基于保角变换的双谱域相位谱估计方法及其在地震子波估计中的应用(英文)
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摘要
地震子波估计是地震资料处理与解释中的重要环节,它的准确与否直接关系到反褶积及反演等结果的好坏。高阶谱(双谱和三谱)地震子波估计方法是一类重要的、新兴的子波估计方法,然而基于高阶谱的地震子波估计往往因为高阶相位谱卷绕的原因,导致子波相位谱求解产生偏差,进而影响了混合相位子波估计的效果。针对这一问题,本文在双谱域提出了一种基于保角变换的相位谱求解方法。通过缩小傅里叶相位谱的取值范围,有效避免了双谱相位发生卷绕的情况,从而消除了原相位谱估计中双谱相位卷绕的影响。该方法与最小二乘法相位谱估计相结合,构成了基于保角变换的最小二乘地震子波相位谱估计方法,并与最小二乘地震子波振幅谱估计方法一起,应用到了地震资料混合相位子波估计中。理论模型和实际资料验证了该方法的有效性。同时本文将双谱域地震子波相位谱估计中保角变换的思想推广到三谱域地震子波相位谱估计中。
Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.
Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.
引文
Bartelt, H., Lohmann, A. W., and Wirnitzer, B., 1984, Phaseand amplitude recovery from bispectra: Applied Optics,23(18), 3121 – 3129.
Brillinger, D. R., 1977, The identification of a particularnonlinear time series system: Biometrika, 64(3), 509 – 515.
Cheng, Q. S., 2003, Digital signal processing: BeijingUniversity Press (in Chinese), 172 – 175.
Edgar, J., and van der Baan, M., 2009, How reliable isstatistical wavelet estimation?: 79th Ann. Internat. Mtg.,Soc. Explor. Geophys., Expanded Abstracts, 3233 –3237.
Huang, J. Y., Li, L. M., and Luo, S. X., 2006, Seismicwavelet estimation based on the high-order spectrum:Journal of Chengdu University of Technology (Scienceand Technology Edition) (in Chinese), 33(2), 188 – 192.
Kang, M. G., Lay, K. T., and Katsaggelos, A. K., 1991,Phase estimation using the bispectrum and its applicationto image restoration: Optical Engineering, 30(7), 976 –985.
Lazear, G. D., 1993, Mixed-phase wavelet estimation usingfourth-order cumulants: Geophysics, 58(7), 1042 – 1051.
Liang, K. M., Liu, F., and Miou, G. Q., 1995, Method ofmathematical physics: Advanced Education Press (inChinese), 423 – 458.
Lii, K. S., and Rosenblatt, M., 1982, Deconvolution andestimation of transfer function phase and coefficients fornon-Gaussian linear processes: The Annals Statistics,10(4), 1195 – 1208.
Lu, W. K., 2005, Blind channel estimation using zero-lagslice of third-order moment: IEEE Signal ProcessingLetters, 12(10), 725 – 727.
Lu, W. K., Zhang, Y. S., Zhang, S. W., and Xiao, H. Q.,2007, Blind wavelet estimation using a zero-lag slice ofthe fourth-order statistics: Journal of Geophysics andEngineering, 4(1), 24 – 30.
Marron, J. C., Sanchez, P. P., and Sullivan, R. C., 1990,Unwrapping algorithm for least-squares phase recoveryfrom the modulo 2π bispectrum phase: Journal of theOptical Society of America A: Optics, Image Science,and Vision, 7(1), 14 – 20.
Matsuoka, T., and Ulrych, T. J., 1984, Phase estimationusing the bispectrum: Proceedings of the IEEE, 72(10),1403 – 1411.
Mendel, J. M., 1991, Tutorial on higher-order statistics(spectra) in signal processing and system theory:theoretical results and some applications: Proceedings ofthe IEEE, 79(3), 278 – 305.
Nikias, C. L., and Petropulu, A. P., 1993, Higher-order spectra analysis: A nonlinear signal processingframework: Prentice Hall.
Pan, R., and Nikias, C. L., 1987, Phase reconstruction inthe trispectrum domain: IEEE Transactions on Acoustics,Speech, and Signal Processing, 35(6), 895 – 897.
Petropulu, A. P., and Pozidis, H., 1998, Phase reconstructionfrom bispectrum slices: IEEE Transactions on SignalProcessing, 46(2), 527 – 530.
Robinson, E. A., 1967, Predictive decomposition oftime series with application to seismic exploration:Geophysics, 32(3), 418 – 484.
Sacchi, M. D., and Ulrych, T. J., 2000, Nonminimum-phasewavelet estimation using higher order statistics: The Leading Edge, 19(1), 80 – 83.
Sundaramoorthy, G., Raghuveer, M. R., and Dianat, S.A., 1990, Bispectral reconstruction of signals in noise:amplitude reconstruction issues: IEEE Transactions onAcoustics. Speech, and Signal Processing, 38(7), 1297 –1306.
Tekalp, A. M., and Erdem, A. T., 1989, Higher orderspectrum factorization in one and two dimensions withapplications in signal modeling and nonminimum phasesystem identification: IEEE Transactions on Acoustics.Speech, and Signal Processing, 37(10), 1537 – 1549.
Xi’an Jiaotong University Higher Mathematics Department,1996, Complex variables functions (Fourth edition):Advanced Education Press (in Chinese), 186 – 191.
Yuan, S. Y., Wang, S. X., and Tian, N., 2009, Swarmintelligence optimization and its application ingeophysical data inversion: Applied Geophysics, 6(2),166 – 174.
Zhang, F., Wang, Y. H., and Li, X. Y., 2008, Mixed-phase wavelet estimation using unwrapped phase ofbispectrum: 70th EAGE Conference and Exhibition.
Zhang, F., Wang, Y. H., and Li, X. Y., 2009, Mixed-phase wavelet estimation using unwrapped phase ofbispectrum: CPS/SEG Beijing International GeophysicalConference and Exposition.
Brillinger, D. R., 1977, The identification of a particularnonlinear time series system: Biometrika, 64(3), 509 – 515.
Cheng, Q. S., 2003, Digital signal processing: BeijingUniversity Press (in Chinese), 172 – 175.
Edgar, J., and van der Baan, M., 2009, How reliable isstatistical wavelet estimation?: 79th Ann. Internat. Mtg.,Soc. Explor. Geophys., Expanded Abstracts, 3233 –3237.
Huang, J. Y., Li, L. M., and Luo, S. X., 2006, Seismicwavelet estimation based on the high-order spectrum:Journal of Chengdu University of Technology (Scienceand Technology Edition) (in Chinese), 33(2), 188 – 192.
Kang, M. G., Lay, K. T., and Katsaggelos, A. K., 1991,Phase estimation using the bispectrum and its applicationto image restoration: Optical Engineering, 30(7), 976 –985.
Lazear, G. D., 1993, Mixed-phase wavelet estimation usingfourth-order cumulants: Geophysics, 58(7), 1042 – 1051.
Liang, K. M., Liu, F., and Miou, G. Q., 1995, Method ofmathematical physics: Advanced Education Press (inChinese), 423 – 458.
Lii, K. S., and Rosenblatt, M., 1982, Deconvolution andestimation of transfer function phase and coefficients fornon-Gaussian linear processes: The Annals Statistics,10(4), 1195 – 1208.
Lu, W. K., 2005, Blind channel estimation using zero-lagslice of third-order moment: IEEE Signal ProcessingLetters, 12(10), 725 – 727.
Lu, W. K., Zhang, Y. S., Zhang, S. W., and Xiao, H. Q.,2007, Blind wavelet estimation using a zero-lag slice ofthe fourth-order statistics: Journal of Geophysics andEngineering, 4(1), 24 – 30.
Marron, J. C., Sanchez, P. P., and Sullivan, R. C., 1990,Unwrapping algorithm for least-squares phase recoveryfrom the modulo 2π bispectrum phase: Journal of theOptical Society of America A: Optics, Image Science,and Vision, 7(1), 14 – 20.
Matsuoka, T., and Ulrych, T. J., 1984, Phase estimationusing the bispectrum: Proceedings of the IEEE, 72(10),1403 – 1411.
Mendel, J. M., 1991, Tutorial on higher-order statistics(spectra) in signal processing and system theory:theoretical results and some applications: Proceedings ofthe IEEE, 79(3), 278 – 305.
Nikias, C. L., and Petropulu, A. P., 1993, Higher-order spectra analysis: A nonlinear signal processingframework: Prentice Hall.
Pan, R., and Nikias, C. L., 1987, Phase reconstruction inthe trispectrum domain: IEEE Transactions on Acoustics,Speech, and Signal Processing, 35(6), 895 – 897.
Petropulu, A. P., and Pozidis, H., 1998, Phase reconstructionfrom bispectrum slices: IEEE Transactions on SignalProcessing, 46(2), 527 – 530.
Robinson, E. A., 1967, Predictive decomposition oftime series with application to seismic exploration:Geophysics, 32(3), 418 – 484.
Sacchi, M. D., and Ulrych, T. J., 2000, Nonminimum-phasewavelet estimation using higher order statistics: The Leading Edge, 19(1), 80 – 83.
Sundaramoorthy, G., Raghuveer, M. R., and Dianat, S.A., 1990, Bispectral reconstruction of signals in noise:amplitude reconstruction issues: IEEE Transactions onAcoustics. Speech, and Signal Processing, 38(7), 1297 –1306.
Tekalp, A. M., and Erdem, A. T., 1989, Higher orderspectrum factorization in one and two dimensions withapplications in signal modeling and nonminimum phasesystem identification: IEEE Transactions on Acoustics.Speech, and Signal Processing, 37(10), 1537 – 1549.
Xi’an Jiaotong University Higher Mathematics Department,1996, Complex variables functions (Fourth edition):Advanced Education Press (in Chinese), 186 – 191.
Yuan, S. Y., Wang, S. X., and Tian, N., 2009, Swarmintelligence optimization and its application ingeophysical data inversion: Applied Geophysics, 6(2),166 – 174.
Zhang, F., Wang, Y. H., and Li, X. Y., 2008, Mixed-phase wavelet estimation using unwrapped phase ofbispectrum: 70th EAGE Conference and Exhibition.
Zhang, F., Wang, Y. H., and Li, X. Y., 2009, Mixed-phase wavelet estimation using unwrapped phase ofbispectrum: CPS/SEG Beijing International GeophysicalConference and Exposition.
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