子波相位不准对反演结果的影响(英文)
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摘要
本文重点讨论在振幅谱估计准确的情况下,采用不同相位谱子波作为实际估计子波进行线性最小二乘反演,并对结果进行分析。除子波相位外,所有其它影响反演结果的因素均忽略。稀疏反射系数模型(块状波阻抗模型)反演结果表明:(1)使用不同相位谱子波进行反演,其反演结果合成的记录与原始记录都非常匹配,但反演的反射系数和声波阻抗结果与真实模型有差异;(2)反演结果的可靠程度主要与不同相位子波z变换的根的分布有关,当估计子波与真实子波Z变换的根的分布仅在单位圆附近有差异时,反演的反射系数和声波阻抗与真实模型很接近;(3)尽管反演前后地震记录都匹配了,并且评价反演结果好坏的柯西准则或改进柯西准则(反演参数没有进行自适应处理)已经达到了最优(最小),但反演结果与真实模型仍存在较大差异。最后,针对子波相位估计不准可能导致反演效果较差这个问题,我们提出采用求L1范数、丰度、变分、柯西准则(反演参数进行了自适应处理)或/和改进柯西准则(反演参数进行了自适应处理)的最优值或次优值作为评价准则的一种解决办法,理论上得到了好的效果。
On the assumption that the seismic wavelet amplitude spectrum is estimated accurately, a group of wavelets with different phase spectra, regarded as estimated wavelets, are used to implement linear least-squares inversion. During inversion, except for the wavelet phase, all other factors affecting inversion results are not taken into account. The inversion results of a sparse reflectivity model (or blocky impedance model) show that: (1) although the synthetic data using inversion results matches well with the original seismic data, the inverted reflectivity and acoustic impedance are different from that of the real model. (2) the inversion result reliability is dependent on the estimated wavelet Z transform root distribution. When the estimated wavelet Z transform roots only differ from that of the real wavelet near the unit circle, the inverted reflectivity and impedance are usually consistent with the real model; (3) although the synthetic data matches well with the original data and the Cauchy norm (or modified Cauchy norm) with a constant damping parameter has been optimized, the inverted results are still greatly different from the real model. Finally, we suggest using the L1 norm, Kurtosis, variation, Cauchy norm with adaptive damping parameter or/and modified Cauchy norm with adaptive damping parameter as evaluation criteria to reduce the bad influence of inaccurate wavelet phase estimation and obtain good results in theory.
On the assumption that the seismic wavelet amplitude spectrum is estimated accurately, a group of wavelets with different phase spectra, regarded as estimated wavelets, are used to implement linear least-squares inversion. During inversion, except for the wavelet phase, all other factors affecting inversion results are not taken into account. The inversion results of a sparse reflectivity model (or blocky impedance model) show that: (1) although the synthetic data using inversion results matches well with the original seismic data, the inverted reflectivity and acoustic impedance are different from that of the real model. (2) the inversion result reliability is dependent on the estimated wavelet Z transform root distribution. When the estimated wavelet Z transform roots only differ from that of the real wavelet near the unit circle, the inverted reflectivity and impedance are usually consistent with the real model; (3) although the synthetic data matches well with the original data and the Cauchy norm (or modified Cauchy norm) with a constant damping parameter has been optimized, the inverted results are still greatly different from the real model. Finally, we suggest using the L1 norm, Kurtosis, variation, Cauchy norm with adaptive damping parameter or/and modified Cauchy norm with adaptive damping parameter as evaluation criteria to reduce the bad influence of inaccurate wavelet phase estimation and obtain good results in theory.
引文
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Puryear, C. I., and Castagna, J. P., 2008, Layer-thicknessdetermination and stratigraphic interpretation usingspectral inversion: Theory and application: Geophysics,73, 37 – 48.
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Wiggins, R., 1985, Entropy guided deconvolution:Geophysics, 50(12), 2720 – 2726.
Yilmaz, O., 2001, Seismic data analysis: processing,inversion, and interpretation of seismic data (Volume I):Society of Exploration Geophysicists, 162 – 211.
Yuan, S. Y., and Wang, S. X., 2010, Noise attenuationwithout spatial assumptions about seismic coherentevents: 80thAnn. Internat. Mtg., Soc. Expl. Geophys.,Expanded Abstracts, 3524 – 3528.
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. C., Liu, J., Ying, X. Y., and Yang, P. J.,2008, Modified Cauchy-constrained seismic blinddeconvolution: Oil Geophysical Prospecting (inChinese), 43(4), 391 – 396.
Lu, W. K., and Liu, D. Q., 2007, Frequency recovery ofbandlimited seismic data based on sparse spike traindeconvolution: 77thAnn. Internat. Mtg., Soc. Explor.Geophys., Expanded Abstracts, 1977 – 1980.
Oldenburg, D. W., Scheuer, T., and Levy, S., 1983,Recovery of the acoustic impedance from reflectionseismograms: Geophysics, 48, 1318 – 1337.
Puryear, C. I., and Castagna, J. P., 2008, Layer-thicknessdetermination and stratigraphic interpretation usingspectral inversion: Theory and application: Geophysics,73, 37 – 48.
Sacchi, M. D., 1997, Reweighting strategies in seismicdeconvolution: Geophysical Journal International, 129,651 – 656.
Velis, D. R., 2008, Stochastic sparse-spike deconvolution:Geophysics, 73(1), R1 – R9.
Walker, C., and Ulrych, T. J., 1983, Autoregressive modeling of the acoustic impedance: Geophysics, 48(10),1338 – 1350.
Wiggins, R., 1985, Entropy guided deconvolution:Geophysics, 50(12), 2720 – 2726.
Yilmaz, O., 2001, Seismic data analysis: processing,inversion, and interpretation of seismic data (Volume I):Society of Exploration Geophysicists, 162 – 211.
Yuan, S. Y., and Wang, S. X., 2010, Noise attenuationwithout spatial assumptions about seismic coherentevents: 80thAnn. Internat. Mtg., Soc. Expl. Geophys.,Expanded Abstracts, 3524 – 3528.
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. C., Liu, J., Ying, X. Y., and Yang, P. J.,2008, Modified Cauchy-constrained seismic blinddeconvolution: Oil Geophysical Prospecting (inChinese), 43(4), 391 – 396.
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