SECT. 5] LONG OCEAN WAVES 655 



for the peakedness of the fundamental node, provided s' <^s and H' -^H. This 

 approximation is certainly not justified for Camp Pendleton and Maui ; for 

 those two cases Q was evaluated numerically. The comparison of computed and 

 observed values indicates : (i) an order of magnitude agreement for localities 

 other than Mar del Plata ; (ii) at Camp Pendleton the inclinations over the shelf 

 and beyond the shelf are both small and their contrast is also small (0.02/0.05). 

 In addition, the relatively small depth of 800 m of the Continental borderland 

 (as compared to the deep sea) yields a relatively small ratio of HjH'. The two 

 circumstances conspire to yield a small Q ; (iii) at Maui the break in slope occurs 

 at relatively large depth {H' = 700 m), and the depth contrast is relatively 

 small," hence Q is small ; (iv) at Guadalupe Island the ratio of inclinations is 

 large, and at Acapulco very large (associated with the drop-off into the Acapulco 

 Trench). This leads to large values in ^ ; (v) at Mar del Plata the observed Q is 

 small and the computed Q is large. As an excuse, one might mention that the 

 theory presumes a dependence of depth on off-shore distance only, and no 

 variation along shore. Over the broad Argentinian shelf, the variations in the 

 two directions are of the same order. Another point is that the peaks appear 

 to be superimposed on a physically distinct monotonic spectrum which fills 

 the troughs and reduces the apparent Q (Inman et al., 1962). 



C. Off-Shore Coherence 



The center and bottom displays of Fig. 5 show the coherence (or phase- 

 stability) between the on-shore and off-shore records, and the corresponding 

 phase relation.! For very low frequencies the two records are in phase. At 

 about 12 c/ks the phase reverses, and for frequencies just above 12 c/ks the 

 instruments are out of phase. There are similar abrupt changes in relative 

 phases at 17 and 22 c/ks. The interpretation might be as follows: the lowest 

 frequencies correspond to the largest wavelengths and the nodal line is far off- 

 shore, beyond both instruments. The two records are then in phase. Increasing 

 frequencies are associated with a diminishing distance from the beach to the 

 nodal line. Presumably the nodal line "passes" the off-shore instrument at 

 12 c/ks so that for frequencies just above this value the two instruments are 

 situated at opposite sides of the nodal lines and accordingly 180° out of phase, 

 as observed. But it should be stated that an attempt to account quantitatively 

 for the successive reversals did not lead to any clear-cut results. We have 

 presented this figure as an illustration of the powerful tool provided by cross- 

 spectra in the diagnosis of features in the power spectra. 



D. Long-Shore Coherence 



At this point a theoretical problem needs to be introduced which is funda- 

 mental to our subject. So far we have discussed the total reflection of long 

 waves which are trigonometric in deep water (beyond x = A + Bm Fig. 6). The 



1 For a detailed discussion of "coherence" and "phase", we must refer to the original 

 paper. 



