Air-gun bubble-ghost interactions

The signals from air guns are reflected from the sea surface, and these reflections (termed the "ghost") interact with the air-gun bubbles, affecting the behavior of the bubble and the emitted signal. In current air-gun modeling, this interaction is either neglected, or it is accounted for using a simplistic approach involving the assumption of spherical symmetry. I have developed a 2D axisymmetric finite-volume model of an air-gun bubble, in which the effects of the sea surface were included through the use of a novel artificial boundary condition, which transmits the ghost wave into a computational domain, where it interacts with the bubble. The interaction between the bubble and the ghost wave is then treated axisymmetrically. The ghost reduces the damping and the period of the bubble. Simulations determine that at the bubble surface, the ghost wave is transmitted into the bubble and reflected back into the water. The bubble focuses the ghost wave on the bubble center, where it is reflected. This process is repeated for a few oscillations, as the energy of the ghost wave within the bubble is transmitted into the water through a series of pulses. The effect of this interaction is that near-field signatures contain components at frequencies between 400 and 600 Hz shortly after the impact of the ghost wave. I present near-field measurements that show this. The interaction between air guns in an array takes the same form as this bubble-ghost interaction, but with greater magnitude, because the separation of neighboring guns is less than the depth at which they are towed. Including this theory of interaction in air-gun modeling will improve the accuracy of modeled results.