Asymptotic theory for imaging the attenuation factors QP and QS.

Linearized inverse scattering problem in anelasticity is solved for perturbations in different parameters treating P-to-P, P-to-S,S-to-P and S-to-S data. Three steps are required for finding the material parameters of the medium, i.e. the density and the complex relaxation functions. In a given smooth reference medium, an high-frequency Green function is expressed as a function of traveltime, amplitude and attenuation factors. For a slightly different medium, the perturbation of the asymptotic Green function is expressed as a linear integral over the diffracting region containing the model perturbations using the first-order Born approximation. The inversion scheme is developed in the frequency domain where we were enable to set up an analytical kernel for the Born approximation of asymptotic anelastic solutions used for the forward problem and an approximate analytical kernel for the linearized inversion. Radiation patterns are analysed to show that the simultaneous multiparameter inversion is possible when one takes into account the parameters related to attenuation. The iterative asymptotic inversion might resolve the difference between the elastic parameters and the attenuation factors. [ABSTRACT FROM AUTHOR]