基于优化差分系数的波场模拟研究
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摘要
为降低波场模拟中的数值频散,提出一种基于自褶积Kaiser窗截断Sinc函数重构信号的优化方法。通过对自褶积Kaiser窗函数进行研究,证明该方法可以有效改善窗函数的性质,并得到优化有限差分系数。分析了不同模型及不同阶数精度下的波场模拟,结果表明,该方法能显著提高波场模拟的精度,降低数值频散,以低阶精度优化差分算子模拟结果代替高阶精度常规差分精度结果。
To reduce the numerical dispersion in the wave field simulation, an optimization method based on self-convolution Kaiser window truncating signal reconstructed by Sinc function was proposed. By studying the self-convolution Kaiser window function, it's proved that the method can effectively improve the properties of the window function and obtain the optimized finite-difference coefficient. Then, different models in different precisions were compared. The results showed that the method can significantly improve the accuracy of wave field simulation and reduce the numerical dispersion. The low-order precision optimization difference operator simulation results can replace the high-order precision conventional differential precision results.
To reduce the numerical dispersion in the wave field simulation, an optimization method based on self-convolution Kaiser window truncating signal reconstructed by Sinc function was proposed. By studying the self-convolution Kaiser window function, it's proved that the method can effectively improve the properties of the window function and obtain the optimized finite-difference coefficient. Then, different models in different precisions were compared. The results showed that the method can significantly improve the accuracy of wave field simulation and reduce the numerical dispersion. The low-order precision optimization difference operator simulation results can replace the high-order precision conventional differential precision results.
引文
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[5]Diniz.P S R,da Silva E A B,Netto S L..Digital Signal Processing System Analysis and Design[M].Beijing:China Machine Press,2012.
[6]张昕焜.双相介质波动方程正演模拟研究[D].成都:成都理工大学,2013:41-43.
[2]Zhou,B.,and Greenhalgh,S.A.,Seismic scalar wave equation modeling by a convolutional differentiator:Bulletin of the Seismological Societyof America[J].1992,82(1):289-303.
[3]Igel,H.,Mora,P.,and Riollet,B.,Anisotropic wave propagation through finite-difference grids:Geophysics[J].1995,60(4):1203-1216.
[4]Chunlei Chu and Paul L.Stoffa.Determination of finite-difference weights using scaled binomial windows.Geophysics[J].2012:17-26.
[5]Diniz.P S R,da Silva E A B,Netto S L..Digital Signal Processing System Analysis and Design[M].Beijing:China Machine Press,2012.
[6]张昕焜.双相介质波动方程正演模拟研究[D].成都:成都理工大学,2013:41-43.