基于Huber范数的地震曲率计算方法
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摘要
本文分析了基于L2范数的曲率计算方法的不足,指出常规曲率计算方法采用二维中值滤波或距离加权的均值滤波,会导致异常值数据拟合出的曲面严重形变,计算出的曲率误差较大。针对此类问题,笔者给出了基于Huber范数的曲率计算方法:在Huber范数误差较小时,运用L1范数;反之,则运用L2范数。模型试算验证了基于Huber范数计算曲率在刻画异常值和跳跃值方面要优于传统的最小二乘法。实际资料的应用结果表明,基于Huber范数的曲率计算方法能够获得比常规的最小二乘法更加清晰而准确的结果。
There are some drawbacks in curvature calculation based on L2 norm.Using 2D median filtering or distance-weighted median filtering,this conventional method leads fitting surface deformation and large curvature errors for data with anomalies.To solve this problem,seismic curvature calculation based on Huber norm is proposed in this paper,which treats large residuals with L1 norm and small residuals by L2 norm.Model tests suggest that the method can describe more fine properties about abnormal values and jump values than the least squares method.Field data tests indicate that finer and more accurate seismic curvature results can be obtained by the method.
There are some drawbacks in curvature calculation based on L2 norm.Using 2D median filtering or distance-weighted median filtering,this conventional method leads fitting surface deformation and large curvature errors for data with anomalies.To solve this problem,seismic curvature calculation based on Huber norm is proposed in this paper,which treats large residuals with L1 norm and small residuals by L2 norm.Model tests suggest that the method can describe more fine properties about abnormal values and jump values than the least squares method.Field data tests indicate that finer and more accurate seismic curvature results can be obtained by the method.
引文
[1]Ekblom Hakan and Madsen Kaj.Algorithms for non-linear Huber estimation.BIT,1989,29(1):60～76
[2]Claerbout Jon.Conjugate-direction Huber regression.Stanford Exploration Project,Report SEP-92,1997:219～226
[3]Guitton Antoine and William W Symes.Robust andstable velocity analysis using the Huber function.Stanford Exploration Project,1999,100(4):239～314
[4]Guitton Antoine and William W Symes.Robust in-version of seismic data using the Huber norm.Geo-physics,2003,68(4):1310～1319
[5]Guitton Antoine.Huber solver versus IRLS algo-rithm for quasi L1inversion.Stanford ExplorationProject Report,SEP-103,2001:255～271
[6]Guitton Antoine.Implementation of a nonlinear sol-ver for minimizing the Huber norm.Stanford Ex-ploration Project Report,SEP-103,2001:281～289
[7]崔树果.东海海域自由表面多次波压制方法研究[博士学位论文].山东青岛:中国海洋大学,2008
[8]Ha Taeyoung,Wookeen Chung and Changsoo Shin.Waveform inversion using a back-propagation algo-rithm and a Huber function norm.Geophysics,2009,74(3):R15～R24
[9]Brossier Romain,Stephane Operto,and Jean Vireux.Which data residual norm for robust elastic frequency-domain full waveform inversion.Geophysics,2010,75(3):R37～R46
[10]Roberts Andy.Curvature attributes and their applica-tion to 3Dinterpreted horizons.First Break,2001,19(2):85～100
[11]Sigismondi Mario E and Juan C Soldo.Curvature at-tributes and seismic interpretation:case studies fromArgentina basins.The Leading Edge,2003,22(11):1122～1126
[12]Marfurt Kurt J.Robust estimates of 3Dreflector dipand azimuth.Geophysics,2006,71(4):P29～P40
[13]Blumentritt Charles H,Marfurt Kurt J and SullivanE Charlotte.Volume-based curvature computationsilluminate fracture orientations-early to mid-paleozo-ic,central basin platform,west Texas.Geophysics,2006,71(5):B159～B166
[14]Fu Dongjun(Taller)et al.Rock-property and seis-mic-attribute analysis of a chert reservoir in the devo-nian thirty-one formation,west Texas,U S A.Geo-physics,2006,71(5):B151～B158
[15]张军华等.曲率属性及其在构造解释中的应用.油气地球物理,2009,7(2):2～7Zhang Junhua et al.Curvature attributes and theirapplication in structural interpretation.PetroleumGeophysics,2009,7(2):2～7
[16]Huber P J.Robust regression:Asymptotics,conjec-tures,and Monte Carlo.Ann Statist,1973,1(5):799～821
[17]Wang Yanfei,Anatoly G Yagola,Yang Changchun.Optimization and Regularization for ComputationalInverse Problems and Applications.Berlin/Beijing:Springer-Verlag/Higher Education Press,2010
[18]Jorge J More and David J Thuente.Line search algo-rithms with guaranteed sufficient decrease.ACMTransactions on Mathematical Software,1994,20(3):286～307
[2]Claerbout Jon.Conjugate-direction Huber regression.Stanford Exploration Project,Report SEP-92,1997:219～226
[3]Guitton Antoine and William W Symes.Robust andstable velocity analysis using the Huber function.Stanford Exploration Project,1999,100(4):239～314
[4]Guitton Antoine and William W Symes.Robust in-version of seismic data using the Huber norm.Geo-physics,2003,68(4):1310～1319
[5]Guitton Antoine.Huber solver versus IRLS algo-rithm for quasi L1inversion.Stanford ExplorationProject Report,SEP-103,2001:255～271
[6]Guitton Antoine.Implementation of a nonlinear sol-ver for minimizing the Huber norm.Stanford Ex-ploration Project Report,SEP-103,2001:281～289
[7]崔树果.东海海域自由表面多次波压制方法研究[博士学位论文].山东青岛:中国海洋大学,2008
[8]Ha Taeyoung,Wookeen Chung and Changsoo Shin.Waveform inversion using a back-propagation algo-rithm and a Huber function norm.Geophysics,2009,74(3):R15～R24
[9]Brossier Romain,Stephane Operto,and Jean Vireux.Which data residual norm for robust elastic frequency-domain full waveform inversion.Geophysics,2010,75(3):R37～R46
[10]Roberts Andy.Curvature attributes and their applica-tion to 3Dinterpreted horizons.First Break,2001,19(2):85～100
[11]Sigismondi Mario E and Juan C Soldo.Curvature at-tributes and seismic interpretation:case studies fromArgentina basins.The Leading Edge,2003,22(11):1122～1126
[12]Marfurt Kurt J.Robust estimates of 3Dreflector dipand azimuth.Geophysics,2006,71(4):P29～P40
[13]Blumentritt Charles H,Marfurt Kurt J and SullivanE Charlotte.Volume-based curvature computationsilluminate fracture orientations-early to mid-paleozo-ic,central basin platform,west Texas.Geophysics,2006,71(5):B159～B166
[14]Fu Dongjun(Taller)et al.Rock-property and seis-mic-attribute analysis of a chert reservoir in the devo-nian thirty-one formation,west Texas,U S A.Geo-physics,2006,71(5):B151～B158
[15]张军华等.曲率属性及其在构造解释中的应用.油气地球物理,2009,7(2):2～7Zhang Junhua et al.Curvature attributes and theirapplication in structural interpretation.PetroleumGeophysics,2009,7(2):2～7
[16]Huber P J.Robust regression:Asymptotics,conjec-tures,and Monte Carlo.Ann Statist,1973,1(5):799～821
[17]Wang Yanfei,Anatoly G Yagola,Yang Changchun.Optimization and Regularization for ComputationalInverse Problems and Applications.Berlin/Beijing:Springer-Verlag/Higher Education Press,2010
[18]Jorge J More and David J Thuente.Line search algo-rithms with guaranteed sufficient decrease.ACMTransactions on Mathematical Software,1994,20(3):286～307
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