The Low-frequency Scaling Laws and Source Levels for Underground Explosions and Other Disturbances

A general approach is used to show that the source spectrum level for the energy radiated from a disturbance is usually proportional to (frequency)2 at low frequencies, and also that this low-frequency energy is proportional to (total energy)2 for body waves. There are differences for one- and two-dimensional propagation, and also for interface waves. The application to underwater explosions is pointed out, using theory and experimental results recently reported by the author. The main application considered is that to underground explosions, and provides the best explanation of the empirical law that seismic amplitude is proportional to charge weight. An account is given of the reason why explosions underwater have much more low-frequency energy than those underground; typically efficiency is 10 per cent compared to 0.05 per cent, making underwater explosions more suitable as sources for seismic investigations. The general method is applicable to a wide range of other mechanical disturbances, and also to electromagnetic pulses.