Application of the unified equation of bubble dynamics for simulating the large-scale air-gun bubble with migration effect

How to effectively reduce the high-frequency output caused by excessively steep initial peak slope and enhance the low-frequency output generated by bubble oscillation has become present research interest in seismic source design. The most effective way to improve the low-frequency content of a seismic source is to increase its chamber volume. However, the size of air-gun bubbles generated by large-volume air-gun sources has increased by several hundred times compared to traditional high-pressure air guns, which has made the migration phenomenon of bubbles no longer negligible. The previous air-gun bubble dynamics models did not comprehensively account for the effects caused by bubble migration phenomenon. In this paper, we have developed an air-gun bubble dynamics model based on unified equation for bubble dynamics, and the newly established model demonstrates a closer alignment with experimental data compared to models based on the Gilmore and Keller equations. Based on this, the influence of the design parameters of air-gun seismic source on the bubble migration is studied. It explores the ramifications of migration on the dynamic properties of air-gun bubbles and the signatures of seismic sources. Additionally, we examine how incoming flow velocity magnitude and air-gun design parameters influence the signatures of air-gun seismic sources. Finally, we investigate the impact of both the spacing between dual guns and the horizontal movement of bubbles caused by mutual attraction on the signatures of dual-gun sources.