On the theory of air‐gun bubble interactions
Calculation of the seismic signatures of marine air‐gun arrays often requires that the interactions among the bubbles from air guns be taken into account. The standard method of doing this is to use the Giles‐Johnston approximation in which a time‐dependent effective ambient pressure is calculated for each bubble as the sum of the true ambient pressure and the local pressure signals of all the other bubbles in the array. These effects of interaction have a relative importance in the dynamics proportional to (R/D), where R and D are the typical bubble radius and interbubble separation, respectively. To ensure that current methods of calculating signatures are accurate, it is necessary to know how good this approximation is. This paper shows that there are no interaction terms in the full dynamical equations proportional to [Formula: see text] or [Formula: see text], and that the errors of the Giles‐Johnston approximation are only of order [Formula: see text]. The Giles‐Johnston approximation is therefore justified even for fairly accurate signature calculations for noncoalescing bubbles. The analysis here also shows how to incorporate bubble motions and deformations into the dynamical equations, so that the errors can be reduced to order [Formula: see text] if desired.