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The oscillatory bubble pulses generated by airguns in seawater are known to produce artefacts in seismic images. Although such artefacts are suppressible by employing larger airgun arrays in acquisition, small airgun arrays are used more often now to minimize the environmental impacts, thus raising the need for further suppressing bubble pulses at data processing stage. For a deep marine reflection dataset recently acquired by a small airgun array, we compare the effectiveness of three popular debubbling methods that estimate the far‐field source signature based on theoretical simulation and wavelets extracted from seafloor reflections and direct arrivals, respectively. In this case, due to the lack of near‐field measurements for calibration, the debubbling via simulation underperforms the two wavelet extraction methods. Overlapping events in the noisy response of seafloor sediments lead to the failure of the wavelet extraction from primary seafloor reflections. The estimated source signature based on direct arrivals achieves the best bubble suppression result, indicating the importance of signal‐to‐noise ratio and a low level of directionality of the small airgun array source.