**Abstract:**

The calculation of eigenvalues for a layered isovelocity oceanic environment and associated vertical modes is very quick and easy to do. A method of transforming the isovelocity problem to a variable velocity problem, by means of a matrix transformation based on the theory of generalized eigenvalues, is described. Along with modern transformation techniques, the rapid reconstruction of variable velocity solutions is demonstrated. It is possible to determine the mode spectrum extremely rapidly by first starting out with those associated with a reference isovelocity eigenvalue set, and then by using an iteration procedure based on integral transform methods, the Householder transformation, polar decomposition theorems, shifting, and deflation methods in linear algebra to converge to the set of eigenvalues rapidly. A first iteration may take a fraction of a second to calculate on a PC, while full iteration takes on the order of a second to calculate 100 eigenvalues. [Work sponsored by ONR, the Naval Res. Lab., and the Univ. of New Orleans.]

ASA 133rd meeting - Penn State, June 1997