In this section, we derive the partial differential equations for
in 2-D and 3-D. From now on, we will denote the square of the Dix
in 2-D and the corresponding matrix by
in 3-D, to avoid the subscript:
Furthermore, we imply that
denotes the one-way
traveltime along the image rays.
Finally, we assume that our domain does
not contain caustics, i.e., the image rays do not cross
on the interval of time we consider.