A Multiresolution Approach for the Effective Properties of Complex Propagation Ducts and Effective Modes/rays Theory

Multiresolution techniques are used to study the eeective properties of propagation in nely struc-tured ducts. A new formulation governing the smoothed component of the eld is derived and compared to the generic formulation governing the complete eld. The relation between the small scale structure of the system heterogeneity and the large scale eld is investigated. In particular, we use multiresolution and wavelet expansion to derive eeective measures for the system heterogeneity. These measures are heterogeneity functions that are simpler (smoother), but can still reproduce the correct large scale behavior of the eld. The eecacy of modal analysis and ray techniques in the new framework is discussed.