Second-order time integration of the wave equation is numerically efficient with time steps close to the limit set by the stability criterion. However, dispersion errors over realistic propagation distances are unacceptable with time steps in this range. Dispersion-free results, using second-order time integration of the wave equation, can be achieved by applying a time-domain prepropagation filter to all source time functions followed by a time-domain postpropagation filter applied to the simulated wavefield at all recording positions. The time-domain implementation of the filtering process is an order of magnitude more effective, in terms of CPU time, compared to an implementation via discrete and fast Fourier transforms. Pre- and postpropagation filters are valid for any simulation time step. The two filters can be calculated once because they are independent of the simulation time step, and they can be applied with any modeling scheme that uses second-order time integration. Second-order time integration results in traveltime and amplitude errors. The amplitude errors depend on the spatial source distribution. The combined application of the two filters removes traveltime-related errors and amplitude-related errors independently of the spatial source distribution.

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