An energy-conserving spectral solution

An energy-conserving spectral solution is derived and tested. A range-dependent medium is approximated by a sequence of range-independent regions. In each region, the acoustic field is represented in terms of the horizontal wave-number spectrum. A condition corresponding to energy conservation is derived for the vertical interfaces between regions. The accuracy of the approach is demonstrated for problems involving sloping ocean bottoms. The energy-conserving spectral solution is less efficient than the energy-conserving parabolic equation solution, but might be suitable for generalization to problems involving elastic bottoms.