Doppler Sonar and Surface Waves: Range and Resolution

Abstract

The performance limitations of an acoustic Doppler sonar system are explored and compared with anticipated requirements for the measurement of surface wave directional/frequency spectra. To obtain measurements to a range D requires a delay ?t between pings long enough for sound to propagate out to D and back: ?t(c/2) ≥ D. This defines a Nyquist frequency, ?N (radiances s?1). Linear dispersion relates this to a ?matched wavenumber,? kN = ?N2/ g. Waves travelling obliquely and harmonics of longer waves appearing at ?N all have smaller wavenumbers, k ≤ kN; thus, kN; defines a maximum wavenumber requirement, or (equivalently) a matched range resolution, ?R. From idealized surface wave spectra, the velocity resolution ?V required to measure spectra out to (?N, kN) can be estimated. For a given sonar ?tone,? the error-product E = ?R?V is a constant, so velocity resolution and range resolution must be traded off. The error product decreases with increasing acoustic frequency f0 and number of tones. Higher frequency sound is also attenuated more rapidly, limiting the maximum range attainable. A practical approach is to define a desired range D, find the highest frequency which can be detected to that range, and then determine the number of tones required to achieve the target velocity and range resolutions. If too many tones are needed, a slight retreat in range resolution yields a relaxation in the velocity requirement as well (because of the steep spectral slope of surface wave spectra). Electronic design and performance is neglected here, on the presumption that the physical limits discussed will eventually be the important ones.