Normal mode solutions for radiation boundary conditions with impedance contrast
Keiko Yamamura, Hitoshi Kawakatsu
Geophys. J. Int., in press , 1998
Abstract
The radiation boundary conditions are Non-Hermitian and frequency-dependent.
Therefore wave propagation problems with radiation boundary conditions
typically cannot be solved by the ordinary eigenfunction expansion method.
We present a method for solving wave propagation problems with
radiation boundary conditions which have impedance contrast in terms
of a superposition of eigenfunctions, using the biorthogonal
eigenfunction expansion method outlined by Morse & Feshbach.
We develop their method so that the calculations other than those of eigenfunctions of
the original and its Hermitian adjoint system are unnecessary
to construct the solution, using variational equation.
We present numerical computations for a one-dimensional
semi-infinite continuum which has impedance contrast.