On triangular tomography |
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Authors: | Michael Longuet-Higgins |
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Institution: | 1. Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, UK;2. Institute of Oceanographic Sciences, Wormley Great Britain |
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Abstract: | Long range acoustic soundings with triads of transducers can determine accurately the vorticity integrated over the corresponding triangular areas of the ocean. However, for a given number n of transducers not all such observations are independent. In this note we show, first, that the number N of possible independent observations is in fact N = (n ? 1) (n ? 2)/2 Secondly, we shall show such observations are in principle able to provide estimates of the vorticity field and its derivatives up to order m = (n ? 3). Thus four transducers yield an accurate estimate of the scalar vorticity ω and its horizontal gradient δ ω, while five transducers will yieldalso the Laplacian δ2ω. |
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