Focal beam analysis has built a bridge between the acquisition parameters on the surface and the image quality of underground targets. However, as a practical matter, it is still difficult to answer how to choose a proper acquisition geometry according to the complexity of medium, especially considering the contradictory effects of multiple reflections on spatial resolution as they can be considered to be either potential signal or additional noise, depending on the envisioned imaging technology. We introduce an order-controlled, closed-loop focal beam method in which the migration operator and the resolution function can be analysed in the process of the closed-loop migration with full control over the order of the surface and internal multiples considered. This method highlights the effects of primary and different-order multiple wavefields on the imaging resolution for different acquisition geometries and various overburden strata. We apply the method to analyse the predicted resolution of seismic acquisition geometries considering multiples as either noise or signal. Results show, in the acquisition geometry design, that when the primaries cannot provide a complete spatial illumination for the subsurface target, e.g. because of the limited-aperture acquisition geometries or the complicated overburden, we should use the closed-loop focal beam analysis to assess the contradictory effects of multiples as both signal and noise, in which the maximum order of multiples ought to be chosen according to the core aim of the acquisition analysis. We can apply the second-order closed-loop focal beam analysis to quantify the effects of acquisition geometries on multiple-wave suppression and can also perform the high-order closed-loop focal beam analysis to quantify the effects of acquisition geometries on high-resolution imaging (migration). This method can also be used to choose the optimal order of multiples in the closed-loop migration.
- Numerical study