Abstract
Summary The propagation of the seismic wave is essentially an evolution of an infinite dimensional Hamiltonian system. If the Hamiltonian property of an algorithm were not guaranteed, the algorithm would not give a correct wave field especially in case of complex media. Symplectic method, which takes care of the symplectic property of the wave propagation, can give theoretically and practically more correct wave fields than ever. Through the conventional algorithm such as implicit finite-difference method is a symplectic method, but the accuracy of the exponential function is not high enough. We develop a symplectic approximation method for the one-way downward propagation operator in order to increase the accuracy of the approximation the exponential function according to Feng K. This approximation is more accuracy than that of the two-step approximation method for the complex exponential function. In practise, the method can be realized by applying the finite-difference method two times. The case study on the Daqing Oilfield data by symplectic method shows that it has a better performance than Kirchhoff method.
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