Abstract

A scale-independent analytic model of seismic radiation from a column of explosive is derived in terms of the blast hole radius (a), charge length, explosive velocity of detonation (VoD), and distance (r) to a monitoring station. The treatment is based on linear viscoelasticity in which the nonlinear response of rock close to the blast hole is modeled as a sufficiently low-Q material having an exponential increase in Q with distance from the source. Although limited by this assumption, the present analytic model avoids the more serious discretization problems associated with numerical models when driven by the high-frequency pressure load. Furthermore, numerical models are not useful in displaying scale independence. Exploration and mining geophysics typically require short explosive charges characterized by a length/radius of approximately 10. The model shows that for such charges ata small ra, the seismic displacement increases with the VoD; however, as the ra increases, the displacement becomes insensitive to the VoD. Field measurements of seismic-wave transmission resulting from short charges show that a plot of rise time against traveltime is approximately linear, with an intercept that traditionally is assumed to be the rise time of the explosive source itself. However, the present model shows that this assumption is incorrect and suggests that if measurements could be made very close to the blast hole, then the rise-time plot would be nonlinear and well might correspond to the region of nonlinear rock response. The extractive mining industry typically requires long explosive columns characterized by a length/radius >100, for which ra<100 typifies the near-field. The model predicts that seismic transmission in this region is dominated completely by P-Mach and S-Mach wave propagation, dependent on the VoD.

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