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

Abstract

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