Modal Expansions for Infrasound Propagation and their Implications for Ground-to-ground Propagation

The use of expansions in vertical eigen-modes for long range infrasound propagation modeling in the effective sound speed approximation is investigated. The question of convergence of such expansions is related to the maximum elevation angles that are required. Including atmospheric attenuation leads to a non-self-adjoint vertical eigenvalue problem. The use of leading order perturbation theory for the modal attenuation is compared to the results of numerical solutions to the non-self-adjoint eigenvalue problem and conditions under which the perturbative result is expected to be valid are obtained. Modal expansions are obtained in the frequency domain; broad band signals must be modeled through Fourier reconstruction. Such broad band signal reconstruction is investigated and the relation between band-width, wavetrain duration and frequency sampling is discussed.