Using the Sharpe Hollow Cavity model to investigate power and frequency content of explosive pressure sources

Christopher Craig Petten, Gary F. Margrave

The nature of elastic waves emitted near the source of an explosive pressure source, such as dynamite, are difficult to predict due to the non-linear behaviour of the subsurface in the presence of an explosion. This problem is often referred to as the "melting problem" in Geophysics and can cause significant limitations when designing exploration surveys around dynamite. The Sharpe Hollow Cavity Model, derived by Joseph A. Sharpe in 1949, assumes that the non-linear region of the explosion process can can be treated as a hollow spherical region containing an arbitrary pressure pulse acting on its walls. Outside of this spherical region, the subsurface behaves in a linear fashion and thus their he motion of the elastic waves propagating in this region can be predicted using the elastic wave equation. This paper explores this model and some of the theoretical predictions set forth regarding the amount of charge that is used. It was found that the power of an explosion increases in a cubic fashion with the cavity radius and the dominant frequency of the emitted waveform decreases with increased charge size. However, it was also observed that the high frequency content of the explosion is diminished with smaller charge sizes and increased burial depth.