地球物理学进展 ›› 2014, Vol. 29 ›› Issue (2): 518-522.doi: 10.6038/pg20140207

• 空间与固体地球物理 • 上一篇    下一篇

地震道重建和重采样的分形插值方法研究

刘红艳1, 陈宇坤1, 李信富2   

  1. 1. 天津市地震局, 天津 300201;
    2. 中国地质大学地球物理与信息技术学院, 北京 100083
  • 收稿日期:2013-06-16 修回日期:2013-10-18 出版日期:2014-04-20 发布日期:2014-04-20
  • 作者简介:刘红艳,女,工程师,2008年7月于中国科学院地质与地球物理研究所获得硕士学位,现在天津市地震灾害防御中心工作,主要从事地震活动性,工程地震,复杂介质的地震波场数值模拟研究等工作.(E-mail:liuhongyan_012@163.com)
  • 基金资助:

    天津市海洋局科技兴海项目和天津市地震局青年基金(编号0905)资助.

Fractal interpolation method for reconstruction and resampling of seismic data

LIU Hong-yan1, CHEN Yu-kun1, LI Xin-fu2   

  1. 1. Earthquake Administration of Tianjin Municipality, Tianjin 300201, China;
    2. School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China
  • Received:2013-06-16 Revised:2013-10-18 Online:2014-04-20 Published:2014-04-20

摘要:

为了对地震数据进行高保真重建,本文给出了分形插值函数的一种替代形式,即利用某一函数的逐段积分表达形式构建相应的分形插值函数,这种形式在以往的地震数据处理文献中未曾提及.这类分形插值函数在分形和线性插值之间建立了一种简单的关系.实际上,利用这种简单关系,许多分形插值函数问题可以简化为一种简单的向量/矩阵表示.此外,利用这种替代形式,借助于压缩因子的显式表达,我们可以进行高精度的地震数据重建.本文借助于这种分形插值函数的替代形式,发展了一种新的地震数据重建和重采样的方法.为了检验本文方法的有效性,我们采用济阳凹陷10个在一条线上的地震台站的数据对该方法进行了检验,实际地震图重建结果表明了本文提出方法的有效性.

Abstract:

To obtain a high fidelity reconstruction result, an alternative form of the fractal interpolation function that is constructed via the piecewise integration of some piecewise linear function, which is not mentioned previously in the seismic data processing literature, is presented in this paper. This kind of fractal interpolation function establishes a simple relationship between fractal and linear interpolation. Actually, many fractal interpolation function problems can be reduced to a simple vector/matrix presentation by using this simple relationship. Moreover, the alternate form of the fractal interpolation function admits the high fidelity seismic data reconstruction with the explicit presentation of the contraction factors and also allows the construction of fractal functions whose piecewise integrals match observed seismic data. In this paper we developed a new fractal reconstruction method by using the alternative form of the fractal interpolation function. To verify the validity of the method presented here, we test the method by using the real data obtained from 10 seismic stations deploying in a line in Jiyang depression. The reconstruction results of a real seismogram verify the validity of the method put forward in this paper. The reconstructed seismograms by using new fractal interpolation function resemble the original seismogram very well. The method put forward in this paper can be easily extended to a variety of geophysical data reconstruction problems.

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