Approximating constant-Q seismic propagation in the time domain

In this study, we investigate the accuracy of approximating constant-Q wave propagation by series of Zener or standard linear solid (SLS) mechanisms. Modelling in viscoacoustic and viscoelastic media is implemented in the time domain using the finite-difference (FD) method. The accuracy of numerical solutions is evaluated by comparison with the analytical solution in homogeneous media. We found that the FD solutions using three SLS relaxation mechanisms as well as a single SLS mechanism, with properly chosen relaxation times, are quite accurate for both weak and strong attenuation. Although the RMS errors of FD simulations using a single relaxation mechanism increase with increasing offset, especially for strong attenuation (Q = 20), the results are still acceptable for practical applications. The synthetic data of the Marmousi-II model further illustrate that the single SLS mechanism, to model constant Q, is efficient and sufficiently accurate. Moreover, it benefits from less computational costs in computer time and memory.