velocity becomes a function of pressure and a steep-wavefront, nonlinear shock wave is developed. The shock wave travels radially outward, gradually diminishing in amplitude and entering the linear propagation regime where the wave velocity is constant. For a 1 kt underwater nuclear explosion, the transition from nonlinear to linear propagation occurs at about 10 km.

Hot gases resulting from the explosion are contained by hydrostatic pressure within a bubble, which expands rapidly. As the bubble expands, the pressure inside decreases. The momentum of the water continues the expansion of the bubble beyond the point at which the internal pressure falls below the external hydrostatic pressure, and the bubble contracts, thereby compressing the gas until its pressure is sufficient to halt the motion of the water, whereupon the cycle repeats, each time with diminished intensity. The oscillating bubble generates a series of pressure pulses, called bubble pulses, which are characteristic of deep underwater explosions. Under ideal conditions it is possible to observe numerous bubble pulse oscillations. Note, however, that long range transmission losses at low frequencies are variable and they can have a major impact on the potential of the bubble pulse as a discriminant. If the explosion is shallow, the bubble vents directly into the atmosphere, and no bubble pulse signature is observed. If the explosion is located above the surface the amount of sound energy coupled into the water is orders of magnitude less than an underwater explosion and again there is no bubble pulse. A 1 kt explosion well coupled to the sound channel (detonated, for example, at 1000 m depth) generates a sound pressure level between 300–310 dB relative to 1 µPa at 1 m (depending upon the depth) and has a bubble pulse period of 0.7 second. A modern airgun array used for seismic exploration can have a sound pressure level of 264–270 dB relative to 1 µPa at 1 m (depending upon volume and pressure of the airgun array) and no discernible bubble pulse.

A signal-to-noise ratio of about 10 dB is usually required to ensure robust detection. With a source level of 280 dB (1 kiloton [kt] explosion at depth), a background 10 Hz noise field of 80 dB (heavy shipping), and a signal integration time of only a few seconds, this signal will remain 50 dB or more above the background noise at global ranges and can be detected easily and distinguished from other sources. However, there are regions in which it may be blocked by bathymetry or attenuated by scattering that arises, for example, from upward refraction in a shoaling sound channel in Arctic waters and scattering from the sea surface and bottom.

A 1 kt explosion detonated 1 km above the sea surface has a calculated source level at the sound channel axis that is 35 dB less, comparable to the intensity of an airgun array. Its intensity at an IMS hydroacoustic sensor can easily be less than the background noise or comparable in level to earthquakes and airguns.