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 l1-l2 inverse problems in an efficient fashion.
I compare three different methods to obtain the velocity panel: (1) least-squares inversion,
(2) l1 inversion, and (3) l1 inversion with l1 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.
Stanford Exploration Project