Interference patterns in range dependent environments Free

Interference patterns in space and frequency occur in ocean acoustics due to coherent multipath propagation. The wave guide invariant beta is commonly used to describe the behavior of these patterns [Brikhosvsky and Lysanov, Fundamentals of Ocean Acoustics, 2nd ed. (Springer‐Verlag, New York, 1991)]. The standard derivation of this invariant uses a normal mode expansion and is limited to range independent and weakly range dependent environments. A different approach is introduced that describes the interfering components in terms of their travel times. This leads to a very simple derivation of basic results that apply equally well to range dependent environments and to situations, such as Lloyd’s Mirror, in which the normal mode representation is inconvenient. Beta can be expressed in terms of the local phase velocities and the difference in travel times for the interfering components. The travel time differences involve integration over the entire path trajectories from the source to the point where the interference pattern is observed. Numerical examples using ray theory will be presented.