P'Ct-j) = w(j)p(tj) (12)' 



in which P(tj) is the measured pressure, and w(j) is a weighting factor. A 

 characteristic of these tapers is that they are unity at the midpoint of the 

 time series and decrease to a lesser value near the two ends. In the present 

 analysis, it was determined through a number of test calculations that although 

 the effect of tapering at an individual frequency could be substantial, the 

 overall effect on Fi^ was quite small, generally less than 4 percent. Thus, no 

 taper was used in the analysis. 



The depth of water. Ad, overlying the pressure sensors is obtained from 

 aj (0) and a2(0) as 



Ad = -— [a^CO) + 82(0)] (13) 



in which y is the specific weight of seawater . The total water depth, d, 

 is the sum of Ad and the distance, Sq, of the pressure sensors above the 

 bottom (0.3 meter). 



Each FFT pressure coefficient is transformed to a water surface displace- 

 ment coefficient by the following linear wave theory relationship: 



[a„(n), bTi(n)J = :^^j-y [sp (n) , bp(n)] (14) 



in which K (n) is 



YKp 



cosh k (S ) 



Kp(n) = ■ " / (15) 



P cosh k d 



In equation (15), k^ is the wave number associated with the angular frequency, 

 Ojj, as obtained from the linear wave theory dispersion relationship 



2 



= gk^ tanh k^^d (16) 



One disadvantage of measuring waves with near-bottom pressure sensors is 

 evident by exam_ining equations (14) and (15) . For higher frequencies (shorter 

 wave periods) Kp is very small, resulting in very small pressure fluctuations 

 near the sea floor for the higher frequency waves. Thus, to avoid contaminating 

 the calculated water surface displacement, n, it is usually necessary to apply 

 a high-frequency cutoff above which the pressure contributions are discarded. 

 The proper selection of this high-frequency cutoff depends on the signal-to- 

 noise characteristics of the pressure sensor and signal conditioning system. 

 For the present analysis, the high-frequency cutoff was established at a wave 

 period of 3.1 seconds. For a nominal 6-meter water depth and a 0.3-meter height 

 of the pressure sensor above the bottom, the pressure signal is attenuated to 

 approximately 16 percent of its surface value. In the survey area, where rea- 

 sonably long Pacific swells occur, neglecting wave energy for periods shorter 

 than approximately 3 seconds appears justified. 



30 



