Ground vibrations produced by surface and near-surface explosions
Abstract Measurements of seismic signatures produced by airborne, near-surface detonations of explosive charges over a variety of ground types show two distinct ground vibration arrivals. In all cases, the earlier arrival (precursor), has a time of arrival consistent with a predominantly underground path and coupling of blast sound to the ground close to the source and is always much smaller than the later vibration, the time of arrival of which is consistent with coupling from the air blast arrival at the receiver. The ratio of the seismic particle velocity to the acoustic pressure at the surface for the air-coupled seismic wave is constant with respect to distance and maximum pressure at a given location, but varies from site to site, with values usually between 1 and 13 μm s −1  Pa −1 . For the precursor seismic wave, a coupling coefficient of 0.16 μm s −1  Pa −1 was measured. A numerical code enabling calculations of the fields due to an impulsive source above a layered poroelastic ground is described. Predictions of the air pressure spectrum above ground and the vertical and radial components of solid particle velocity near the ground surface are found to compare tolerably well with the measured spectra and waveforms of acoustic and seismic pulses at about 100 m range in seismically-hard and -soft soils and with a snow cover present. The predicted seismic responses in ‘soft’ soil confirm that the existence of a near-surface S-wave speed less than that in air is responsible for the observed ‘ringing’, i.e. a long low-frequency wavetrain associated with coupling to the dispersive Rayleigh wave. The predicted seismic pulses in the presence of the (shallow) snow cover explain the observed phenomenon whereby a high frequency ground vibration is modulated by a lower frequency layer resonance. An empirical equation relating ground vibration from explosions to distance predicts that the commonly-used vibrational damage peak velocity criterion of 12 or 25 mm s −1 will be exceeded when the peak positive pressure exceeds 480 Pa (147.6 dB) or 1 kPa (154.0 dB), respectively. Either of these levels is much higher than the current U.S. Army overpressure damage criterion of 159 Pa (138 dB). Thus in most situations damage from blast overpressure will occur long before damaging levels of ground vibration are reached, so it is likely that civilian perceptions of vibration are produced by coupling from the airblast.
Empirical Scaling Laws for Truck Bomb Explosions Based on Seismic and Acoustic Data
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.
Reflection of impulses as a method of determining acoustic impedance
An impulse technique has been developed which allows investigation of the reflection of acoustic transients at different angles from an impedance boundary. From measurements of the direct and reflected impulses, the complex surface impedance has been calculated from the ratio of the corresponding Fourier components. The surfaces were modeled as a locally reacting boundary between homogeneous media; this representation was found to be adequate for grassland and a carpet layer but unsatisfactory for a thick fiberglass layer. There was no need to include a ground wave term when reconstituting pulse shapes at different angles over grass or carpet for the range of frequencies and angles investigated in this paper.