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 reconstru
cting the background velocity model, like migration-velocity methods,
often assume an isotropic subsurface and can yield inaccurate reservoi
r descriptions when the subsurface contains anisotropic rock formation
s. 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 w-k d
omain. As the anisotropic background velocity model is generally descr
ibed by several elastic coefficients, it is important to adopt an effi
cient 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 a
zimuthally isotropic velocity model. The procedure is then repeated fo
r different common azimuthal sections; each common azimuthal section l
eads to a new azimuthally isotropic velocity model if the medium is az
imuthally anisotropic. The number of common azimuthal sections, and th
erefore 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 sect
ions are needed for an orthorhombic medium.