Accurate full-waveform seismic modeling is a powerful tool for understanding wave propagation and building subsurface images. However, it can be computationally expensive for viscoelastic media. Viscoacoustic seismic modeling is much cheaper, but at the trade-off of using incomplete physics. We have developed a modified viscoacoustic wave simulation algorithm for modeling the viscoelastic effects of P-waves. The algorithm contains two viscoacoustic forward-modeling steps; the first is the same as the traditional viscoacoustic modeling, whereas the second propagation is generated using a residual error source, which is derived by comparing the viscoacoustic and viscoelastic wave equations in the form of stress-particle velocity formulations. The corrected P-wave particle velocities can be obtained by adding the wavefield from the second simulation step to the original (the first simulation step) viscoacoustic wavefield. Only P-waves are modeled. The overall cost is about twice that of viscoacoustic modeling, but it is significantly less than a viscoelastic propagation because there are fewer calculations, and we can use a coarser grid and larger time steps for the same accuracy. Numerical examples indicate that the P-wave waveforms, after correction, match those from viscoelastic wave modeling better than those from the original viscoacoustic simulation. Our method provides a cost-efficient alternative for approximating the viscoelastic effects in P-wave modeling.

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