Azimuthally-dependent scattering potentials and full waveform inversion sensitivities in low-loss viscoelastic orthorhombic media

Shahpoor Moradi, Kristopher A. H. Innanen

The problem of seismic wave scattering from anisotropic and attenuative inclusions is analyzed within the mathematical framework of the Born approximation. Specifically, a Born scattering model is used to extract scattering potentials, which generalize linearized reflection coefficients and sensitivity kernels, and which in the latter form are a basis for multi-parameter seismic full waveform inversion (FWI) updates. To derive the scattering potentials, a point scatterer comprising a perturbation in each medium property is inserted in a homogeneous isotropic background. The amplitudes, or scattering radiation patterns, associated with incoming and outgoing wave vector pairs provide the weights used to simultaneously invert for viscoelastic and anisotropic medium properties. Analysis of the angle-dependence of the scattering patterns provide qualitative and quantitative insight into inter-parameter trade-offs and cross-talk. We explicitly derive scattering potentials for elastic and viscoelastic P-to-P, P-to-SV and P-to-SH waves in a weak anisotropic, low-loss viscoelastic orthorhombic media. We assume the background or reference medium to be either isotropic-elastic or isotropic-viscoelastic. The results generalize reflection coefficient expressions derived from linearization of exact solutions of the Zoeppritz equation for transversely isotropic viscoelastic media with both vertical (VTI) and horizontal (HTI) axes of symmetry.