SECT. 5] 



LONG OCEAN WAVES 



649 



"surf beat", whereas the pronounced undulations (unusually active) of about 

 2 cycles per hour are a "shelf resonance". A drop in the mean level by about 

 1 chart inch in two hours indicates a falling tide. This sample record of back- 

 ground activity illustrates very nicely our subject matter and its frequency 

 boundaries : from swell to surf beat to shelf resonance to tide. Surf beat and 

 shelf resonance are more prominent in the instrument output than swell and 

 tides ; the filtering has succeeded in inverting a spectral canyon into a spectral 

 hump. This is a sensible procedure, no matter how sophisticated the subsequent 

 analysis is to be. 



For a further discussion, the representation in terms of power spectra ^ is as 

 convenient here as it is for ordinary ocean waves. Miles of wiggly curves in the 



Cycles per kilosecond 



Fig. 3. A typical spectrum for Camp Pendleton, California. The two curves designate the 

 spectra of surface elevation at distances of 8000 and 13,000 ft from the beach, 

 respectively, and corresponding water depths of 20 and 100 ft. 



time domain are condensed to a few simple traces in the frequency domain. 

 All evidence regarding phase (which is not reproducible) is suppressed, and 

 the resulting information concerning the distribution of energy in the fre- 

 quency domain is stable and reproducible. The distortion arising from instru- 

 mental filtering (or lack thereof) is explicit. Fig. 3 shows a typical spectrum for 

 southern Cahfornia. The trace marked "20 ft" corresponds more or less to 

 the sample record in Fig. 2. Allowance has been made for instrumental response 

 factors. The Snodgrass instrument measures pressure on the sea-bed; ac- 

 cordingly the high frequencies are suppressed relative to a record of surface 

 elevation. The spectrum in Fig. 3 has been corrected for this attenuation in 



1 See Chapter 15. Most of the spectra in this discussion were made by digital methods. 

 A cookbook of numerical recipes is contained in Munk, Snodgrass and Tucker (1959). 



