Linear and parabolic τ-p transforms revisited

New derivations for the conventional linear and parabolic τ-p transforms in the classic continuous function domain provide useful insight into the discrete τ-p transformations. For the filtering of unwanted waves such as multiples, the derivation of the τ-p transform should define the inverse transform first, and then compute the forward transform. The forward transform usually requires a p-direction deconvolution to improve the resolution in that direction. Numerical examples are presented to demonstrate event focusing in τ-p space after deconvolution. -from Authors