Tóm tắt
We have introduced a concise time-domain wave equation to accurately simulate wave propagation in viscoacoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero because we can construct the viscoacoustic wave equation to honor the relaxation property of the medium for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, whereas the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for weakly and strongly attenuating media in terms of the dissipation and dispersion, and the attenuation is precisely linear with respect to the frequencies. The CWE easily and flexibly models dispersion-only, dissipation-only, or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and we achieved nearly perfect matches. When extending to heterogeneous media, the results are consistent with those computed from the nonstationary operator-based Fourier integral method and from the standard linear solid equations.
