On the Resolution of Inversion for Orthorhombic Anisotropy

We investigate the resolution of elastic anisotropic inversion for orthorhombic media with P-waves by remapping classic radiation patterns into the wavenumber domain. We show analytically that dynamic linearized inversion (linearized reverse-time migration and full-waveform inversion) for orthorhombic anisotropy based on longitudinal waves is fundamentally sensitive to emph{six} parameters only and density, in which the perturbing effects can be represented by particular anisotropy configuration. Singular value decomposition of spectral sensitivities allows us to provide estimates of the number of parameters one could invert in specific acquisition settings, and with certain parametrization. In most acquisition scenarios, a hierarchical parameterization based on the $P$, and $S$-wave velocities, along with dimensionless parameters that describe the anisotropy as velocity ratio in the radial and azimuthal directions, minimizes the tradeoff and increases the sensitivity of the data to velocity compared to the standard (stiffness, density) parametrization. These features yield more robust velocity estimation, by focusing the inversion on a subset of invertible parameters.