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Marine Airgun Array Bubble Pulse Calculator engineering
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Marine Airgun Array Bubble Pulse Calculator

Marine geophysics & seismic reflection exploration: Calculate airgun bubble oscillation period ($T_b$), peak acoustic source signature ($P_{peak}$), primary-to-bubble ratio (PBR), and ghost notch interference frequencies.

Airgun Chamber & Tow Geometry

Acoustic Signature & Ghost Notch Metrics

Bubble Period $T_b$
--
ms (Rayleigh-Willis period)
Peak Output Pressure $P_{peak}$
--
bar-m (@ 1 m broadside)
Primary-to-Bubble Ratio (PBR)
--
ratio ($P_{primary} / P_{bubble}$)
1st Source Ghost Notch $f_{notch1}$
--
Hz ($c / 2z_{gun}$)
Equivalent Source Level $SL$
--
dB re 1 µPa @ 1 m (peak-peak)
Total Array Volume
--
$\text{in}^3$ (liters)

Airgun Far-Field Acoustic Signature Waveform

Time $t$ (milliseconds) Acoustic Pressure Primary Pulse Ghost Pulse Bubble Pulse
Rapid compressed air release fires a sharp primary spike. The sea-surface reflection creates an inverted ghost pulse, followed by oscillatory bubble pulses at period $T_b$.

Rayleigh-Willis Formula & Surface Ghost Notches

When an airgun fires, the compressed air bubble expands against hydrostatic pressure, overshooting equilibrium, and periodically contracts. The oscillation period obeys the Rayleigh-Willis equation:

$$T_b = K_w \frac{P_{\text{ch}}^{1/3} \, V_{\text{ch}}^{1/3}}{(P_{\text{amb}} + \rho g z_{\text{gun}})^{5/6}}$$ $$f_{\text{notch}} = \frac{n \, c}{2 z_{\text{gun}}} \quad (n = 1, 2, 3 \dots)$$

Destructive interference between the downward direct wave and the upward wave reflected from the sea surface ($R_{\text{surf}} \approx -1$) introduces severe spectral notches at $f_{\text{notch}}$. Tuning airgun cluster volumes cancels out secondary bubble pulses, yielding high Primary-to-Bubble Ratios ($PBR > 10$).

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