D. E. Weston 59 
e 
ie 
23 20 
a 2 : 
‘ES Summation 
aS formula 
5% 10 
Energy Flux Spectrum Level (dB wert. | 
2 4 6 810 2 4 6 8100 2 4 6 81000 2 4 6 810000 
Frequency (C/s) 
Fig. 3.5. Theoretical source spectrum for 20-fathom, 1-lb charge. 
It may be mentioned that Weston [10] shows some measure of agreement 
between theory and experiment for depth dependence. This dependence is mainly 
due to the changing bubble-pulse frequency and is only important below, say, 
140 cps for 1-lb charges where, however, it can be very large. 
The position has been reached where the acoustic spectra of underwater 
explosions are generally well understood, though many small points remain to 
be explained. It is still usually bettertouse experimental rather than theoretical 
figures for differences and for source levels. 
3.6. COMPARISON WITH UNDERGROUND EXPLOSIONS 
It is interesting to compare explosions underwater and underground, though 
the latter are much less well understood. Their mechanisms have been broadly 
described as a spreading explosive pulse which causes shattering or plastic 
flow of the solid material out to a critical radius, beyond which there is normal 
elastic wave propagation. The most notable thing about the transmitted signal is 
that seismic amplitude is experimentally found to be directly proportional to 
charge weight (O'Brien [6], Weston [9]). This is of course the same as the low- 
frequency W? energy law of section 3.3, which applies because all the high- 
frequency energy is attenuated in passing through the ground. It should be noted 
that this law with low-frequency energy proportional to the square of the total 
energy can work only if the low-frequency energyis a small fraction of the total. 
Efficiency as a seismic source improves as the size of the charge increases. 
There are very few measurements on underground-source spectrum levels, 
though the work of McDonal et al. [5] provides experimental verification of the 
f?law. The source spectrum may, however, be calculated from the model as- 
sumed [9]; Fig. 3.6 shows a much-simplified comparison of the spectra in the 
two media. The total energy radiated does not change much whether the explo- 
