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

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 ‫ן‬ 10 3 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 ‫ן‬ 10 3 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.

Partitioning of Seismoacoustic Energy and Estimation of Yield and Height-of-Burst/Depth-of-Burial for Near-Surface Explosions

“…Note that these first-arriving P-wave velocity records are very simple and remarkably similar across the recording network in both directions. The amplitudes vary slightly less quickly than 1=r 2 as expected from previously reported studies (e.g., Flynn and Stump, 1988;Reamer and Stump, 1992;Koper et al, 2002), as the scaled amplitudes in Figure 5 increase with range.…”

“…This measurement takes the PPV in the seismogram in the time window between the first P wave and the air-blast arrival (∼330 m=s) and thus impacted by the waveform variability seen in Figure 3. We found that this variability made the low-frequency spectral measurement of Koper et al (2002) highly path dependent (up to a factor of 10) and an undesirable candidate for a transportable estimator of source properties. suggests that the amplitude of the first P-wave arrival is less affected by the path-dependent propagation as shown by Figure 3.…”

“…They find b, the scaled-distance exponent, to be around 1.6 with little difference when square-root-or cube-root-scaled distance is employed. Koper et al (2002) developed empirical scaling laws for seismic and air-blast amplitudes for surface explosions to estimate yield. They used data from the Dipole Might (DM) series of explosions at White Sands Missile Range that was designed to emulate truck bomb explosions (emplacement just above the ground surface, HOB ∼ 1:5 m and W 3000-12;000 kg TNT equivalent).…”

Ground vibrations produced by surface and near-surface explosions

“…Birds have sometimes been observed to respond to these precursor seismic waves a few seconds before the arrival of a loud sonic boom [21]. Precursor seismic waves have also been observed in short range measurements using blank pistol shots as the acoustic source [22], and in long range measurements using large explosive charges [15,16,23,24].…”

Development of a matched filter detector for acoustic signals at local distances from small explosions

“…Equation (1) has the nice property of producing an impulse of unit amplitude. Other blast wave characterizations will be used along with scaling curves for both period and amplitude (e.g., Koper et al, 2002) as work progresses. Equation (1) contains three parameters that are unknown in practice and must be estimated through some means ðs 0 ; f c ; AÞ where we note that A is not in Eq.…”