分形插值地震数据重建方法研究
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摘要
对分形插值方法作了较详细的探讨,给出了分形插值函数的显式表达方式,同时给出了垂直比例因子的局部显式表达式,旨在提高地震道插值重建的精度及突出局部信息,并从单道地震图的角度分析其在地震道插值重建中的应用效果.利用该方法对理论模型和济阳坳陷实际地震台站资料进行了重建处理,结果表明,分形插值重建的地震道是原始地震道的良好近似.缺失道的振幅和相位都得到了很好的恢复.该法克服了随机分形插值方法必须进行多步迭代的弱点。提高了计算效率.通过对单道地震图插值重建结果的分析,说明了本文分形插值方法具有较高的精度和较高的效率,有深入研究的潜力.本文提出的显式分形插值方法既能够突出地震道数据的局部信息,又较好地保持了地震道数据的总体变化趋势.
In order to improve the accuracy of the reconstructed seismic data,this paper makes a detailed investigation into the fractal interpolation method on the basis of the former work,and analyzes theoretically a special kind of fractal interpolation function.The explicit presentation of the fractal interpolation function is applied and the locally explicit expression for the vertical scaling factors has been put forward.At the same time the interpolating accuracy has been investigated from the point of accordingly seismic traces.The influence of the vertical scaling factors to the precision of the fractal interpolation has been investigated.The numerical experiments demonstrate that the interpolating residual is in proportion to the exponent function with increasing vertical scaling factors.This explicit fractal interpolation method avoids the iteration that is inevitable in traditional interpolation method,and then it improves the computational efficiency.By analyzing the theoretical seismograms and the reconstructed seismograms and the differences between them,the numerical results demonstrate that the fractal interpolation method put forward here has high accuracy and efficiency,the most node error is no more than 3% with respect to the numerical computation.The method not only makes the local information obvious but also preserves the overall characteristics well of the data investigated.
In order to improve the accuracy of the reconstructed seismic data,this paper makes a detailed investigation into the fractal interpolation method on the basis of the former work,and analyzes theoretically a special kind of fractal interpolation function.The explicit presentation of the fractal interpolation function is applied and the locally explicit expression for the vertical scaling factors has been put forward.At the same time the interpolating accuracy has been investigated from the point of accordingly seismic traces.The influence of the vertical scaling factors to the precision of the fractal interpolation has been investigated.The numerical experiments demonstrate that the interpolating residual is in proportion to the exponent function with increasing vertical scaling factors.This explicit fractal interpolation method avoids the iteration that is inevitable in traditional interpolation method,and then it improves the computational efficiency.By analyzing the theoretical seismograms and the reconstructed seismograms and the differences between them,the numerical results demonstrate that the fractal interpolation method put forward here has high accuracy and efficiency,the most node error is no more than 3% with respect to the numerical computation.The method not only makes the local information obvious but also preserves the overall characteristics well of the data investigated.
引文
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[17]陆克政，漆家福．渤海湾新生代含油气盆地构造模式．北京：地质出版社，1997 Lu K Z,Qi J F.Tectonic Model of Cenozoic Petroliferous Basin Bohai Bay Province(in Chinese).Beijing:Geological Publishing House,1997
[2]Barsley M F.Fractal functions and interpolation. Constructive Approximation,1986,(2):303～329
[3]胡瑞安，胡纪阳，徐树公．分形的计算机图像及其应用．北京：中国铁道出版社，1995．61～85 Hu R A,Hu J T,Xu S G.Computer Graphics and Applications of Fractal(in Chinese).Beijing:China Railway Press,1995.61～85
[4]Larner K,Gibson B,Rothman D.Trace interpolation and the design of seismic surveys.Geophysics,1981,46:407～415
[5]Kabir M M N,Verschuur D J.Restoration of missing offsets by parabolic Radon Transformation.Geophys.Prosp.,1995, 43:347～368
[6]Spitz S.Seismic trace interpolation in F-X domain. Geophysics,1991,56:785～794
[7]Porsani M J.Seismic trace interpolation using half-step prediction filters.Geophysics,1999,64:1461～1467
[8]Wang Y.Seismic trace interpolation in the f-x-y domain. Geophysical Prospecting,2003,51:75～87
[9]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)：299～305 Liu X W,Liu H,Liu B.A study on reconstruction of de- aliased uneven seismic data.Chinese J.Geophys.(in Chinese),2004,47(2):299～305
[10]孟小红，刘国峰，周建军．大间距地震数据重建方法研究．地球物理学进展，2006，21(3)：687～691 Meng X H,Liu G F,Zhou J J.The study of reconstruction of large gap seismic data.Progress in Geophysics(in Chinese),2006,21(3):687～691
[11]Craig M,Wittenbrink.IFS Fractal Interpolation for 2D and 3D Visualization.Proceedings of the 6th IEEE Visualization Conference(VISUALIZATION 95),1995.77～84,
[12]范玉红，栾元重，王永等．分形插值与传统插值方法相结合的研究．测绘科学，2005．30(2)：76～77，80 Fan Y H,Luan Y C,Wang Y,et al.The method study of combination of fractal interpolation and linear interpolation. Science of Surveying and Mapping(in Chinese),2005,30 (2):76～77,80
[13]杨杰．分形插值及其分形维数研究．武汉工业学院学报，2006，25(1)：9～11 Yang J.Study on Fractal interpolated and its fractal dimension.Journal of Wuhan Polytechnic University(in Chinese),2006,2S(1):9～11
[14]沙震．阮火军编著．分形与拟合．杭州：浙江大学出版社，2005．123～130 Sha Z,Ruan H J.Fractal and Fitting(in Chinese). Hangzhou:Zhejiang University Press,2005.123～130
[15]刘兴材，杨申镳．济阳复合油气区勘探理论与方法．中国油气，1995，2：20～22 Liu X C,Yang S B.Exploration theory and method in Jiyang composite oil and gas area.China Oil and Gas(in Chinese), 1995,2:20～22
[16]Allen M B,Macdonald DIM,Zhao X,et al.Early Cenozoic two-phase extension and late Cenozoic thermal subsidence and inversion of the Bohai Basin.Northern China,Mar.Pet. Geol.,1997,14:951～972
[17]陆克政，漆家福．渤海湾新生代含油气盆地构造模式．北京：地质出版社，1997 Lu K Z,Qi J F.Tectonic Model of Cenozoic Petroliferous Basin Bohai Bay Province(in Chinese).Beijing:Geological Publishing House,1997
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