On triangular tomography

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.