Full viscoelastic waveform inversion: a mathematical framework

Shahpoor Moradi, Kristopher A. Innanen

In this report we study the multiparameter Full Waveform Inversion (FWI) in viscoelastic medium with five viscoelastic parameters. Parameters are, density, unrelaxed bulk modulus and shear modulus, and the differences between the relaxed and unrelaxed moduluses. Based on the Born approximation we derived the explicit form of the Frchet kernels. We showed that five viscoelastic parameters can be inverted in terms of the time and space partial derivatives of the forwarded and backwarded scattered wavefields. We also derived the Jacobian matrix that transform the three model of parametrization for inversion.