Airguns discharging in the neighbourhood of each other modulate the external pressure field seen by the other guns. This means that simple linear superposition of airgun signatures recorded or modelled for only one gun will not work – each of the signatures as its bubble oscillates, self-adjusts to the modulated external pressure field caused by other guns in its vicinity. The effect is called airgun interaction and its effects are clearly visible in signatures when guns are closer than around 4 metres. The effect was first described by Ziolkowski and collaborators. For modern arrays, where guns are deployed much closer than this, interaction effects become dominant in determining the overall signature of the array. The most obvious desirable effect of airgun interaction is to suppress the bubble relative to the primary, enhancing the primary to bubble ratio of the overall signature. A somewhat less desirable effect when guns are deployed too close is suppression of the primary itself as a particular gun has to work against the locally increased external pressure due to other very close guns. This was first described by Vaage and collaborators. Cluster design is therefore a careful trade-off between primary suppression and bubble suppression. For most modern clusters, this corresponds to separation distances of 0.8 – 1.0m and occasionally for small guns, a little smaller.
(Note that there is another form of interaction which acts over a rather longer range. This is called energy interaction and was first described by Laws, Hatton and Haartsen in 1988.)
A notional source is a computational device. The notional source is an imaginary source which can be linearly superposed because it incorporates all the interaction effects, ie the modulations of the external pressure field, internally not externally. It was an invention of Ziolkowski, Parkes, Hatton and Haugland in 1982. They are described in detail in Parkes and Hatton (1986), “The Marine Seismic Source”. In essence, they can be linearly superposed because they are constructed to produce the same external pressure field of the array against a constant external pressure field.
This simple computational device has proven enormously successful in modelling airgun signatures. An approximation to a notional source can be obtained in practice by taking a near-field measurement of a gun sufficiently close that the measurement is dominated by that gun. In practice, this is best achieved from a hydrophone above and behind the airgun so the rising oscillating bubble stays close to the near-field hydrophone for as long as possible. Note that even when there is a single gun firing, the near-field hydrophone measurement is still an approximation (although a very good one) for a notional source because of the interacting effects of the ghost.
Laws in 1988 showed that the notional sources can also be used to provide a fast and accurate measure of the acoustic energy budget of an interacting airgun array.
Because notional sources give the exact pressure field when linearly superposed, they can be used for a variety of purposes with suitable delays (including of course the notional sources of the ghosts). The most common are:-
In Gundalf, the notional sources can be requested in a text format whenever an array is modelled. They are a natural output of any proper airgun modelling program. The individual signatures (one for each gun) can be extracted in order to be used as described above. The format for these is given in a separate help page.