Improved seismic survey design by maximizing the spectral gap with global optimization

Random subsampling is increasingly being used in the acquisition of seismic data to shorten the acquisition time and to reduce costs. However, the design of optimal acquisition geometries is still an ongoing area of research. Matrix completion (MC) is a computationally efficient method to reconstruct fully sampled wavefields from sparsely sampled seismic data. In MC theory, the spectral gap (SG), which is a measure of the connectedness of the graph in expander graph theory, has been used to predict, and to some degree quantify, the quality of wavefield reconstruction, given a specific subsampling scheme (acquisition mask). Building on these insights, we propose an optimization scheme, based on simulated annealing, which finds subsampling masks with large SGs that improve the quality of wavefield reconstruction with MC. The experimental results show that the proposed method successfully increases the SG of the subsampling mask starting from randomly initialized masks. Increasing the SG leads to improved connectivity between the sources and receivers and therefore of the wavefield reconstruction. Numerical experiments confirm a direct relationship between increased SG and improved reconstruction quality. This confirms the value SG analysis brings to the design of seismic surveys without the need to carry out expensive wavefield reconstructions to optimize the acquisition design.