Sensor importance-based optimal seismic acquisition design for surface waves

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Surface wave methods aim to monitor the shallow subsurface non-invasively. Traditional multichannel surface wave acquisitions adopt evenly spaced receivers for convenience and simplicity. However, seismic acquisitions are often performed with coarse sampling due to financial constraints and practical issues with physical access. Compressive sensing (CS) has been extensively studied for industrial-scale seismic explorations, predominantly utilizing random undersampling of tens of thousands of receivers. These undersampling methods do not answer the critical question of optimality when small-scale, shallow seismic surface wave acquisition only allows tens of receivers and a few source locations. We propose an optimal seismic acquisition design (OSAD) framework, where the importance of each receiver is evaluated in a constrained sparse inversion framework for more accurate data reconstruction. Instead of randomized sampling, OSAD exploits the physical information available in previously acquired or simulated synthetic data. The sparsity of the acquisition geometry and of the seismic data in a transform domain is explored by nested convex optimizations for alternating directions by solving each sub-problem to find a solution to an overarching minimization objective function. We apply the OSAD framework to synthetic and field datasets. We focus on deriving optimal receiver geometry for seismic acquisition with a single source. The derived geometry automatically honors wave physics where high- and low-frequency data are prevalent for near- and far-offsets, respectively. We explicitly demonstrate the optimality of the acquisition by comparing the data reconstruction error resulting from OSAD with two existing random undersampling methods adapted to surface wave acquisition.