A comparison of Heelan and exact solutions for seismic radiation from a short cylindrical charge

A numerical comparison is made between the Heelan approximation and an exact (full-field) solution for the radiation of seismic waves at a distance r, produced by a short cylindrical charge in a dry borehole of radius a. The explosive source model is based on direct pressure measurements within the blast hole, and its spectral output classified by a mean frequency ωA. To generalize comparisons, this source model is incorporated within a scale-independent treatment of the Heelan and full-field solutions. If α is the material P-wave velocity, then a mean dimensionless source frequency may be defined by ΩA=aωA/α. For sufficiently large r/a, the Heelan solution is a valid far-field approximation only, provided ΩA<0.1. However, for the present radiation model, the far-field condition is given by ΩAr/a5 (approximately), which implies that the Heelan solution is never valid if r/a<50, irrespective of ΩA. If ΩA0.1, the Heelan solution significantly overestimates the true seismic motion, irrespective of r/a.