三维叠前傅里叶变换法模型并行算法
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摘要
本文应用傅里叶变换法模型算法实现三维叠前声波模型的并行计算,得到了三维合成地震记录,并且应用射线理论分析对此算法进行了验证。算法允许速度纵横向变化。三维叠前模型计算的最大困难是内存需求量和计算量庞大,算法的主要优点在于各主体计算部分均采用快速傅里叶变换,成功地将向量化技术和复序列傅氏变换与实序列傅氏变换的关系用于二维、三维快速傅里叶变换(FFT),从而优化了程序,提高了计算效率并节省了内存。理论分析和实际试算表明:适当调节空间和时间采样间隔、震源子波的主频和长度,可减少因差分逼近微分引起的频散,得到更佳的模拟效果。利用消息传递并行编程环境和微机机群运行并行程序,大大提高了计算效率,节省了计算时间;同时将波场快照与速度剖面相结合,可以更好地观测到波的传播过程。模型试算得到的合成记录表明,此项算法可行且有效。
The paper used the Fourier transform algorithm to implement the parallel algorithm of 3-D prestack sonic model, obtained 3-D synthetic seismographs and applied the ray theory analysis to prove the algorithm. The algorithm allows the ve-locity to change both in vertical and in lateral directions. The largest difficulty of calculating 3-D prestack model is a large amount of memory and computational efforts,the main advantages are that calculating parts of main bodies are carried out by FFT, the vectorization technique and the relationship between complex sequence of Fourier transform and real sequence of Fourier transform are successfully used for 2-D and 3-D FFT so that the program can be optimized, the computational efficiency can be improved and the memory can be saved. The theoretic analysis and real data test showed that adequately adjusting special and temporal sampling intervals and dominant frequency and length of source wavelet can reduce the dispersion resulted from the difference approaching the differential that can get better simulation results. Using information-transmitting-parallel programming environment and parallel program of microcomputer cluster operation can greatly increase the computational efficiency and reduce the computational times;meanwhile,combination of snap shot plotting wavefield with velocity sections can better observe wave-spreading process. The synthetic seismographs of model testing showed the feasibility and effectiveness of the algorithm.
The paper used the Fourier transform algorithm to implement the parallel algorithm of 3-D prestack sonic model, obtained 3-D synthetic seismographs and applied the ray theory analysis to prove the algorithm. The algorithm allows the ve-locity to change both in vertical and in lateral directions. The largest difficulty of calculating 3-D prestack model is a large amount of memory and computational efforts,the main advantages are that calculating parts of main bodies are carried out by FFT, the vectorization technique and the relationship between complex sequence of Fourier transform and real sequence of Fourier transform are successfully used for 2-D and 3-D FFT so that the program can be optimized, the computational efficiency can be improved and the memory can be saved. The theoretic analysis and real data test showed that adequately adjusting special and temporal sampling intervals and dominant frequency and length of source wavelet can reduce the dispersion resulted from the difference approaching the differential that can get better simulation results. Using information-transmitting-parallel programming environment and parallel program of microcomputer cluster operation can greatly increase the computational efficiency and reduce the computational times;meanwhile,combination of snap shot plotting wavefield with velocity sections can better observe wave-spreading process. The synthetic seismographs of model testing showed the feasibility and effectiveness of the algorithm.
引文
[1]莫则尧,袁国兴.消息传递并行编程环境MPI.北京:科学技术出版社,2001
[2]Marfurt K J.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.Geophysics,1984,49:533~549
[3]Kelly K R et al.Synthetic seismograms:A finite-difference approach.Geophysics,1976,41:2~27
[4]Gazdag J.Modeling of acoustic wave equation by tran-sform methods.Geophysics,1981,46:854~859
[5]Kosloff D et al.Forward modeling by a Fourier meth-od.Geophysics,1982,47:1402~1412
[6]程乾生.信号数字处理的数学原理.北京:石油工业出版社,1979
[2]Marfurt K J.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.Geophysics,1984,49:533~549
[3]Kelly K R et al.Synthetic seismograms:A finite-difference approach.Geophysics,1976,41:2~27
[4]Gazdag J.Modeling of acoustic wave equation by tran-sform methods.Geophysics,1981,46:854~859
[5]Kosloff D et al.Forward modeling by a Fourier meth-od.Geophysics,1982,47:1402~1412
[6]程乾生.信号数字处理的数学原理.北京:石油工业出版社,1979
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