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《Geophysical Prospecting for Petroleum》 2009-01
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The travel time calculation method via lateral derivative of velocity and its application in pre-stack time migration

Liu Hong Liu Guofeng Li Bo Wang Xiumin Tong Xiaolong Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China  
In pre-stack time migration by Kirchhoff integral,the travel time of the two points are repeatedly used.However,the computa- tion amount(or storage cost)of conventional travel time computa- tion method is limited by computer conditions.In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator.The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold.The travel time are expressed as polynomials of the hori- zontal offset between the two points,and the single-square-root operator in frequency-wavenumber domain are expressed as polyno- mials of wavenumber.Coefficients of travel time polynomials and that of single-square-root operator are related each other and calcu- lated by Lie algebraic integrand,exponential map and the saddle- point method.Comparing to conventional expansion,our paraxial travel time expansion increases asymmetric terms of the horizontal offset in the expression.In Kirchhoff migration,the coefficients of travel time polynomials are calculated and stored before seismic da- ta input(number of the coefficients are about 10).Travel times are calculated via the coefficients during Kirchhoff stacking of seismic data.A Magnus method calculated from Lie algebraic integrand polynomials,exponent mapping polynomials is given,which uses the tree-root scheme to compute high order terms based on lower order terms in the expansion method.The numerical comparison between our formulas,the results of finite difference method,sym- metry formula and our formula are compared by numerical model- ing.The results show that our method has higher accuracy than symmetry travel time formula.
【Fund】: 国家重点基础研究发展计划(973)项目(2007CB209603);; 国家自然科学基金项目(40674072,40774069);; 中国科学院知识创新工程重要方向KZCX3-SW-147共同资助
【CateGory Index】: P631.4
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