Directional Recording of Swell from Distant Storms - Department of ...

DIRECTIONAL RECORDING OF SWELL FROM DISTANT STORMS 525determination becomes unstable. Thus we have determined ko and ao (or alternativelylo, in) without recourse to wave theory. However, in the routine computations we consideredko as a known function off, and this reduced the number of unknowns by one(?7 (d)).t\H,,nin \/01 08 0o9 10 11 12k kiheory tFIGURE 8. Empirical determination of wave number. The example pertainsto 29 October for a frequency band centred on 46 c/ks.Perhaps the most rapid means of determining 10 and mo is as follows. The distribution ofE'(l, m,f) is merely the sum of three sinusoids in 1, m space and can in fact be writtenE'(l, m, ) =[c0+ 2 'JTn cos anwhereTncos 7n = Cn, TnJsin Rn = Qnna + 2+2(lXn + m Yn).The problem now is to find what set of angles ac,, cc2 and a3 maximize E'; the values 10, mO thatprovide these angles can be calculated afterwards.It should be noted that since the separations Xn and Yn are taken in cyclic order round thetriangle of detectors then n3 n=3Xn =EYn = ?1 1so that the sum of the three angles a is a known constantn=3 n=3E an = E n1 1Begin therefore by noting the two greatest amplitudes, say Tj and T2, and supposing thatn-3al and cc2 are zero. Evaluate E' knowing that a3-is E n Then try in turn values of al and cc2that are not zero, knowing that a3 must becc3n-3= E tJ-cc1-c2. 2Values that produce an increased E' are adopted. This ' hunting' prcocess rapidly establishesthe values of cc1 and cc2 that maximize E' and from them one calculates l0, in0.64-3