表驱动的二维非规则采样快速傅里叶变换
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摘要
非规则采样快速傅里叶变换(NFFT)主要用于快速计算非规则采样数据的频谱及重建.该方法为非规则采样数据频谱重建技术的核心算法.在实现NFFT算法时,高速度和高精度计算是其应用的前提和关键.本文针对二维NFFT计算效率,应用表驱动思路进行改进,将Gauss褶积算子由矩形改进为椭圆以减少计算量,将e指数计算改进为乘法以加快计算速度,并建表解决NFFT算法在地震资料处理中的应用问题.本文同时给出了非规则采样地震数据NFFT谱重建方法.最后本文给出算例验证提出方法的计算速度和精度,和非规则采样地震资料重建结果.
Non-uniform sampling fast Fourier transform(NFFT) is a method for efficient spectrum calculation of nonequispaced data.It′s the fundamental algorithm of reconstruction techniques by spectra estimation of irregularly sampled signals.High efficiency and precision is the key for its application.In order to achieve high performance for 2-D case,I utilize table-driven techniques to reformulate Gauss convolution operator into elliptic form to reduce numerical operations and substitute exp function by multiplication operation to accelerate computing efficiency.I also create several tables to introduce NFFT to seismic data processing.Based on these works I explain how to reconstruct nonuniform sampled seismic data via 2-D NFFT.At last three numerical experiments are shown to illustrate computation speed,calculation accuracy and reconstruction results for irregular sampled seismic data respectively.
Non-uniform sampling fast Fourier transform(NFFT) is a method for efficient spectrum calculation of nonequispaced data.It′s the fundamental algorithm of reconstruction techniques by spectra estimation of irregularly sampled signals.High efficiency and precision is the key for its application.In order to achieve high performance for 2-D case,I utilize table-driven techniques to reformulate Gauss convolution operator into elliptic form to reduce numerical operations and substitute exp function by multiplication operation to accelerate computing efficiency.I also create several tables to introduce NFFT to seismic data processing.Based on these works I explain how to reconstruct nonuniform sampled seismic data via 2-D NFFT.At last three numerical experiments are shown to illustrate computation speed,calculation accuracy and reconstruction results for irregular sampled seismic data respectively.
引文
[1]Duijndam AJ W,Schonewille M,Hindriks K.Reconstructionof seismic signals,irregularly sampled along one spatialcoordinate.Geophysics,1999,64:524~538
[2]Hindriks K O H,Duijndam A J W.Reconstruction of 3-Dseismic signals irregularly sampled along two spatialcoordinates.Geophysics,2000,65:253~256
[3]刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究.地球物理学报,2004,47(2):299~305Liu X W,Liu H,Liu B.A study on algorithm forreconstruction of dealias uneven seismic data.Chinese J.Geophys.(in Chinese),2004,47(2):299~305
[4]Greengard L,June-Yub L.Accelerating the Nonuniform FastFourier Transform.SIAMRev.,2004,46(3):443~454
[5]Dutt A,Rokhlin V.Fast Fourier transforms fornonequispaced data.SIAMJ.Sci.Statist.Comput.,1993,14:1368~1393
[6]Duijndam AJ W,Schonewille M A.Nonuniformfast Fouriertransform.Geophysics,1999,64:539~551
[7]Potts D,Steidl G,Tasche M.Fast Fourier transforms fornonequispaced data:Atutorial.In:Modern Sampling Theory:Math and Applications,Birkhuser,2001.253~274
[8]Steidl G.Anote onfast Fourier transforms for nonequispacedgrids.Advances in Computational Mathematics,1998,9:337~352
[9]Feichtinger H,Gr chenig K,Strohmer T.Efficient numericalmethods in non-uniform sampling theory.Numer.Math.,1995,69:423~440
[2]Hindriks K O H,Duijndam A J W.Reconstruction of 3-Dseismic signals irregularly sampled along two spatialcoordinates.Geophysics,2000,65:253~256
[3]刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究.地球物理学报,2004,47(2):299~305Liu X W,Liu H,Liu B.A study on algorithm forreconstruction of dealias uneven seismic data.Chinese J.Geophys.(in Chinese),2004,47(2):299~305
[4]Greengard L,June-Yub L.Accelerating the Nonuniform FastFourier Transform.SIAMRev.,2004,46(3):443~454
[5]Dutt A,Rokhlin V.Fast Fourier transforms fornonequispaced data.SIAMJ.Sci.Statist.Comput.,1993,14:1368~1393
[6]Duijndam AJ W,Schonewille M A.Nonuniformfast Fouriertransform.Geophysics,1999,64:539~551
[7]Potts D,Steidl G,Tasche M.Fast Fourier transforms fornonequispaced data:Atutorial.In:Modern Sampling Theory:Math and Applications,Birkhuser,2001.253~274
[8]Steidl G.Anote onfast Fourier transforms for nonequispacedgrids.Advances in Computational Mathematics,1998,9:337~352
[9]Feichtinger H,Gr chenig K,Strohmer T.Efficient numericalmethods in non-uniform sampling theory.Numer.Math.,1995,69:423~440
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