The study of far-field pressure wavelet of air-gun bubble is the basic research of air-gun sources. In this paper, a boundary element bubble model is established to simulate the dynamics of bubble, and an energy equivalent method is put forward to solve the bottleneck of bubble jet. In our simplified model, the bubble model takes into consideration the thermodynamic factors such as heat transfer and gas release, and the numerical results agree with the data of Nucleus software well. Based on the established model, the influence of heat transfer coefficient, air-gun firing time, and specific heat at constant volume on the pressure wavelet are studied. Finally, the three-dimensional bubble merging numerical method is put forward, which is an expansion of the axisymmetric model. Thus, the preliminary study of coherent air-gun is conducted, especially the influence of the space between two bubbles on the wavelet. This paper provides a reference for the research of air-gun.