An Ambiguity of Reconstruction Parameters in Media with Attenuation

The inverse problem of seismology for viscoelastic media is considered in this paper. Media with attenuation can be described by Generalized Standard Linear Solid. It was investigated the possibility of reconstructing of the density, impedances and attenuation properties. Numerical method, in which a misfit between the recorded and calculated data is minimized in L2 norm was used in this work. In the numerical solution certain parameterizations can be coupled, it means that true heterogeneity of the only one of parameters can be restored only as a perturbation of another. By using diffraction patterns we can determine whether the parameters are coupled. To study the possibility of recovering the parameters in practice was used singular value decomposition. Properties of the solution were considered by truncating the singular value decomposition. Coupling appears on the attenuation properties and impedances separately corresponding to the pressure wave and shear wave. It is also should be noted that with increasing frequency range and the condition number coupling decreases.