(10^ 



where tl'^i i^ nondecreaslng and the largest value is given by equation (9), 

 Hence, once C (t J is known, the power spectrum of the surface follows 

 directly from the operations indicated in equation (lO). The adopted 

 values of A (t J over the significant band of frequencies can be attenu- 

 ated to a given depth as outlined previously. The result will be the 

 pressure power spectrujii. The procedure for analyzing this spectrum to 

 obtain some characteristics of pressure on the bottom of the ocean will 

 be described nexto 



D. ANALYSIS OF FRESSIIRE Pa^^E'R SPECTRUM 



Writing equation (10) as A p (+) aT" = d E p C"t) and integrating 

 both sides of the equation results in 



\ k\W i^ - Ep(*>- 



00 



tp(+) can be described as the area under the power curve for a give 



range of frequencies. More explicitly, £.oi.^^ is the area under Ap (-f 1) 



from +»**» to T - CL , If it is assumed that tpC^) starts with the 



value zero at-t-D the cut-off frequency, then Epy^^q^C-t) will not differ 



appreciably f ix)m the sum of the amplitudes squared, obtained by integrating 



over the entire range of frequencies from t- O to -f- *>«> . Thus Entr\cix ( ' "^ 



is the total area under A* p C4- ^ over the significant band of frequencies. 



It should be noted that the expression Ep(xt)raay be obtained by replacing 



-+■ by its equivalent value z^ /qiT • 



12 



