87 



X = (A;^, ky^ a, a) 

 for the single wave method, and: 



P {X;Xn,yn,tm) = Oi COS (fc^^j^n + ky^il/n - LJitm +Ofi) 



+ a2 COS {k:r^2Xn + ky^2yn - '^2'tm + «2 j 



X = (fci,!, Kyj, Qi, fcx,2? fi^3/,25 0^2) ^J^l: O2) 



^^n — Y ^i;,n + S," 



for the two wave method. The frequencies are determined from the Hnear dispersion 

 relation: 



Un = \/gkn tanh knh + knlJn (5.21) 



where C/„ is defined by Eq. 5.17 This optimization results in a linear estimate for the 

 water surface that fits the measured records most closely in the segment considered. 

 This procedure has been performed on a segment of the records large enough to 

 resolve the directional structure of the wave field, usually a complete wave from crest 

 to following crest, or trough to following trough. The final step in computing the 

 initial estimates for the final window-by-window optimization is to compute a full 

 order global solution to this larger segment of the record. The initial parameters 

 for this full order global optimization are provided by the computed linear fit to the 

 water surface records, with the amplitudes adjusted for the potential function: 



A„ = ^ (5.22) 



The higher order Fourier amplitudes are all initially set to zero. 



Using these linear wave theory estimates as the first guess, the full order optimiza- 

 tion, (Eq. 5.6), is computed to determine the best full order fit to a global segment of 

 the record. The parameters of the potential function computed by this optimization 

 are then used as the initial estimate for the final optimization in each defined small 

 window in time. 



