Effective Vertical Modes and Horizontal Rays for Wave Propagation in Complex Inhomogeneous Ducts

Wave propagation in complex inhomogeneous, quasi-layered, 3D media is addressed using multires-olution analysis (MRA). The complexity is characterized by a fast, nely structured, variation of the system heterogeneity in the vertical (stratiication) direction, and a slow horizontal variation of the system heterogene-ity and/or the vertical boundaries (\fast" and \slow" here are relative to the wavelength reference scale). The new formulation utilizes previous results (see B.Z. Steinberg and J. Oz; this issue]) which show that the modal elds in a strictly stratiied medium can be described by eeective modes obtained via an MRA smoothing of the medium heterogeneity. We therefore use the MRA to derive a 3D eeective inhomogeneous wave equation, expressed in terms of the large scale heterogeneities of the medium (the eeective measures of the medium). In general this MRA introduces an eeective anisotropy. The wave solution is then expressed as a sum of local vertical eeective-modes whose horizontal propagation properties are described by solving an eeective horizontal ray equation for each of these mode, that accounts for the horizontal variations of the medium.