seismic wavelet ARMA model mainly.We determined the Average (AR) part order using the SVD method based on autocorrelation firstly,and then proposed a new MA order determination method which introduced information theoretic criteria function into MA order determination based on higher-order cumulant.In the premise of ensuring the accuracy of seismic wavelets,this method reduced the model order as much as possible so as to obtain high-efficiency and the high-precision seismic wavelet model order determination.Theoretical analysis and numerical simulations demonstrated that the computing cost of the SVD method based on autocorrelation is low and the method can be used with moderate noises;and the new method can effectively improve the stability and accuracy of MA model order determination.
Seismic wavelets estimated by the current wavelet extraction technology have low resolution and the computing cost is high.Based on seismic record characteristics,assumptions and boundary constraints,we have analyzed various attributes and characteristics of seismic wavelets,broken through the seismic wavelet extraction technology based on Moving Average (MA) model,and proposed a parsimonious parameters Autoregressive Moving Average (ARMA) model which was used to model the parameterized seismic wavelet accurately,and studied the order determination of seismic wavelet ARMA model mainly.We determined the Average (AR) part order using the SVD method based on autocorrelation firstly,and then proposed a new MA order determination method which introduced information theoretic criteria function into MA order determination based on higher-order cumulant.In the premise of ensuring the accuracy of seismic wavelets,this method reduced the model order as much as possible so as to obtain high-efficiency and the high-precision seismic wavelet model order determination.Theoretical analysis and numerical simulations demonstrated that the computing cost of the SVD method based on autocorrelation is low and the method can be used with moderate noises;and the new method can effectively improve the stability and accuracy of MA model order determination.
引文
[1] 陆文凯,丁文龙,张善文,等.基于信号子空间分解的三维地震资料高分辨率处理方法[J].地球物理学报,2005,48(4) :896～90． Lu W K, Ding W L, Zhang S W, et al. A high-resolution processing technique for 3-D seismic data based on signal sub space decomposition[J]. Chinese J. Geophys. (in Chinese),2005,48(4) :896～901．
[2] 高静怀,毛剑,满蔚仕,等.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报,2006,49(4) :1155～1163． Gao J H, Mao J, Man W S, et al. On the denoising method of prestack seismic data in wavelet domain [ J ]. Chinese J.Geophys. (in Chinese), 2006,49(4) : 1155～1163．
[3] 高少武,赵波,贺振华,等.地震子波提取方法研究进展[J].地球物理学进展,2009,24(4) :1384～139． Gao S W, Zhao B, He Z H, et al. Research progress of seismic wavelet extraction [ J ]. Progress in Geophys. (in Chinese), 2009,24(4) : 1384～139．
[4] 李亚峻,李月,高颖.基于双谱幅值和相位重构的地震子波提取[J].地球物理学进展,2007,22(3) :947～952． Li Y J, Li Y, Gao Y. A method of extracting seismic wavelet based on bispectrum amplitude and phase reconstruction[J]. Progress in Geophys, 2007,22(3) :947～952．
[5] Lazear G D, “Mixed-phase Wavelet Estimation Using Fourthorder Cumulants”, Geophysics, 1993, 58(7) : 1042～1051．
[6] 王荐,朱仕军,文中平,等.基于高阶累积量拟合和混合蚁群算法的地震子波估计[J].勘探地球物理进展,2009,32(5) :330～333+307． Wang J, Zhu S J, Wen Z P, et al. Seismic wavelet estimation via cumulant based fitting method and Hybrid ant colony algorithm[J]. Progress in Exploration Geophysics, 2009,32 (05) :330～333+307．
[7] 路荣亮,张海燕.基于PSO＆GA结合算法的地震子波估计[J].微计算机信息,2007,(25) :293～294+297． Lu R L, Zhang H Y. Seismic wavelet estimation via improved genetic algorithm and improved particle swarm optimization [J]. Mini-Computer Information, 2007, (25) : 293 ～ 294 +297．
[8] 戴永寿,王俊岭,王伟伟,等.基于高阶累积量ARMA模型线性非线性结合的地震子波提取方法研究[J].地球物理学报,2008,51(6) :1851～1859． Dai Y S, Wang J L, Wang W W, et al. Seismic wavelet extraction via cumulant-based ARMA model approach with linear and nonlinear combination[J]. Chinese J. Geophys. (in Chinese), 2008, 51(6) :1851～1859．
[9] 王少水,戴永寿,王芳,等.参数化地震子波估计模型定阶方法研究综述[J].地球物理学进展,2009,24(4) :1405～1410． Wang S S, Dai Y S, Wang F, etal. The summarization of the research on the order determination of the seismic wavelet parameterized estimation model [J]. Progress in Geophys, 2009, 24(4) :1405～1410．
[10] Cadzow J A. “Spectral estimation: An overdetermined rational model equation approach” [J]. IEEE, 1982, 70(9) : 907～939．
[11] Giannakis G B, Mendel J M. “ Cumulant-based order determination of non-Gaussian ARMA models” [J]. IEEE Trans. Signal Processing, 1990, 38:1411～1423．
[12] Zhang X D, Zhang Y S. “Singular value decomposition-based MA Order Determination of Non-Gaussian ARMA Model” [J]. IEEE transactions on signal processing, 1993, 41(8) : 265～266．
[2] 高静怀,毛剑,满蔚仕,等.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报,2006,49(4) :1155～1163． Gao J H, Mao J, Man W S, et al. On the denoising method of prestack seismic data in wavelet domain [ J ]. Chinese J.Geophys. (in Chinese), 2006,49(4) : 1155～1163．
[3] 高少武,赵波,贺振华,等.地震子波提取方法研究进展[J].地球物理学进展,2009,24(4) :1384～139． Gao S W, Zhao B, He Z H, et al. Research progress of seismic wavelet extraction [ J ]. Progress in Geophys. (in Chinese), 2009,24(4) : 1384～139．
[4] 李亚峻,李月,高颖.基于双谱幅值和相位重构的地震子波提取[J].地球物理学进展,2007,22(3) :947～952． Li Y J, Li Y, Gao Y. A method of extracting seismic wavelet based on bispectrum amplitude and phase reconstruction[J]. Progress in Geophys, 2007,22(3) :947～952．
[5] Lazear G D, “Mixed-phase Wavelet Estimation Using Fourthorder Cumulants”, Geophysics, 1993, 58(7) : 1042～1051．
[6] 王荐,朱仕军,文中平,等.基于高阶累积量拟合和混合蚁群算法的地震子波估计[J].勘探地球物理进展,2009,32(5) :330～333+307． Wang J, Zhu S J, Wen Z P, et al. Seismic wavelet estimation via cumulant based fitting method and Hybrid ant colony algorithm[J]. Progress in Exploration Geophysics, 2009,32 (05) :330～333+307．
[7] 路荣亮,张海燕.基于PSO＆GA结合算法的地震子波估计[J].微计算机信息,2007,(25) :293～294+297． Lu R L, Zhang H Y. Seismic wavelet estimation via improved genetic algorithm and improved particle swarm optimization [J]. Mini-Computer Information, 2007, (25) : 293 ～ 294 +297．
[8] 戴永寿,王俊岭,王伟伟,等.基于高阶累积量ARMA模型线性非线性结合的地震子波提取方法研究[J].地球物理学报,2008,51(6) :1851～1859． Dai Y S, Wang J L, Wang W W, et al. Seismic wavelet extraction via cumulant-based ARMA model approach with linear and nonlinear combination[J]. Chinese J. Geophys. (in Chinese), 2008, 51(6) :1851～1859．
[9] 王少水,戴永寿,王芳,等.参数化地震子波估计模型定阶方法研究综述[J].地球物理学进展,2009,24(4) :1405～1410． Wang S S, Dai Y S, Wang F, etal. The summarization of the research on the order determination of the seismic wavelet parameterized estimation model [J]. Progress in Geophys, 2009, 24(4) :1405～1410．
[10] Cadzow J A. “Spectral estimation: An overdetermined rational model equation approach” [J]. IEEE, 1982, 70(9) : 907～939．
[11] Giannakis G B, Mendel J M. “ Cumulant-based order determination of non-Gaussian ARMA models” [J]. IEEE Trans. Signal Processing, 1990, 38:1411～1423．
[12] Zhang X D, Zhang Y S. “Singular value decomposition-based MA Order Determination of Non-Gaussian ARMA Model” [J]. IEEE transactions on signal processing, 1993, 41(8) : 265～266．
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心