** Next:** Evaluation of imaging condition
** Up:** REFERENCES
** Previous:** Band-limited lattices

In this section we apply the double square root (DSR) operator to
extrapolate the recorded wavefield of equation (13)
through the depth coordinate of the lattice. After initially Fourier
transforming the wavefield into , , and , the first
application of the DSR yields a new wavefield at depth step
. Mathematically, this is represented by:
| |
(13) |

| |

| |

The periodicity of the lattice over depth coordinate enables the
Shah function index *u*_{z} to be shifted by such that equation
(14) reads,
| |
(14) |

By extension, any continuation step operating on a wavefield will take the same
form.
Applying an inverse Fourier transform over coordinates and yields,
| |
(15) |

where , for convenience, *H* is defined by,
| |
(16) |

where is the Fourier transform operator.
It is important to note here that the convolution of lattice with filter *H* does not change the location of the sample points.
Rather, it operates only on the amplitudes at the predefined locations.

** Next:** Evaluation of imaging condition
** Up:** REFERENCES
** Previous:** Band-limited lattices
Stanford Exploration Project

5/23/2004