The 45 migration is a little harder than
the 15
migration because
the operator in the time domain is higher order,
but the methods are similar to those of the 15
equation
and the recursive dip filter.
The straightforward approach is just to write down the differencing stars.
When I did this kind of work I found it easiest
to use the Z-transform approach where
is
represented by the bilinear transform
.There are various ways to keep the algebra bearable.
One way is to bring all powers of Z to the
numerator and then collect powers of Z.
Another way, called the integrated approach,
is to keep 1/(1-Z) with some of the terms.
Terms including 1/(1-Z) are represented in the computer by buffers
that contain the sum from infinite time to time t.
The Z-transform approach systematizes the stability analysis.