** Next:** Acknowledgments
** Up:** Adaptive subtraction of multiples
** Previous:** Poststack land data multiple

When a model of the multiples is adaptively subtracted from the data
in a least-squares sense, we implicitly assume that the signal
(primaries) has minimum energy and is orthogonal to the noise
(multiples). This paper demonstrates that the minimum energy
assumption might not hold and that another norm, the
norm, should be used instead. Based on Chapter
, I propose using the Huber norm for the filter
estimation problem.
I demonstrate with 1-D and 2-D data examples that the Huber norm
with a small threshold gives a much improved multiple attenuation
results when the signal has not minimum energy: the multiples are well
separated and the primaries are preserved. This Chapter exemplifies
that the Huber norm can be used for many geophysical applications
whenever robustness is sought. Chapter will
further illustrate this point with an interpolation problem of noisy data.

** Next:** Acknowledgments
** Up:** Adaptive subtraction of multiples
** Previous:** Poststack land data multiple
Stanford Exploration Project

5/5/2005