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《Chinese Journal of Geophysics》 2001-03
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SEISMIC WAVE MODELING WITH IMPLICIT SYMPLECTIC METHOD BASED ON SPECTRAL FACTORIZATION ON HELIX

LUO MING QIU LIU HONG LI YOU MING (Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100101, China)  
Based on the common equation of seismic wave field and its Hamiltonian formalism, an implicit symplectic method (ISM) is proposed for seismic wave modeling in this paper. Combined with helix boundary conditions, the spectral factorization method is applied to give a fast way for the ISM modeling. The propagation of seismic wave can be described by the acoustic equation of a single scalar quantity in the constant, complex isotropy and anisotropy media. With the assumption of no dissipation, the scalar equation gives the symplectic evolution of seismic wave field, which is an infinite dimensional Hamiltonian system. Therefore, its Hamiltionian formalism and symplectic schemes can be given. Compared with explicit symplectic method (ESM), ISM is unconditionally stable method. Consequently, a long time step and a long time calculation are possible for ISM, which may be impossible for ESM in the same conditions. Unfortunately, it is unavoidably to calculate the inverse of large matrix in each step of ISM, which is time consuming process. Fortunately, however, the matrix has striped shape with a helical boundary conditions. And more, the nonzero units in each row of the matrix not only are located in the same relative positions but have similar values. Therefore, spectral factorization method can be used to get the inversion of the matrix in a very quick way. Based on spectral factorization method, an ISM scheme with second order in time is applied to get the wave fields in constant velocity, layer velocity and Marmousi velocity models. As the results indicates, with the help of spectral factorization, ISM is a quite good method in seismic wave modeling.
【Fund】： 国家自然科学基金委资助;; 大庆石油管理局资助项目!( 49774 2 38)
【CateGory Index】： P315.31
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