title: Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions.
abstract: A normal mode solution to the ocean acoustic problem of the Pekeris waveguide with an elastic bottom using a Green's function formulation for a compressional wave point source is considered. Analytic solutions to these types of waveguide propagation problems are strongly dependent on the eigenvalues of the problem; these eigenvalues represent horizontal wavenumbers, corresponding to propagating modes of energy. The eigenvalues arise as singularities in the inverse Hankel transform integral and are specified by roots to a characteristic equation. These roots manifest themselves as poles in the inverse transform integral and can be both subtle and difficult to determine. Following methods previously developed [S. Ivansson et al., J. Sound Vib. 161 (1993)], a root finding routine has been implemented using the argument principle. Using the roots to the characteristic equation in the Green's function formulation, full-field solutions are calculated for scenarios where an acoustic source lies in either the water column or elastic half space. Solutions are benchmarked against laboratory data and existing numerical solutions.
authors.affiliation: Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401.
authors.forename: Brittany A
authors.initials: BA
authors.lastname: McCollom
authors.affiliation: Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401.
authors.forename: Jon M
authors.initials: JM
authors.lastname: Collis