Most of the contents of this paper refer to the following linear
partial differential equation:
(1)
Equation (1) describes an artificial
(non-physical) process of transforming reflection seismic data
in the offset-midpoint-time domain. In
equation (1), stands for the half-offset
(, where and are the source and the receiver
surface coordinates), is the midpoint (), and is the time
coordinate after normal moveout correction is applied:
(2)
The velocity is assumed to be known a priori.
Equation (1) belongs to the class of linear
hyperbolic equations, with the offset acting as a time-like
variable. It describes a wave-like propagation in the offset
direction.