Numerical study on attenuation of bubble pulse through tuning the air-gun array with the particle swarm optimization method

•A numerical method for improving the quality of the signal generated by an air-gun array is presented.•Particle swarm optimization is used in conjunction with the theory of the oscillating spherical bubble.•Two sets of objective functions were built to screen the array.•Four typical arrays were investigated, including planar array, spatial array, irregular array and delayed array.•The far-field signal can be largely improved just through tuning the air gun array. A numerical method for improving the quality of the far-field signal generated by a marine seismic air-gun array is presented, in which particle swarm optimization is used in conjunction with the theory of the oscillating spherical bubble to tune the array. Two sets of objective functions, including the primary-to-bubble ratio and the variance of the normalized amplitude spectrum, are built to screen the array. With this method, attempts are made to improve the far-field signals generated by four typical arrays, including the planar array, spatial array, irregular array and delayed array. It is concluded that the far-field signal can be largely improved just through the simple adjustment of the chamber volume, the firing depth, the horizontal location or the firing time of each individual gun in the array. We believe that this method will be useful in the air-gun array design and helpful to find a desirable array from a population of air-gun array distributions for a brief time.