We designed a system to enable the signature of an air gun array to be calculated at any point in the water from a number of simultaneous independent measurements of the near-held pressure held [subject of a patent application]. The number of these measurements must not be less than the number of guns in the array. The underlying assumption in our method is that the oscillating bubble produced by an air gun is small compared with the wavelengths of seismic interest. Each bubble thus behaves as a point source, both in the generation of seismic waves and in its response to incident seismic radiation produced by other nearby bubbles. It follows that the intcraction effects between the bubbles may be described in terms of spherical waves. The array of interacting guns is equivalent to a notional array of noninteracting guns whose combined seismic radiation is identical. The seismic signatures of the equivalent independent elements of this notional array can be determined from the near-held measurements. The seismic radiation pattern emitted by the whole array can be computed from these signatures by linear superposition, with a spherical correction applied. The method is tested by comparing far-field signatures computed in this way with field measurements made in deep water. The computed and measured signatures match each other very closely. By comparison, signatures computed neglecting this interaction are a poor match to the measurements.