Equation 11 can be rewritten in the following form
(17)
where
is the left-hand side of equation 11.
As in 2-D, we rewrite system 9 in the time-domain
coordinates
. Then we get
(18)
(19)
where
is given by equation 17, and the gradients
are taken with respect to
.
Then the PDE for
is
(20)
The initial conditions are
,
.
The required input
is well-approximated
by the squares of the Dix velocity obtained
from the 3-D prestack time migration.
We emphasize that despite the fact that
is a
matrix in 3-D, scalar data are enough for its computation.
Time-to-depth conversion and seismic velocity estimation using time-migration velocity