Abstract: Starting from the formulas in classical F-K migration, we present an F-K demigration theory in constant velocity media and the corresponding implementation steps as well as its applications in inhomogeneous media, by way of mapping wavenumbers into angular frequencies. In comparison to the Kirchhoff type demigration theory under the same conditions, the theory given here contains no approximations. Therefore, it is an exact demigration theory for models with constant velocity. For general inhomogeneous media, we use the method of the localization, which is widely used in establishing migration theory in inhomogeneous media, and the basic idea of the phase shift plus interpolation (PSPI) migration. Specifically, for treating the demigration problem in inhomogeneous media we assume that the migrated image is thoroughly determined by the velocity distribution in a thin slab corresponding to the current downward extrapolation interval. Furthermore, it is assume that the demigrated wavefield is a continuous function of the velocity. As a result, we can use the local (windowed) Fourier transform with respect to the depth interval under consideration and a set of constant reference velocities to construct the approximate solution to the demigration problem in inhomogeneous media. In algorithmic aspect, the constant velocity F-K demigration is a one-step procedure without recursion, and the varying velocity F-K demigration is a multi-step recursive procedure. Specifically, in a varying velocity F-K demigration the computation should be started at the bottom of the model and realized in a layer-by-layer way from the bottom of the model towards the surface, until the surface is reached.

Key words: demigration, frequency-wavenumber domain, constant-velocity, interpolation plus inverse phase shift