最小加权范数插值与调制升频结合的地震数据重建研究
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摘要
提出一种新的反假频地震数据重建的两步算法,将最小加权范数插值(MWNI)方法与调制升频方法有效地结合起来.首先利用MWNI方法构建数据谱的低频部分,为了提高计算效率,在低频重建算法中,引入了预条件共轭梯度法求解反问题方程,并使用了与频率有关的变波数带宽技术;然后,基于重建的低频数据,采用调制升频方法重构数据的高频部分.调制升频方法灵活,简便,能有效地从低频资料中恢复出高频成分,克服了以往AR模型预测高频走不远的限制,当数据存在严重的空间假频时,亦能获得较好的重建效果.该两步算法不仅可用于规则地震数据的内插重建,也可用于含空道地震数据的重建.理论模型和实际地震数据重建试验表明,该方法效率高,精度高,反假频能力强,重建剖面波形连续、自然,与正确完整的地震剖面相似程度高,具有良好的实用价值和应用前景.
A new two-step algorithm to reconstruct non-alias seismic data is proposed. The algorithm combines minimum weighted norm interpolation (MWNI) and band extension via modulation method effectively. Firstly,we reconstruct the low frequency part of the data spectra using MWNI method. In order to improve calculation efficiency,pre-conditional conjugate gradient method was used during reconstruction and the varying wave number band width frequency was adopted in the paper. Then,based on the reconstructed low frequency data,the high frequency part of the data spectra are reconstructed with the band extension via modulation method,which is convenient and flexible,overcoming the limit that the high frequency from AR model prediction can not go far. By using this method,it can get good reconstruction effect while obvious spatial alias exits. The applicability of the proposed method is examined using synthetic and field data examples. The two-step algorithm is used to reconstruct not only for regular seismic data interpolation,but also for irregular data gap filling. Theoretical model and actual seismic data reconstruction tests show that the proposed method has high efficiency and accuracy,and the waveforms of reconstructed data are continuous and natural. Reconstructed sections are similar to the correct or complete seismic sections. The proposed method also has strong de-aliasing ability. It is prospective in future application.
A new two-step algorithm to reconstruct non-alias seismic data is proposed. The algorithm combines minimum weighted norm interpolation (MWNI) and band extension via modulation method effectively. Firstly,we reconstruct the low frequency part of the data spectra using MWNI method. In order to improve calculation efficiency,pre-conditional conjugate gradient method was used during reconstruction and the varying wave number band width frequency was adopted in the paper. Then,based on the reconstructed low frequency data,the high frequency part of the data spectra are reconstructed with the band extension via modulation method,which is convenient and flexible,overcoming the limit that the high frequency from AR model prediction can not go far. By using this method,it can get good reconstruction effect while obvious spatial alias exits. The applicability of the proposed method is examined using synthetic and field data examples. The two-step algorithm is used to reconstruct not only for regular seismic data interpolation,but also for irregular data gap filling. Theoretical model and actual seismic data reconstruction tests show that the proposed method has high efficiency and accuracy,and the waveforms of reconstructed data are continuous and natural. Reconstructed sections are similar to the correct or complete seismic sections. The proposed method also has strong de-aliasing ability. It is prospective in future application.
引文
国九英,周兴元,俞寿朋.1996.FX域等道距内插[J].石油地球物理勘探,31(1):28-34.
国九英,周兴元.1996.FK域等道距内插[J].石油地球物理勘探,31(2):211-218.
刘喜武,刘洪,刘彬.2004.反假频非均匀地震数据重建方法研究[J].地球物理学报,47(2):299-305.
陆文凯,张善文.2004.基于频率搬移的地震资料约束测井资料的外推[J].地球物理学报,47(2):354-358.
孟小红,郭良辉,张致付,李淑玲,周建军.2008.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建[J].地球物理学报,51(1):235-241.
王维红,裴江云,张剑锋.2007.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,50(3):851-859
曾锐,刘洪,秦月霜,崔宝文,牛彦良.2007.基于自动增益控制调制法的高频重建技术[J].地球物理学进展,22(3):850-859.
Duijindam AJ W,Schonewille M A,Hindriks C O H.1999.Reconstruction of band-li mited signals,irregularly sampledalong one spatial direction[J].Geophysics,64(2):524-538.
Gulunay N.2003.Seismic trace interpolationin the Fourier transformdomain[J].Geophysics,68(1):355-369.
Hindriks K,Duijindam AJ W.2000.Reconstruction of3-Dseismic signals irregularly sampled along two spatial coordinates[J].Geophysics,65(1):253-263.
Huang Y,Ng MK,Wen Y.2008.Afast total variation mini mization methodfor i mage restoration[J].Multiscale Mod-el Si mul,7(2):774-795.
Kabir M MN,Verschuur DJ.1995.Restoration of missing offsets by parabolic radontransform[J].Geophys Prosp,43(3):347-368.
Liu H,Liu B,Sacchi MD.2004.Dealiasing band-li mited uneven data using alinear prediction and adapted weightedleastsquare[C]∥CPS/SEG Beijing2004International Geophysical Conterence and Exposition.Beijing:198-201.
Liu B,Sacchi M D.2001.Mini mum weighted norminterpolation of seismic data with adaptive weights[J].Soc ExplorGeophys Ann Internat Mtg,Expanded Abstracts:1921-1924.
Liu B,Sacchi MD.2004.Mini mum weighted norminterpolation of seismic records[J].Geophysics,69(6):1560-1568.
Naghizadeh M,Sacchi M D.2007.Multistep autoregressive reconstruction of seismic records[J].Geophysics,72(6):v111-v118.
Porsani M.1999.Seismic trace interpolation using half-step prediction filter[J].Geophysics,64(5):1461-1467.
Sacchi M D,Liu B.2005.Mini mum weighted norm wavefield reconstruction for AVAi maging[J].Geophys Prosp,53(6):787-801.
Spitz S.1991.Seismic trace interpolationin the F-X domain[J].Geophysics,56(6):785-794.
Wang Y.2003.Sparseness-constrainedleast-squaresinversion:Application to seismic wave reconstruction[J].Geophys-ics,68(5):1633-1638.
Zwartjes P M,Sacchi MD.2007.Fourier reconstruction of nonuniformly sampled,aliased seismic data[J].Geophysics,72(1):v21-v32.
国九英,周兴元.1996.FK域等道距内插[J].石油地球物理勘探,31(2):211-218.
刘喜武,刘洪,刘彬.2004.反假频非均匀地震数据重建方法研究[J].地球物理学报,47(2):299-305.
陆文凯,张善文.2004.基于频率搬移的地震资料约束测井资料的外推[J].地球物理学报,47(2):354-358.
孟小红,郭良辉,张致付,李淑玲,周建军.2008.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建[J].地球物理学报,51(1):235-241.
王维红,裴江云,张剑锋.2007.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,50(3):851-859
曾锐,刘洪,秦月霜,崔宝文,牛彦良.2007.基于自动增益控制调制法的高频重建技术[J].地球物理学进展,22(3):850-859.
Duijindam AJ W,Schonewille M A,Hindriks C O H.1999.Reconstruction of band-li mited signals,irregularly sampledalong one spatial direction[J].Geophysics,64(2):524-538.
Gulunay N.2003.Seismic trace interpolationin the Fourier transformdomain[J].Geophysics,68(1):355-369.
Hindriks K,Duijindam AJ W.2000.Reconstruction of3-Dseismic signals irregularly sampled along two spatial coordinates[J].Geophysics,65(1):253-263.
Huang Y,Ng MK,Wen Y.2008.Afast total variation mini mization methodfor i mage restoration[J].Multiscale Mod-el Si mul,7(2):774-795.
Kabir M MN,Verschuur DJ.1995.Restoration of missing offsets by parabolic radontransform[J].Geophys Prosp,43(3):347-368.
Liu H,Liu B,Sacchi MD.2004.Dealiasing band-li mited uneven data using alinear prediction and adapted weightedleastsquare[C]∥CPS/SEG Beijing2004International Geophysical Conterence and Exposition.Beijing:198-201.
Liu B,Sacchi M D.2001.Mini mum weighted norminterpolation of seismic data with adaptive weights[J].Soc ExplorGeophys Ann Internat Mtg,Expanded Abstracts:1921-1924.
Liu B,Sacchi MD.2004.Mini mum weighted norminterpolation of seismic records[J].Geophysics,69(6):1560-1568.
Naghizadeh M,Sacchi M D.2007.Multistep autoregressive reconstruction of seismic records[J].Geophysics,72(6):v111-v118.
Porsani M.1999.Seismic trace interpolation using half-step prediction filter[J].Geophysics,64(5):1461-1467.
Sacchi M D,Liu B.2005.Mini mum weighted norm wavefield reconstruction for AVAi maging[J].Geophys Prosp,53(6):787-801.
Spitz S.1991.Seismic trace interpolationin the F-X domain[J].Geophysics,56(6):785-794.
Wang Y.2003.Sparseness-constrainedleast-squaresinversion:Application to seismic wave reconstruction[J].Geophys-ics,68(5):1633-1638.
Zwartjes P M,Sacchi MD.2007.Fourier reconstruction of nonuniformly sampled,aliased seismic data[J].Geophysics,72(1):v21-v32.
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