Empirical Scaling Laws for Truck Bomb Explosions Based on Seismic and Acoustic Data

by Keith D. Koper,* Terry C. Wallace, Robert E. Reinke, and John A. Leverette

Abstract

We analyze seismic and acoustic data from a series of controlled truck bomb explosions to develop scaling laws and functional relations between charge size and various waveform properties. The explosions had yields of 3–12 × 10³ kg trinitrotoluene (TNT), and the receivers were placed at distances of 1–16 km, so the data mimic the data previously recorded from actual terrorist truck bombings. We examine four airblast properties (peak overpressure, impulse per unit area, pulse duration, and average shock velocity) and three seismic properties (peak displacement of P wave, low-frequency asymptote of displacement spectrum, and the corner frequency of displacement spectrum) as potential yield estimators. Impulse per unit area and pulse duration observations prove to be the most robust yield indicators; however, peak overpressure, peak displacement, and low-frequency spectral asymptote have significant utility as well. The acoustic scaling laws are more portable than the seismic scaling laws because regional differences in atmospheric structure can be well described by pressure and temperature observations, while regional differences in geologic structure are dependent on a large number of less accessible parameters. We apply the scaling laws developed here to seismic waveforms of the 1998 Nairobi bombing and find a yield of 2.0–6.0 × 10³ kg TNT. This value is consistent with but more precise than a previous estimate made via a time domain waveform inversion. Additional testing indicates that our functional relations are likely applicable to surface chemical explosions in general and not limited solely to truck bombs.

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