We describe in this paper a new way of solving the two-way wave equation called the two-step Explicit Marching method. Compared to the conventional explicit finite-difference algorithms, which can be second or fourth order but are subject to stability conditions and dispersion problems that limit the magnitude of the time steps used to propagate the wavefieds, the proposed method is based on a high order differential operator and allows arbitrary large time steps with guaranteed numerical stability and minimized dispersion. Synthetic and real data examples show that it allows the reverse time migration to be performed with the Nyquist time step, based on the maximum frequency of the input data, which is the maximum time step that can be used for proper imaging.


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