Quick and accurate Q parameterization in viscoelastic wave modeling

We introduce a procedure for including the attenuation factor Q in a consistent manner in seismic modeling and show 3D examples. The Q fitting over a chosen frequency band involves two algorithms: The first creates starting values of relaxation times, and the second does nonlinear inversion using the results of the first as initial values. The resulting Q function gives a good approximation to a constant Q over the chosen frequency band. The algorithm is combined with a finite-difference (F-D) code that includes topographies in 3D seismic media. The velocity-stress formulation for viscoelastic wave modeling is used with an arbitrary number of relaxation mechanisms to model a desired Q behavior. These equations are discretized by high-order F-Ds in the interior of the medium, and we gradually reduce the F-D order to two at the stress-free surface, where we implement our free-surface boundary conditions. The seismic F-D algorithm is applied to a marine seismic experiment, with and without viscoelasticity, to emphasize the importance of including physical attenuation and dispersion in seismic modeling. Their inclusion, even for marine surveys, is clearly important for lossy ocean bottoms. Our procedure for more accurate modeling of physical dispersion and attenuation may increase future motivation to include viscoelasticity in seismic inversion.