A PHASE FUNCTION FOR FINDING NORMAL-MODE EIGENVALUES OVER A LAYERED ELASTIC BOTTOM

A method is described for the determination of normal mode eigenvalues in shallow water over a layered elastic bottom. The method avoids the usual search for eigenvalues in the complex plane by deriving a compl ex phase function which is a multiple of rr at the normal mode eigenva lues. The path in the complex plane along which the phase function is real gives a simple curve which passes systematically through all the eigenvalues including those for the leaky modes. Along this path the p hase function is real and monotonic. The eigenvalues can be found by f ollowing this path.