By taking equation (14) and changing the integration variable from to . In the same time the new variable becomes function of only two variables in ,in the form given by equation (11).
Special attention should be given to the new field . As the variable is replaced with , each value of has to be associated with the appropriate value of the field
The new field represents a remapping (or interpolation) of the original field .Each value in the new field with coordinates corresponds to the value in the field with coordinates . A more detailed analysis of this mapping is done in a companion paper in this report: Popovici (1993).
From equation (10) the Jacobian is
In the next step we change the integration order
Equation (18) represents zero-offset downward continuation and imaging as introduced by Gazdag (1978) or Stolt (1978). Equation (19) represents a way of obtaining zero-offset section from constant-offset sections.
The operations needed to obtain the zero-offset stacked section from the constant-offset field described in equation (19) are: