Usually geophysicists wish that there were no boundaries on the sides, or that they were infinitely far away. There are two kinds of side conditions to think about, those in x, and those in k.
Often the side conditions on x are best approximated by zero-slope side conditions. It is possible to use more general side conditions because we have previously learned to solve any tridiagonal system of equations.
The side conditions in k-space relate to the steepest dips. A way to handle these dips is to use to represent k2. This introduces another adjustable parameter , which must be kept less than 1/4.