** Next:** Introduction
** Up:** Adaptive subtraction of multiples
** Previous:** Adaptive subtraction of multiples

A strategy for multiple removal consists in estimating a model of the
multiples and then adaptively subtracting this model to the data by
estimating shaping filters. A possible and efficient way of computing
these filters is by minimizing the difference or misfit between the
input data and the filtered multiples in a least-squares sense.
Therefore, the signal is assumed to have minimum energy and to be
orthogonal to the noise. Some problems arise when these conditions are not met.
For instance, for strong primaries with weak multiples,
the multiple model might be matched to the signal (primaries) and not to the noise
(multiples). Consequently, when the signal does not exhibit minimum
energy, I propose using the norm as opposed to the norm
for the filter estimation step. This choice comes from the well-known
fact that the norm is robust to ``large'' amplitude differences when measuring data misfit.
The norm is approximated with the Huber norm (Chapter )
minimized with a quasi-Newton method.
This technique is an excellent approximation to the norm. I illustrate this method with synthetic and field data where
internal multiples are attenuated. I show that the norm
leads to a much improved attenuation of the multiples when the minimum
energy assumption is violated. In particular, the multiple model is
fitted to the multiples in the data only, while preserving the primaries.

** Next:** Introduction
** Up:** Adaptive subtraction of multiples
** Previous:** Adaptive subtraction of multiples
Stanford Exploration Project

5/5/2005