THE SCALING OF AIRGUN ARRAYS,INCLUDING DEPTH DEPENDENCE AND INTERACTIONS*

The article provides a theoretical basis for the extension of the method of scaling law deconvolution to three dimensions using airgun arrays as a sound source. Earlier papers by the author required the dimensions of the scaled sources to be different while the depths and firing pressures were maintained the same in order to preserve the same dynamics of the scaled sources at scaled time. However, this forces the source ghost to be considered as part of the impulse response of the earth rather than as part of the downgoing source wave. And, in fact, the dynamics of the scaled sources are not the same at the same depth because the ghost reflection modulates the behaviour of the oscillating bubbles generated by the airguns, and this modulation does not scale. To force the sources to scale properly, including the ghost interaction, the larger source must be put at greater depth, where hydrostatic pressure is greater, and the initial firing pressure must be adjusted accordingly. Thus, the depth, initial firing pressure and gun volume are all variables. The interaction among guns in scaled airgun arrays also scales exactly if the geometry of an array and the depth of its deployment are scaled by the same factor.