Approximating constant-Q seismic propagation in the time domain

In this study, we investigate the accuracy of approximating constant-Q by a series of Zener or standard linear solids (SLS) mechanisms. Modeling of approximately constant-Q in a viscoacoustic medium is implemented in time domain using finite-difference (FD) approach. The accuracy of numerical solutions is evaluated by comparison with the analytical solution of the constant-Q model. We found the FD solutions using three SLS (relaxation mechanisms) as well as a single SLS mechanism are quite accurate for weak and strong attenuation. Although the RMS errors of FD simulations using the single relaxation mechanism become larger with increasing offset, especially for strong attenuation (Q=20), the results are still acceptable. The simulated synthetic data of the complex 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 time and memory. Therefore, we suggest that the single relaxation is a promising choice to model constant-Q for computational intensive seismic modeling and inversion.