We tend to think of normal mode models as primarily suitable for range-independent problems, however, it is in principle easy to extend them to provide range-dependent solutions. One way of doing this is to divide the range axis into a number of segments and approximate the field as range-independent within each segment. The solution within a range independent segment is constructed using the standard normal mode solution and interface conditions (continuity of pressure and normal velocity) are used to `glue' the solutions together.
This ``coupled mode'' approach is straightforward but leads to a computationally intensive procedure. For this reason it is, at least at the present, primarily useful for providing an exact solution for verifying simpler approximate models such as the PE technique. The full two-way solution is not actually implemented in KRAKEN , however, it provides a useful starting point for discussing two successive simplifications in which we ignore 1) the back-scattered component, and 2) coupling between different modes at the interfaces (the adiabatic approximation). These approximations are frequently a reasonable compromise between accuracy and run-time.