** Next:** A new fitting goal
** Up:** Attenuation of the ship
** Previous:** Attenuation of the ship

An earlier strategy to remove the ship tracks is to filter the
residual during the inversion as follows Fomel and Claerbout (1995):
| |
(40) |

where is the derivative along the track and minimizing
| |
(41) |

The purpose of the derivative is to remove the drift, which is assumed
to have a zero frequency component. The derivative poses two types of
problem, however. First, it attenuates the bathymetry as well, which has
frequency components very close to zero. Second, it creates more bad
data points for the high frequency noise. Both effects are illustrated
in Figure b where almost all the details inside the lake
have disappeared after the minimization of equation ().
In addition, the map is more noisy due to the aggravating effect
of the derivative on bad data points.
Recently, Brown (2001) proposed estimating
systematic errors between tracks by analyzing measurements at points
where the acquisition swaths cross. This approach has the advantage
of preserving the resolution of the depth map compared to the
derivative along the tracks. Brown (2001) uses this idea as a preprocessing
step, however. Based on Brown's idea 2001
and following Chapter , I propose introducing an operator
that will adaptively model and subtract the systematic shift within the inversion scheme.

In the next section, I show that by incorporating a modeling operator
for the drift in the data, the ship tracks can be effectively removed
without any loss of resolution in the estimated depth map.

** Next:** A new fitting goal
** Up:** Attenuation of the ship
** Previous:** Attenuation of the ship
Stanford Exploration Project

5/5/2005