The finite-difference (FD) wave equation is widely implemented in seismic imaging for oil exploration. But the numerical dispersion due to discretization of time and space derivatives can introduce severe numerical errors. We have investigated time dispersion, which might distort the phase and introduce severe artifacts to the data and images, especially for long-time propagation. We first studied precisely how the time dispersion was produced, and then we developed an efficient approach — the time dispersion transforms — to cope with time dispersion errors in wave propagation. The proposed forward time dispersion transform can predict or simulate the time dispersion errors, and it can be applied to remove time dispersion errors in reverse time migration. The inverse time dispersion transform can be used to eliminate time dispersion errors from synthetic data after modeling. The proposed method is general and works for low- and high-order time FD schemes. By using this method, large time steps were allowed in wave propagation; thus, we can remove the time dispersion errors at a negligible numerical cost, and the efficiency is not affected. To test the effectiveness and robustness of the proposed time dispersion transforms, we used isotropic and anisotropic examples, as well as modeling and imaging examples.

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