Page 44 - Volume 9, Issue 3

If p is exactly 2 the function k(z) is hyperbolic which is fairly close to the cosh case, and again b → ∞. If p is greater than 2 then b is positive, and if it is less than 2, b is negative. If p is large then k(z) remains flat but has a very sudden rise for az > 1, resembling a step in the sound speed profile or a reflecting sur- face. As one might hope, in the limit this results in b → 1. If p is small then k rises rapidly for small z but then flattens out for large – this is not very likely oceanographically, but it results in b → –1. An illustration of these profiles is shown in Fig. 5.
Conclusions
So the moral (to the signal processing fraternity) is, if you see some fringes, don’t throw them away, they could be useful. In underwater acoustics the sound spectrum of a distant source may stretch or shrink as the receiver moves away. This leads to a streaky pattern of fringes or striations, and their gradient is quantified by the waveguide invariant b (Eq. 2). If the sound speed is constant then the fringes radiate from the source and b = 1. The limiting case of the cosh profile (Eq. 12) results in a repeated perfect focus for which b → ∞. Generally the sign of b depends on whether the ray cycle distance increases or decreases with angle. If it decreases with angle then b is posi- tive, as in the isovelocity case. If it increases with angle then b is negative as in the uniform gradient upward or downward refracting case where b is –3. Given some knowledge of the value of b and a moving platform there is promise of measur- ing ranges with a single hydrophone.AT
Acknowledgements
The author thanks Dr. Peter Nielsen for running the examples with the wave propagation model ORCA.
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Chris Harrison received his MA in Natural Sciences from Clare College, Cambridge in 1968. Subsequently, at the Scott Polar Research Institute, Cambridge he studied radio propaga- tion in ice and spent two summer sea- sons in the Antarctic, completing his PhD in 1972. He started work in acoustics at Admiralty Research Laboratory, Teddington, and spent two
years, from 1976 to 1978, as Exchange Scientist at Naval Research Lab, Washington where he worked on long distance reverberation in the Norwegian Sea. From 1978 to 1999 he worked as an acoustics consultant, mainly under contract to the UK MOD in a software company that is now a part of British Aerospace. His interests included development of prop-
agation, noise, and sonar performance models. After joining the NATO Undersea Research Centre’s (NURC) Acoustics Division in March 1999 he developed three experimental tech- niques from scratch to measure the seabed’s reflection loss, sub-bottom layering, and geoacoustic properties using ambi- ent noise and a drifting array. These were evaluated in a num- ber of collaborative experiments south of Sicily. Simultaneously he developed the multistatic sonar perform- ance model SUPREMO and the fast reverberation and sonar performance model ARTEMIS for use in tactical planning.
Chris was awarded the 1992 AB Wood Medal and the 2008 Rayleigh Medal by the UK Institute of Acoustics. He is current- ly a Visiting Professor at the Institute of Sound and Vibration, U. Southampton, and Emeritus scientist at the Centre for Marine Research and Experimentation (formerly NATO Undersea Research Centre), Italy. He is a Fellow of the ASA.
The Waveguide Invariant 43