Continuous modes and shallow water sound propagation

The continuous mode contribution to the acoustic field in shallow water arises as a branch line integral which can be interpreted in various ways. With the `EJP´ branch cut the vertical wave number in the bottom is real and the branch line integral has resonances which correspond to virtual modes. With the `Pekeris´ branch cut there are residues at complex poles and for the field in the water, the branch line integral is negligible unless a pole is near the branch point. The residues at these complex poles give rise to leaky modes. In changing bathymetry these poles move systematically in the complex plane. When combined with the adiabatic approximation and an approximate normalization, the leaky modes provide a convenient, smooth description of the acoustic field in the water as a mode passes through cutoff. Leaky modes are not useful for calculating the field in the bottom as the Pekeris branch line integral cannot be neglected