一种快速收敛的抗噪POCS地震数据重构方法（英文）
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摘要
地震数据重构是地震数据处理的重要步骤之一,重构算法的精度、效率与抗噪性是地震数据重构技术的核心研究内容。研究针对傅里叶域凸集投影(POCS)算法,在定义的最优阈值评价标准基础上,提出了反比例阈值模型,该模型具有在大系数区间比指数模型更快下降速率、而在小系数区间比指数模型更慢下降速率,从而在保证弱反射信号重构精度的同时有效提高POCS地震数据重构算法计算效率。为提高反比例阈值对不同地震数据特点的适应性,在地震数据谱能量分布差异性特征分析基础上,研究提出了在反比例阈值模型分母上增加适应地震数据谱能量特征的因变参数,通过调节该因变参数获得适应不同地震数据特点的最佳阈值曲线,进一步提高算法的计算精度与计算效率。为了实现重构过程中随机噪音的自适应衰减,提高重构后地震数据信噪比,研究提出了数据驱动的加权回加系数计算策略,利用每次迭代对应数据驱动阈值占阈值区间的百分比获得加权回加系数。研究将新方法应用于模拟三维数据和实际三维地震数据,分析结果表明反比例阈值相对传统阈值在提高数据重构计算效率和精度方面具有明显的优越性,新提出的加权回加系数计算策略能有效提高重构数据的信噪比。
The effi ciency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets(POCS) algorithm, we propose an inversely proportional threshold model that defi nes the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coeffi cient section and slower than in the exponential threshold in the small-coeffi cient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak refl ections. To improve the fl exibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and fi eld data. The results suggest that the inversely proportional threshold model improves the computational effi ciency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.
The effi ciency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets(POCS) algorithm, we propose an inversely proportional threshold model that defi nes the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coeffi cient section and slower than in the exponential threshold in the small-coeffi cient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak refl ections. To improve the fl exibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and fi eld data. The results suggest that the inversely proportional threshold model improves the computational effi ciency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.
引文
Abma,R.,and Kabir,N.,2006,3D interpolation of irregulardata with a POCS algorithm:Geophysics,71(6),E91–E97.
Duijndam,A.W.,Schonewille,M.A.,and Hindriks,K.,1999,Reconstruction of band-limited signals irregularlysampled along one spatial direction:Geophysics,64(2),524–538.
Galloway,E.,and Sacchi,M.D.,2007,POCS method forseismic data reconstruction of irregularly sampled data:CSPG-CSEG-CWLS Joint Convention,555.
Gao,J.J.,Chen,X.H.,Li,J.Y.,et al,2010,Irregularseismic data reconstruction based on exponentialthreshold model of POCS method:Applied Geophysics,7(3),229–238.
Gao,J.J.,Stanton,A.,Naghizadeh,M.,Sacchi,M.D.,et al,2013,Convergence improvement and noise attenuationconsideration for beyond alias projection onto convexsets reconstruction:Geophysical Prospecting,61(suppl.1),138–151.
Gerchberg,R.W.,and Saxton,W.O.,1972,A practicalalgorithm for the determination of phase from image anddiffraction plane pictures:Optik,35(2),227–246.
Hennenfent,G.,and Herrmann,F.,2006,Seismic denoisingwith nonuniformly sampled curvelets:Computing inScience and Engineering,8(3),16–25.
Kabir,M.M.N.,and Verschuur,D.J.,1995,Restorationof missing offsets by parabolic Radon transform:Geophysical Prospecting,43(3),347–368.
Kong,L.Y.,Yu,S.W.,Chen,L.,et al.,2012,Application ofcompressive sensing to seismic data reconstruction:ActaSeismologica Sinica,34(5),659–666.
Kreimer,N.,and Sacchi,M.D.,2011,Evaluation of anew 5D seismic volume reconstruction method:Tensorcompletion versus Fourier reconstruction:TensorCompletion vs.Fourer,Reconstruction:CSPG-CSEGCWLS Joint Convention,1–5.
Li,H.F.,and Du,M.H.,2003,Super-resolution ImageRestoration Based on Improved POCS Algorithm:Journal of South China University of Technology(inChinese),31(10),24–27.
Liu,G.C.,Chen,X.H.,Guo,Z.F.,et al.,2011,Missingseismic data rebuilding by interpolation based on curvelettransform:Oil Geophysical Prospecting(in Chinese),46(2),237–246.
Malcolm,A.E.,Hoop,M.V.D.,and Rousseau,J.H.L.,2005,The applicability of dip moveout/azimuth moveoutin the presence of caustics:Geophysics,70(1),S1–S17.
Menke,W.,1991,Applications of the POCS inversionm ethodtointer polating topography and othergeophysical fi elds:Geophysical Research Letters,18(3),435–438.
Naghizadeh,M.,and Sacchi,M.D.,2010,Beyond aliashierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data:Geophysics,75(6),WB189–WB202.
Naghizadeh,M.,and Sacchi,M.D.,2009,f-x adaptiveseismic-trace interpolation:Geophysics,74(1),V 9–V16.
Oropeza,V.,and Sacchi,M.,2011,Simultaneous seismicdata denoising and reconstruction via multichannelsingular spectrum analysis:Geophysics,76(3),V25–V32.
Papoulis,A.,1975,A new algorithm in spectral analysisand band limited extrapolation:IEEE Transactions onCircuits and Systems,CAS–22(9),735–742.
Ronen,J.,1987,Wave-equation trace interpolation:Geophysics,52(7),973–984.
Spitz,S.,1991,Seismic trace interpolation in the F-Xdomain:Geophysics,56(6),785–794.
Trad,D.O.,2009,Five-dimensional interpolation:Recovering from acquisition constraints:Geophysics,74(6),V123–V132.
Trad,D.O.,Ulrych,T.J.,and Sacchi,M.D.,2002,Accurate interpolation with high-resolution time-variantRadon transform:Geophysics,67(2),644–656.
Trickett,S.,Burroughs,L.,Milton,A.,et al,2010,Rankreduction-based trace interpolation:80th Ann.Internat.Mtg.,Soc.Explor.Geophys.,Expanded Abstracts,1989–1992.
Wang,S.,Gao,X.,and Yao,Z.,2010,Accelerating POCSinterpolation of 3D irregular seismic data with graphicsprocessing units:Computers and Geosciences,36(10),1292–1300.
Wang,S.Q.,and Zhang,J.H.,2014,Fast imaging inpainting using exponential-threshold POCS plusconjugate gradient:The Imaging Science Journal,62(3),161–170.
Zhang,H.,and Chen,X.H.,2013,seismic data reconstruction based on jittered sampling and curvelettransform.Chinese Journal of Geophysics(in Chinese),56(6),1637–1649.
Duijndam,A.W.,Schonewille,M.A.,and Hindriks,K.,1999,Reconstruction of band-limited signals irregularlysampled along one spatial direction:Geophysics,64(2),524–538.
Galloway,E.,and Sacchi,M.D.,2007,POCS method forseismic data reconstruction of irregularly sampled data:CSPG-CSEG-CWLS Joint Convention,555.
Gao,J.J.,Chen,X.H.,Li,J.Y.,et al,2010,Irregularseismic data reconstruction based on exponentialthreshold model of POCS method:Applied Geophysics,7(3),229–238.
Gao,J.J.,Stanton,A.,Naghizadeh,M.,Sacchi,M.D.,et al,2013,Convergence improvement and noise attenuationconsideration for beyond alias projection onto convexsets reconstruction:Geophysical Prospecting,61(suppl.1),138–151.
Gerchberg,R.W.,and Saxton,W.O.,1972,A practicalalgorithm for the determination of phase from image anddiffraction plane pictures:Optik,35(2),227–246.
Hennenfent,G.,and Herrmann,F.,2006,Seismic denoisingwith nonuniformly sampled curvelets:Computing inScience and Engineering,8(3),16–25.
Kabir,M.M.N.,and Verschuur,D.J.,1995,Restorationof missing offsets by parabolic Radon transform:Geophysical Prospecting,43(3),347–368.
Kong,L.Y.,Yu,S.W.,Chen,L.,et al.,2012,Application ofcompressive sensing to seismic data reconstruction:ActaSeismologica Sinica,34(5),659–666.
Kreimer,N.,and Sacchi,M.D.,2011,Evaluation of anew 5D seismic volume reconstruction method:Tensorcompletion versus Fourier reconstruction:TensorCompletion vs.Fourer,Reconstruction:CSPG-CSEGCWLS Joint Convention,1–5.
Li,H.F.,and Du,M.H.,2003,Super-resolution ImageRestoration Based on Improved POCS Algorithm:Journal of South China University of Technology(inChinese),31(10),24–27.
Liu,G.C.,Chen,X.H.,Guo,Z.F.,et al.,2011,Missingseismic data rebuilding by interpolation based on curvelettransform:Oil Geophysical Prospecting(in Chinese),46(2),237–246.
Malcolm,A.E.,Hoop,M.V.D.,and Rousseau,J.H.L.,2005,The applicability of dip moveout/azimuth moveoutin the presence of caustics:Geophysics,70(1),S1–S17.
Menke,W.,1991,Applications of the POCS inversionm ethodtointer polating topography and othergeophysical fi elds:Geophysical Research Letters,18(3),435–438.
Naghizadeh,M.,and Sacchi,M.D.,2010,Beyond aliashierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data:Geophysics,75(6),WB189–WB202.
Naghizadeh,M.,and Sacchi,M.D.,2009,f-x adaptiveseismic-trace interpolation:Geophysics,74(1),V 9–V16.
Oropeza,V.,and Sacchi,M.,2011,Simultaneous seismicdata denoising and reconstruction via multichannelsingular spectrum analysis:Geophysics,76(3),V25–V32.
Papoulis,A.,1975,A new algorithm in spectral analysisand band limited extrapolation:IEEE Transactions onCircuits and Systems,CAS–22(9),735–742.
Ronen,J.,1987,Wave-equation trace interpolation:Geophysics,52(7),973–984.
Spitz,S.,1991,Seismic trace interpolation in the F-Xdomain:Geophysics,56(6),785–794.
Trad,D.O.,2009,Five-dimensional interpolation:Recovering from acquisition constraints:Geophysics,74(6),V123–V132.
Trad,D.O.,Ulrych,T.J.,and Sacchi,M.D.,2002,Accurate interpolation with high-resolution time-variantRadon transform:Geophysics,67(2),644–656.
Trickett,S.,Burroughs,L.,Milton,A.,et al,2010,Rankreduction-based trace interpolation:80th Ann.Internat.Mtg.,Soc.Explor.Geophys.,Expanded Abstracts,1989–1992.
Wang,S.,Gao,X.,and Yao,Z.,2010,Accelerating POCSinterpolation of 3D irregular seismic data with graphicsprocessing units:Computers and Geosciences,36(10),1292–1300.
Wang,S.Q.,and Zhang,J.H.,2014,Fast imaging inpainting using exponential-threshold POCS plusconjugate gradient:The Imaging Science Journal,62(3),161–170.
Zhang,H.,and Chen,X.H.,2013,seismic data reconstruction based on jittered sampling and curvelettransform.Chinese Journal of Geophysics(in Chinese),56(6),1637–1649.