A fast field model for three-dimensional wave propagation in stratified environments based on the global matrix method

A three-dimensional fast field program (FFP) model based on the global matrix method will be presented. Compared to traditional propagator matrix methods, the global matrix method allows for a more efficient, and, furthermore, numerically stable computation. The three-dimensional expansion does not restrict sources to be on the center axis, but allows for an arbitrary source geometry—as opposed to earlier two-dimensional versions. As a consequence, the solution includes simultaneously both vertically and horizontally polarized shear waves. A mathematical description will be given and the numerical aspects will be discussed. Some of the features of the model will be illustrated in two test cases: free-space and shallow water with strongly reflecting bottom. The free-space case shows that the three-dimensional solution gives results identical to those obtained by the two-dimensional model except for ranges close to the axis r≡0 of a cylindrical coordinate system. For the shallow water case, the well-known energy transportation in discrete modes above critical wavenumber is first demonstrated. Then the model is used to analyze the field radiated by a long horizontal array, and it is shown that different modes will propagate in slightly different directions.