BOTTOM REFLECTION. SHALLOW-WATER TRANSMISSION 



235 



for the first mode for various types of bottoms. 

 Figure 35 shows the theoretical dependence of the 

 frequency of the first mode on the time, for these 

 same types of bottoms, and shows also the observed 

 frequencies as recorded in a particular region on the 

 low-frequency Mark II channel, whose frequency 

 response has been shown in Figures 31 and 33. Be- 

 cause of its suppression of high frequencies, the record 

 of this channel should consist principally of the con- 

 tribution of the first mode. It will be noticed that at 

 the highest frequencies the slope of the theoretical 

 frequency-time curve is nearly independent of the 

 assumed structure of the bottom, and that the ob- 

 served points show the same slope. Note that the 

 frequency corresponding to a given group velocity 

 over a uniform bottom varies inversely as the depth 

 of the water, a relation which is easily verified from 

 equation (24). This relation is fairly well confirmed 

 experimentally. 



The observed points in Figure 35 do not follow 

 any of the curves for a uniform bottom but indicate 

 rather that the velocity of sound increases with 

 depth. A rough estimate of the scale and nature' of 

 this increase can be obtained by studjang P'igures 34 

 and 35 together. Thus at higher frequencies than 

 that corresponding to fh/c equal to 4.5, the points of 

 Figure 35 scatter evenly about the curve for Ci/c 

 equal to 1.1. According to Figure 34, ior fh/c equal 

 to 4.5, 99 per cent of the wave energy in the bottom 

 is confined within a layer of thickness 0.2 times the 

 depth of the water. We may therefore say that the 

 velocity of sound in the bottom is 1.1c down to a 

 depth of the order of 20 ft. A similar readingof the two 

 figures at fh/c equal to 1.5 gives the result that some 

 sort of weighted average of the velocities over a depth 

 in the bottom of the order of half the depth of the 

 water has a value intermediate between 1.3c and 

 1.5c. These rough conclusions are confirmed by 

 the fact that the points of Figure 35 fall between 

 the dotted and dashed curves. Information ob- 

 tained from study of the ground waves regarding 

 the deeper layers of the bottom should, of course, 

 be borne in mind when studying the water waves 

 in this way. 



Measurements have been made on the maximum 



intensity of the water wave as recorded by the various 

 channels. These indicate a decrease of the recorded 

 maximum intensity with distance, which in different 

 regions varies from an inverse fourth or fifth power to 

 an inverse 2.4 power. Theoretically, if there is no 

 absorption or scattering, the energy in any normal 

 mode should vary inversely as the first power of the 

 distance, because the normal modes spread out hori- 

 zontally but not vertically. Since the duration of the 

 signal increases proportionally to the range, the peak 

 intensity of any normal mode should decrease about 

 as the inverse square of the range; the more refined 

 calculations of reference 24 show an inverse 5/3 power 

 dependence. Thus, although the experimental data 

 are scattered and hard to interpret, there appears to 

 be a discrepancy between theory and experiment. 

 One would, of course, not expect perfect agreement 

 with a theory which neglects absorption and scat- 

 tering in the bottom, especially since most of the ex- 

 periments were conducted over soft bottoms. 



At one of the stations where shots were made, 

 near the Orinoco delta, it was found that no fre- 

 quencies below about 300 c appeared in the water 

 wave, although a normal dispersion record was ob- 

 served in deeper water in the same locality. The 

 ground wave on the anomalous records was fairly 

 normal. 



A few shots were made near the Virgin Islands 

 with land between the shot and the hydrophone. 

 These showed a ground wave similar to that which 

 would have been observed in the absence of the land, 

 but the water waves were entirely absent. A related 

 observation is that blasting explosions on land gave 

 weak ground waves at a hydrophone in the sea off- 

 shore, but no water waves. 



Shots made near Solomons, Md., produced low- 

 frequency disturbances of periods from 0.1 to 0.3 sec 

 which were propagated with a low velocity, about 

 1,700 ft per sec. These disturbances have been tenta- 

 tively ascribed to the so-called Rayleigh wave, which 

 is a surface-bound' wave in the bottom whose propa- 

 gation involves shearing stresses. Such waves fall 

 outside the province of the theory of the preceding 

 Section 9.4.2, which idealizes the bottom as a fluid 

 medium. 



