** Next:** Synthetic data
** Up:** BEAM STACK
** Previous:** Beam Stack Model Space

The beam stacking operator is represented in the time domain by:
| |
(2) |

where (*t*,*x*) is the time and offset of the input gather and is the time, offset and slowness in model space. Each location in
model space, , corresponds to the component of energy with the dip *p* at the location in the data. The factor *w*(*x*,*x*_{m}) is a
weighting function that is generally used for the purpose of reducing
truncation artifacts. The forward operator is as follows:
| |
(3) |

Fourier transforming both sides of the above
equation in time results in a nice formulation in the frequency domain:
- Adjoint:
| |
(4) |

- Forward:
| |
(5) |

Examination of the above frequency domain representation reveals that
the action of the operator appears in a multiplicative exponential
term. This representation allows the operator to be split into
separate operators for each frequency. This frequency domain
representation allows the operator to be applied selectively to those
frequencies of interest.

** Next:** Synthetic data
** Up:** BEAM STACK
** Previous:** Beam Stack Model Space
Stanford Exploration Project

11/11/1997