Zero-offset migration is usually implemented as a downward continuation operation. The exploding reflector model is used to form an image of the subsurface. The wavefield at the surface is extrapolated downwards in depth using a one-way wave equation and the zero-time slice is extracted at each depth to form an image of the reflectivity as a function of depth.
The derivation of the method starts with the scalar wave equation for constant velocity media,
or its equivalent in the Fourier domain
The one-way wave equation is obtained by solving for kz or its space-domain equivalent, :
Here, represents the 2-D Laplacian operator in x and y.
To perform migration we wish to extrapolate the wavefield at some depth z to another depth .There are two main classes of finite difference scheme that are used to do this: Explicit and Implicit schemes.