Marine vibrators and emerging sources

Air-gun arrays have been the marine workhorse since the 1970s: simple, robust and well understood. Two pressures push the industry toward alternatives. Regulators limit the peak sound pressure near a survey and ask for protection zones for marine mammals, and full-waveform inversion (FWI) wants energy below 5 Hz, where an air-gun array is weak. A marine vibrator answers both by spreading its energy over a sweep several seconds long. In Figure 1.7 you give a sweep and an eight-gun array the same far-field energy, then change the sweep’s length, its band and how long it dwells at the low end, and the depth at which both are towed.

What spreading the energy buys

A marine vibrator is a submerged vibroseis: a piston or flextensional shell, driven hydraulically or electrically, that sweeps through its band for several seconds. The energy of a shot is the time integral of the squared pressure, $E = \\int p^2\\,dt$, and it sets the sound exposure level, $\\mathrm{SEL} = 10\\log\_{10}\\bigl(E/(1\\,\\mu\\mathrm{Pa}^2\\,\\mathrm{s})\\bigr)$. At a fixed $E$ the mean-square pressure of a sweep of length $T$ is $E/T$, so the peak falls by about 3 dB each time the sweep doubles. In the figure’s opening state the 8 s sweep peaks 28 dB below the air-guns at the same exposure. Duncan et al. (2017), modelling a realistic marine vibrator array against an air-gun array of similar downward energy below 100 Hz, found peak-to-peak levels 20 dB lower at 100 m from the source, narrowing to 12 dB at 5 km.

A sweep also stops at its end frequency $f\_2$. The air-guns’ sharp primary puts about a fifth of their energy above 100 Hz, where porpoises and dolphins hear best; a sweep that ends at 60 Hz puts almost nothing there (exercise 4). The exposure inside the sweep’s own band is not smaller, though: an animal that hears in that band receives the same energy, spread over seconds instead of milliseconds.

The low end is not automatic

A sweep does not deliver the band below 5 Hz just because it starts there. At the same energy, what it puts there grows with the time it spends there. A linear sweep from 2 to 100 Hz over 8 s spends 0.24 s below 5 Hz, all of it inside its 0.25 s start taper, and puts 6 dB less there than the air-guns. Whatever gives the low end more of the sweep’s time raises it. Stopping the same linear sweep at 40 Hz gives it 0.63 s below 5 Hz and a 6 dB surplus; dwelling at the low end by 6 dB per octave gives it 4.9 s and a 20 dB surplus; a deeper tow raises it too, as the next paragraph shows. Dwell has a price. The sweep races through its upper band, crossing 40 to 100 Hz in a quarter of a second at 6 dB per octave and in 17 ms at 9, so that band thins: at 6 dB per octave its level at 80 Hz falls by 7 dB. And because it spends most of its time where the ghost is weak, it needs more amplitude to carry the same energy, so its peak rises by about 9 dB. Real vibrators pay a second price the figure leaves out: at a fixed piston stroke the radiated pressure falls by 12 dB per octave toward low frequency, so a unit built for the lowest octave has to be large. BP’s purpose-built Wolfspar source recorded signal at frequencies as low as 1.6 Hz at offsets beyond 30 km (Dellinger et al., 2016).

Both sources also fight the sea surface. A source at depth $d$ is followed by its own ghost, reflected with the opposite sign, so the far field is $p(t) - p(t - 2d/c)$: a notch at $c/2d$ and, at low frequency, an amplitude that shrinks as $2\\sin(2\\pi f d/c)$. Towing deeper lifts the lows of both sources and brings the notch down, to 30 Hz at 25 m (exercise 3); at 25 m even the linear sweep puts 11 dB more below 5 Hz than the air-guns. The low band matters because FWI updates a smooth starting model by matching waveforms: at low frequency the modelled and recorded arrivals stay within half a cycle of each other, so the inversion does not cycle-skip into a wrong model.

Why they are not the default yet

• Reliability: a moving mechanical projector in seawater is harder to keep running for months than a compressed-air gun.
• Output per unit: one vibrator delivers less energy per sweep than a large air-gun array, so a survey needs several units or longer sweeps.
• Cost: the development has been spread over few surveys.
• Repair at sea: a failed unit is hard to service from the vessel.
• Track record: air-gun arrays have fifty years of field validation.

Development continues. The Marine Vibrator Joint Industry Project, sponsored by ExxonMobil, Shell and TotalEnergies since 2011, has funded three separate prototype designs. Other routes to a quieter or lower-frequency source are air-guns redesigned to release their air more slowly, which trims their high-frequency output, deeper tow, and purpose-built low-frequency sources such as Wolfspar.

References

• Dellinger, J., Ross, A., Meaux, D., Brenders, A., Gesoff, G., Etgen, J., Naranjo, J., Openshaw, G., Harper, M. (2016). Wolfspar, an “FWI-friendly” ultralow-frequency marine seismic source. SEG Technical Program Expanded Abstracts, 4891-4895.
• Duncan, A. J., Weilgart, L. S., Leaper, R., Jasny, M., Livermore, S. (2017). A modelling comparison between received sound levels produced by a marine Vibroseis array and those from an airgun array for some typical seismic survey scenarios. Marine Pollution Bulletin, 119(1), 277-288.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
• Ziolkowski, A. (1970). A method for calculating the output pressure waveform from an air gun. Geophysical Journal International, 21(2), 137-161.