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《Progress in Geophysics》 2007-02

## Symbol description to integral solution of one-way wave operator

LIU Hong1,WANG Xiu-min1,ZENG Rui1,LI You-min1,GOU Yong-feng2(1.Institute of Geology & Geophysics,Chinese Academy of Sciences,Beijing 100029,China;Petroleum and Gas Resource Key Laboratory,Chinese Academy of Sciences,Beijing 100029,China;2.Daqing Geophysical Exploration Company,CNPC,Daqing 163357,China)
Extrapolation operator of one-way wave field has great application in seismic migration imaging.According to their implement,these operators can be classified into three kinds: Kirchhoff integral method,implicit definite difference in space domain and Fourier transform method.They represent different operator expression methods.Different precisions will be got while using the operators in these methods in different truncate order.Represent in symbol in the method of derivation and accuracy analysis.Symbol of operator is the function of operator acting on sine function.Symbol of operator is the extension of convolution operator's Fourier transform.Fourier transform method can be directly derived from symbol function's separable approximation.Implicit space difference can be solved by padè approximation or part fraction.Integral of one way wave operator in depth domain.The symbol solution of one-way wave integral is deduced,the first several order operator expressions of symbol's algebra operation are given.These expressions haven't been found in any previous reference.Green function that adapts to Kirchhoff integral method could be derived from symbol function and saddle point method.The symbolic expression,which based on integral solution give the equation of asymmetric traveltime,have great significance on focusing capability of Kirchhoff integral method.
【Fund】： 中国科学院知识创新工程重大项目(编号KZCX1-SW-18);; 重点研究项目(KZCX3-SW-147);; 国家自然科学基金面上项目(编号40674072)联合资助
【CateGory Index】： P631.4
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