The energy source evaluated in this paper is the pneumatic air gun now being used by Texas Instruments, Inc. of Dallas, Tex. in their marine seismic operations. To the author's knowledge, the only efficiency that has been previously determined on the gun was an acoustical effectiveness, based on an isothermal system. The present analysis will show that the system is, not isothermal and that the efficiency of the gun decreases proportionately to the gun's operating depth.
The principle of operation of the pneumatic source is that a volume of high pressure air (2,000 psia) is suddenly released underwater to form an air bubble. The resulting air bubble oscillates (expands and contracts) until all of its energy is dissipated; part of the energy is radiated acoustically and the rest is dissipated viscously.
In examining the sequence of events in greater detail, an acoustic pulse is emitted when the volume of high pressure air is suddenly released. The amplitude and rise time of this acoustic pulse depend primarily on the air gun chamber pressure (Pc) and volume (Vc) and on the local hydrostatic pressure. A portion of the energy is liberated in this first pulse and the rest resides as potential energy of the bubble to do work on the surrounding water. The bubble then starts to contract due to this pressure deficit, and its inward motion is checked due to the compressibility of the air bubble. Hence, a damped oscillatory system is set up by inertia of the water and elastic properties of the air and water, with damping being provided by viscous effects. The number of oscillations the bubble undergoes, depends on the initial conditions of the bubble (Pc and Vc), the depth at which the gun is fired, and the damping properties of the surrounding water.
The efficiency of the energy source can be described as
(Equation available in full paper)
To determine each of these energy terms, the following analysis will be made, using the principles from the first law of thermodynamics.
(Equation available in full paper)
