地球物理学进展 ›› 2010, Vol. 25 ›› Issue (4): 1313-1322.doi: 10.3969/j.issn.1004-2903.2010.04.020

• 应用地球物理 • 上一篇    下一篇

快速Fourier变换波动方程基准面校正方法研究

卢回忆, 符力耘, 蒋 韬 中国科学院地质与地球物理研究所, 岩石圈演化国家重点实验室, 北京 100029100029   

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  • 收稿日期:2009-09-15 修回日期:2009-11-20 出版日期:2010-08-20 发布日期:2010-08-20
  • 作者简介:卢回忆,1980年生,中国科学院地质与地球物理研究所在读博士研究生,主要从事复杂地表地震成像和近地表速度建模研究.(E-mail:luhuiyi@mail.igcas.ac.cn)
  • 基金资助:

    国家科技重大专项(2008ZX05008-006)资助.

Wave-equation datuming based on fast fourier transform

LU Hui-Yi, FU Li-Yun, JIANG Tao   

  1. State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Science, Beijing 100029, China
  • Received:2009-09-15 Revised:2009-11-20 Online:2010-08-20 Published:2010-08-20

摘要: 当地表起伏剧烈、近地表速度横向变化较大时,基于地表一致性假设的常规静校正方法存在着较大误差.波动方程基准面静校正方法能很好地解决起伏地表和复杂近地表结构问题,但计算量巨大,特别是三维波动方程基准面校正,适应横向任意速度变化、计算精度较高的有限差分或其混合的方法波动方程基准面校正涉及海量的计算和存储操作.为了提高波动方程基准面校正的计算效率,本文研究一类只用快速Fourier变换(FFT)实施波动方程基准面校正的方法,采用相移(PS)、分裂步(SSF)和一阶退化(DP1)三种具有相同算法结构、但不同计算效率、适应不同地表复杂程度的Fourier变换延拓算子.PS和SSF算子只适应于速度横向变化较弱的起伏地表;DP1通过在两个分裂步之间作波数域线性插值来实现波场延拓,将常规的SSF算法推广适应强速度横向变化介质和大角度传播波场.本文着重比较了基于这三种延拓算子的逐层延拓累加波动方程基准面校正方法对地表起伏和近地表速度横向变化的适应能力和计算效率,给出了一个相对定量的评估,以便针对不同的地表复杂程度合理选择合适的FFT波动方程基准面校正方法,既满足了精度又提高了计算效率.

Abstract: In the areas with substantial surface topography and large-contrast lateral velocity variation, there are huge errors for using the conventional time-shift static correction based on near-surface consistence. Wave-equation datuming with finite-difference scheme or hybrid method based on non-flat surface can resolve these problems very well, but their computational cost and data store is huge, especially for three dimensional data. To improve computational efficiency, we study a category of wave-equation datuming operators- PS, SSF and DP1 that permit the implementation of seismic datuming using fast Fourier transform alone. These operators implement the same arithmetic structure, but have different computational efficiency and adaptation for velocity contrast in heterogeneous media. PS and SSF methods tolerate the low or modest contrast, DP1 method extend the SSF to large-contrast media at the cost of one more Fourier transform for each extrapolation step through a linear interpolation between two split-step terms in the wave domain. The paper emphasize to compare the adaptation for the surface topography and lateral velocity variation and the computational cost of three operators through a series of synthetic examples. We have sum up some quantitative and semi-quantitative conclusions for the computational accuracy and cost, in order to enable to choose optimum datuming operator based on FFT for different surface complexity which satisfy demand of computation accuracy and the most efficiency.

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