133 



for the single wave method, and: 



f^'' {X; Xn^Vn, tm) = «! COS (/e^^ja^n + ky^Vn - ^l^m + Ql ) 



+ a2 COS {k^^2Xn + ky^2yn " ^itm + Q2) 



X = (n^x,!, ^t/,1? <^1: ^x,2? %,27 <^2: ^^l? ^2) 



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



relation: 



Wn = \/gKntanh.Knh + A'„f/„ (6.20) 



where [/„ is defined by Eq. 6.16 This optimization results in a linear estimate for 

 the dynamic pressure that fits the measured records most closely in the segment 

 considered. 



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 large 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„ cosh Knh 



pLOn cosh hn{h + Zp) 



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



Water Surface The location of the water surface at M nodes in the center of the 

 array throughout the segment is estimated from the linear pressure response function 

 with stretching (Nielsen 1989): 



_ Pd, (tm) cosh (k{h + Pd{tm)/pg)) . 



pg cosh k{h + Zp) 



where k is the mean of the two wave numbers, Zp is the elevation of the pressure 

 array, and rjm is the elevation of the water surface node at the center of the array at 

 tm- Pd{tm) is computed from Eq. 6.8 or Eq. 6.9. 



