53 



depth is uj'^hjg ^ 2.5, which is considered to be deep water. In deep water, the 

 action of the waves decays very quickly with depth, so that little energy is expected 

 to remain at half the water depth, the depth at which the pressure measurements 

 were taken. 



The third plot in figure 3.17 is the spectrum of the subsurface pressure record. 

 The solid line was computed from the measured record, and the dashed line was 

 computed from the water surface record, using the linear pressure response factor: 



/ N / ,COShfc(/l + ^b) , ^ 



a,{u) = a,H TTTTT^ 3.18 



cosh(A;n) 



where ap[uj) and ar,{ui) are the magnitude of the pressure and water surface amplitude 

 spectra at a given frequency, and the wave number, k, is computed from the linear 

 dispersion relationship: 



{u - kUf = gktanhikh) (3.19) 



The predicted spectrum matches the measured spectrum very closely. This indicates 

 that the loss of high frequency information in the subsurface pressure record is the 

 result of the predicted decay with depth of the energy at the higher frequencies, rather 

 than a result of the frequency response of the pressure gauge used. 



The final plot in figure 3.17 is the spectrum of the water surface record. The 

 solid line was computed from the measured water surface, and the dashed line was 

 computed from the pressure record, also using the linear pressure response factor. The 

 predicted spectrum of the water surface matches the measured spectrum well near 

 the peak frequency, but strongly over-predicts the high frequencies. If this method 

 were used to predict the water surface, a somewhat arbitrary high frequency cut off 

 would have to be established. 



An examination of the top plot in figure 3.17 reveals what appears to be two 

 dominant free modes in the water surface. There is a large low frequency mode 

 with a period of approximately 2s, and a higher frequency mode with a period of 

 approximately Is. If the LFI method were applied to the water surface record (Sobey 

 1992), the moving widow could capture a different dominant mode in each window. 

 Unfortunately, the higher frequency mode has decayed with depth too much to be 



