Consider a set of image rays coming to the surface.
Suppose we are tracing them all backwards in time
together with the quantities
Let us eliminate the unknown velocity
in system 9
using equation 10.
Moreover, let us eliminate the differentiation
using the definition
and rewrite it in the time-domain
Therefore, system 9 becomes
in system 13, we get
the following partial differential equation (PDE) for
The initial conditions are
Equation 14 simplifies in terms of the negative
equation 14 becomes