Air-gun arrays: bubbles, ghosts, tuning

Part 1 — Sources

Learning objectives

Explain bubble oscillation as the defining secondary effect of an air-gun shot
Apply the Rayleigh-Willis scaling T_b ∝ V^(1/3) to predict bubble period from gun size
Describe how mixing gun sizes in an array cancels bubbles while keeping primaries coherent
State the industry target bubble-to-primary (B/P) ratio < 0.2 for a clean far-field signature

A single air-gun fires, the gas escapes, a bubble forms in the water, expands, collapses, expands again. That oscillation emits a decaying sinusoid for several hundred milliseconds after the primary pulse — the bubble train. Left alone, the bubble train contaminates every reflection.

Rayleigh-Willis

The bubble oscillation period is governed by Rayleigh’s bubble equation. For a single gun at depth h below the surface firing at pressure P, with internal volume V:

T_b \propto \frac{P^{1/3}\,V^{1/3}}{(h + 10)^{5/6}}

Larger guns oscillate at longer periods. A 150 cu-in gun at 6 m depth has T_b ≈ 120 ms; a 40 cu-in gun at the same depth, T_b ≈ 80 ms. Those two bubbles destructively interfere in the stacked wavefield while both primaries stack coherently at t=0.

Array tuning

A modern marine source array has 18–24 guns arranged in 3 sub-arrays, with guns sized from ~20 to ~250 cu-in and deliberately spread to span a range of T_b. Industry’s QC metric is the bubble-to-primary ratio (B/P), measured as peak absolute amplitude after 50 ms vs peak amplitude within the first 50 ms. B/P < 0.2 is the target.

What depth does to the spectrum

Like dynamite (§1.2), the submerged gun has a surface ghost notch at f = V_water/(2h) = 750/h Hz. Guns at 6 m give a 125 Hz notch (above the useful band); at 15 m, a 50 Hz notch (inside the useful band). Deeper sources give better sub-5 Hz content that FWI wants, at the cost of pushing the notch into the seismic band and making source-sled handling harder.

References

Dragoset, B. (1990). Air-gun array specs: a tutorial. Geophysics, 55(11), 1426–1440.
Ziolkowski, A. (1970). A method for calculating the output pressure waveform from an air gun. Geophysical Journal International, 21(2), 137–161.
Pritchett, W. C. (1990). Acquiring Better Seismic Data. Chapman & Hall.