In this paper, we use an explicit anisotropic correction filter in addition to the normal isotropic operator. For each z step, we first regard the medium as an isotropic medium and extrapolate the wavefield using an isotropic operator with the velocity in the direction parallel to the symmetry axis. The isotropic operator can be the split-step method Stoffa et al. (1990), the general screen propagator Huang and Wu (1996), or Fourier finite difference (FFD) Ristow and Ruhl (1994). Then we correct the wavefield with an explicit correction operator.
After we extrapolate the wavefield with an isotropic operator, the resulting error relative to anisotropic extrapolation is:
and kza is one of the four roots of the dispersion-relation equation (4). We design the explicit correction operator by weighted least squares. The obtained explicit operator is approximately the same as F(kx) in the wavenumber domain for desired wavenumbers.