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Chapter expands the filtering technique of
Chapter to the problem of multiple attenuation with
2-D data. The basic idea is to separate multiples from primaries according
to their pattern, or multivariate spectra.
To do so, I approximate covariance operators for both the data
and the model with multidimensional prediction-error filters.
These PEFs can be seen as proxies for the primaries and multiples.
This method is a two steps technique. First, the PEFs for the
multiples and the primaries are estimated. The noise PEFs (multiples)
are estimated from a multiple model, generally derived by
convolving shot gathers Verschuur et al. (1992). To estimate the
signal PEFs, I introduce the Spitz approximation
Spitz (1999). Then, the multiples and primaries are
separated in a least-squares sense with the PEFs for covariance
operators. One important result of this Chapter is that 3-D filters
lead to a better multiple removal than 2-D filters. Comparing with
the adaptive subtraction technique of Chapter ,
I also show that the pattern-based technique is less sensitive to modeling
errors present in the multiple model.

** Next:** Multiple attenuation: A 3-D
** Up:** Multidimensional seismic noise attenuation
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Stanford Exploration Project

5/5/2005