Multiparameter full-waveform inversion (FWI) usually suffers from the inherent tradeoff in the multiparameter nature of the model space. In orthorhombic anisotropy, such tradeoff is magnified by the large number of parameters involved in representing the elastic or even the acoustic approximation of such a medium. However, using a new parameterization with distinctive scattering features, we can condition FWI to invert for the parameters to which the data are sensitive at different stages, scales, and locations in the model. Specifically, with a combination made up of a velocity and particular ratios of the elastic coefficients, the scattering potential of the anisotropy parameters has stationary scattering radiation patterns as a function of the type of anisotropy. With our new parameterization, P-wave data are mainly sensitive to the scattering potential of four parameters: the horizontal velocity in the x direction, v; -, which provides scattering mainly near zero offset in the x-x vertical plane; -, which is the ratio of the horizontal velocity squared in the x and x directions; and describing the anellipticity in the horizontal plane. Since, with this parameterization, the radiation pattern for the horizontal velocity and - is azimuthally independent, we can perform an initial VTI inversion for these two parameters, and then use the other two parameters to fit the azimuthal variation in the data. This can be done at the reservoir level or any region of the model. Including the transmission from reflections, the migration velocity analysis (MVA) component, into the picture, multiazimuth surface seismic data are mainly sensitive to the long-wavelength components of v, two dimensionless parameters through the diving waves, and three other dimensionless parameters in the transmission to or from reflectors (especially, in the presence of large offsets). They are also sensitive to the short-wavelength component of v and -.