A study of coupling between viscoelastic parameters using the singular value decomposition analysis

The solution of a linearized inverse seismic problem of viscoelasticity is studied. The generalized standard linear solid model and the $\tau$ method are used to describe media with attenuation. If the heterogeneity of one of the sought parameters influence the variability of another one during the process of numerical solution, then such parameters are said to be called coupled. Such a coupling is a sign of ill-posedness of the original problem. A regularization is necessary to overcome this difficulty. To accomplish this, we propose the truncation of the singular value decomposition to simultaneously determine the P-velocity and its attenuation. A combination of the Lame parameters and the quality factor are used as the parametrization of the medium under consideration.