A knowledge of the background velocity model is crucial to achieve the accurate reservoir description now expected from three-dimensional (3-D) prestack imaging and inversion. Conventional methods for reconstructing the background velocity model, like migration-velocity methods, often assume an isotropic subsurface and can yield inaccurate reservoir descriptions when the subsurface contains anisotropic rock formations. Here, we generalize the migration-velocity concept by (1) replacing migration with linearized inversion and (2) permitting the background velocity to be anisotropic. The scheme consists of scanning different anisotropic velocity models using a linearized inversion in the ω-k domain. As the anisotropic background velocity model is generally described by several elastic coefficients, it is important to adopt an efficient scanning procedure. We have chosen to work with common azimuthal sections. For a given common azimuthal section, we sequentially scan two parameters: normal move-out velocity and the anisotropic parameter known as anellipticity. These two scans allows us to reconstruct an azimuthally isotropic velocity model. The procedure is then repeated for different common azimuthal sections; each common azimuthal section leads to a new azimuthally isotropic velocity model if the medium is azimuthally anisotropic. The number of common azimuthal sections, and therefore the number of azimuthally isotropic velocity models, needed to reconstruct an azimuthally anisotropic velocity model is dependent on the type of symmetries. For example, only three common azimuthal sections are needed for an orthorhombic medium. ¿ American Geophysical Union 1996