Publications
Design of mode filters using WKB-like approximations
Abstract
A number of matched field and tomographic applications rely on estimating the modal content of signals incident on a vertical line array (VLA). Spatial filtering for modes requires knowledge of the modeshapes, which requires knowledge of the environment. Unfortunately, environmental information is often incomplete. For example, during the North Pacific Acoustic Laboratory experiment the receiver environment was sampled by temperature sensors mounted on one of the VLA's. These sensors provided a year-long time series of temperature across the 1400 m span, but there is no record of the temperature above and below the array. Solving for the modeshapes requires a complete temperature profile. One way to facilitate the mode calculation is to use archival data for the missing parts of the profile. Another approach is to use an approximation for the modeshapes that does not require knowledge of the sound speed (thus the temperature) above and below the VLA. WKB theory provides such an approximation for modes spanned by the VLA. Using standard WKB theory to construct the mode filter is problematic because the approximate modeshapes it generates are singular at the turning points. Uniform WKB-like approximations, such as those described by Langer [1] and Miller and Good [2], are continuous at the turning points. This paper discusses the design of mode filters using uniform WKB-like approximations and analyzes their performance.
[1] Phys. Rev. 51, 669, 1937.
[2] Phys. Rev. 91, 174, 1953.
This talk was presented at the 2003 Underwater Acoustic Signal Processing Workshop (UASP) , sponsored by the IEEE Providence Section in cooperation with the IEEE Signal Processing Society. The abstract may be found on the UASP website.