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I present one possible formulation of the signal/noise separation
problem as exemplified by
Abma and Claerbout (1995); Brown and Clapp (2000); Guitton et al. (2001); Soubaras (1994).
To simplify, we have the two following fitting goals:
| |
(8) |

where the data is equal to the sum of the noise and signal , is the PEF for the noise
(), is the PEF for the signal
(), and a constant.
Solving for we have
| |
(9) |

The signal-noise attenuation is then separated into two distinct
steps: first we estimate the noise and signal filters and
, then we estimate the signal based on the fitting
goals in equation (8).

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Stanford Exploration Project

7/8/2003