RATIONAL OPERATORS FOR FILTERING

The parabolic equation (PE) method has been applied to approximate the wave equation, construct radiation conditions, solve scattering probl ems, construct initial conditions, and derive energy flux conditions. A new application of the PE method, filters based on rational approxim ations of depth operators, is described and tested. The rational appro ximation is designed to act as the identity operator on the desired pa rt of the spectrum of the depth separated wave equation and to annihil ate other parts of the spectrum. This approach does not require explic it knowledge of the spectrum. The applications of the filter include d irectly solving eigenvalue problems, annihilating components of the wa ve-number spectrum, generating initial conditions at the source range, and eliminating Gibbs oscillations that arise in energy-conserving PE solutions. (C) 1997 Acoustical Society of America.