Wave-equation simulation based on the k-space method produces nearly dispersion-free wavefields and enhances simulation stability. However, for simulation in heterogeneous media, the conventional first-order k-space method requires many mixed-domain operators, which are the most expensive part of the wave-extrapolation process. We have analyzed and summarized the problem of the conventional k-space method as symmetrical factorization of the wave propagators. Based on this analysis, we develop a novel asymmetrical factorization-based k-space method that can significantly reduce the number of mixed-domain operators without compromising modeling accuracy. By using this method, the number of mixed-domain operators is reduced by half, and thus, the computational cost decreases significantly. Furthermore, we have compared our method to the conventional pseudospectral method. The comparison finds that, at comparable accuracy, our method is more efficient due to its ability to use a larger time step. Acoustic and elastic examples demonstrate the correctness and effectiveness of our method.

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