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This paper will describe my production of a velocity domain
where multiples and primaries are easily identifiable and separable by the use of the Hyperbolic
Radon Transform (HRT) and inverse theory. The **Huber function** Huber (1973), or Huber norm,
allows us to solve hybrid *l*^{1}-*l*^{2} inverse problems in an efficient fashion.
I compare three different methods to obtain the velocity panel: (1) least-squares inversion,
(2) *l*^{1} inversion, and (3) *l*^{1} inversion with *l*^{1} regularization. These velocity panels are
then used to perform the multiple suppression Lumley et al. (1995).
In this paper I will first review the theory of the velocity transform operator.
Next, I introduce the Huber norm and the inverse problem
I intend to solve to produce the velocity field. Finally, I apply a multiple attenuation
technique for different inverse problems to a complete 2-D data set (Mobil AVO data).
I will show that the multiple reflections are favorably attenuated
with no noticeable differences between the different inverse problems.

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Stanford Exploration Project

4/27/2000