Marine air-gun sources can be sequence-encoded by firing their individual elements independently over a short period of time. Using near-orthogonal firing sequences, whose crosscorrelation is minimal, as encoding sequences for multiple sets of air-gun sources, enables us to exploit their orthogonality as a separation feature. We find that, by distributing air guns over depths from 5 to 30 m, firing sequences can be designed whose direct, down-going wavefield is close to orthogonal to its source-ghost wavefield. The fundamentally new aspect of this approach is that the source-ghost signal is no longer just a time-delayed, opposite-polarity version of the down-going wavefield, but due to the different air-gun depths results in a different source sequence. This enables the consideration of the ghost wavefield as a separate source. We generate a set of such firing sequences by minimizing the crosscorrelation of these wavefields and optimizing their respective autocorrelations to achieve sharp peaks. The obtained, optimized firing sequences are then used for marine seismic source encoding. By adapting a multifrequency algorithm originally developed for simultaneous source separation, we determine that the ghost-source wavefield can be separated as a separate source from the direct, down-going wavefield.

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