654 MUNK [chap. 18 



topography beyond the shelf, as if there were a precipitous cHfiF at the edge of 

 the shelf. 



We have derived the formulae for the case of normal incidence on a two-step 

 topography (as shown in Fig. 6), consisting of a continental shelf of width A 

 and constant inclination s', and a continental slope of width B and inclination s. 

 The derivation is based on patching the known solution for constant slope 

 (Lamb, 1932 p. 276). Details are cumbersome and uninteresting. The result is 



where j8 depends in a complicated manner on the ratios s'js and H'jH. Thus the 

 frequency is increased in the ratio 4j8/7r over the result (1). For the case s' <^s 

 and H' <^H, we obtain 4^/77= 1.54. 



Fig. 6. Idealized bottom profile. The continental shelf extends from .^ = to x^A, with 

 depth h increasing linearly from to H'. The continental slope extends from a; = ^ to 

 x = A + B, with depth increasing linearly from H' to H. 



The computed values of /o according to (1) are given in Table I. In three 

 cases the agreement with the observed peaks is misleadingly good ; in the other 

 two cases the values differ by factors of 2 and 3, respectively. One can improve 

 the agreement by various devices. Thus the correction factor 4|8/7r helps because 

 it is relatively large (close to 2) for the two discrepant cases (Guadalupe Island 

 and Mar del Plata) where the ratio H'/H is relatively small. Furthermore, one 

 has considerable freedom in fitting the actual bottom topography into a "two 

 step" straight jacket. It does not seem profitable to pursue such refinements. 

 The only valid point is that for the station here considered an observed varia- 

 tion of /o by two orders of magnitude is consistent with the assumption that 

 these spectral peaks are the result of resonance over the continental shelf, 

 somewhat in the manner of resonance in open (though tapered) organ pipes. 



B. Sharpness of Peak 



Here the results are even more uncertain than in the case of /o. The 

 "observed" values of Q in the third line of Table I are a compromise between 

 using the spectral width Af—foQ~''- and the energy amplification Q^ as a basis 

 for estimating Q. 



The two-step topography yields as a solution 



Qo = l.QSViHIH') 



