SLANT STACK TRANSFORMATION

We first have to transform the wavefield in CDP gather from the (x,t) domain to the $(\tau,p)$ domain. Let d(x,t) be the wavefield and $u(\tau,p)$ be the transformed slant stack wavefield Claerbout (1985) so that  

$$u(\tau,p) = \int d(x,\tau+px)dx$$ (1)

where

$\tau=t-px$

p:slant parameter

x:offset

A lot of care needs to be taken to construct a high-quality slant stack CMP gather, several methods exist to achieve this Kostov (1990) . The causes of poor quality are probably due to very coarse offsets and missing offsets beyond the ends of the cable. Those missing offsets must be interpolated or extrapolated before slant stack transformation .