It is acknowledged that Full Waveform Inversion (FWI) techniques are sensitive to the set of model parameters that we choose for the minimization procedure. This model parametrization and sensitivity analysis for FWI has been extensively studied for acoustic and isotropicelastic media. In order to obtain an accurate image of subsurface earth, it is necessary to include both anisotropy and attenuation in inversion procedures as subsurface materials are far from being isotropic or elastic. In this thesis, we formulate the sensitivity analysis for FWI in viscoelastic-isotropic/anisotropic media. To develop such analysis, we construct a framework based on the first order perturbation theory called the Born approximation to find the sensitivity of the FWI to isotropic, anelastic and anisotropic parameters. Sensitivities are, essentially, radiation patterns induced by scattering of the seismic waves from inclusions in medium properties in an isotropic background. Most importantly, we investigate the effect of the inhomogeneity angle which is unique to viscoelastic waves, on these radiation patterns (scattering potentials) and also on amplitude-variation-with-offset or azimuth (AVO/AVAz) analysis. By decomposition of the scattering potentials into isotropic, viscoelastic and anisotropic components, we specify the effects of anelasticity, inhomogeneity of wave and anisotropy on radiation patterns and the linearized AVO/AVAz equations. Moreover, we show how the obtained scattering potentials reduce to the linearized AVO/AVAz equations without using the solution of Zoeppritz equations. This analysis is the starting point for any FWI strategy in a complex media exhibiting both attenuation and anisotropy, as the scattering potentials that we obtained can be effectively implemented to choose a suitable model parametrization.
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