Fréchet kernels for FWI of multicomponent data for a linear isotropic viscoelastic media are derived by using the Born approximation applied to the Green’s integral solution of the wave equation. The kernels that also called scattering potentials are the functions of opening angle between the incident and scattered waves and attenuation angle that characterized the maximum direction of the attenuation. Sensitivities of the full recorded viscoelastic wave-field are obtained in three types of model parametrization, density-velocity-quality factor, [ ρ, V P , V S , Q P , Q S ], density-impedance-quality factor [ ρ, Z P , Z S , Q P , Q S ], and density-Lamé parameter-quality factor, [ ρ, λ, μ, Q P , Q S ]. We also study the radiation patterns of point sources and moment tensor sources, among them, a dipole and double couple sources in a viscoelastic medium, this analysis can be used for the inversion of the seismic sources in an attenuative medium.
View full article as PDF (11.86 Mb)