Graph Spectrum Based Seismic Survey Design

Randomized sampling techniques have become increasingly useful in seismic data acquisition and processing, allowing practitioners to achieve dense wavefield reconstruction from a substantially reduced number of field samples. However, typical designs studied in the low-rank matrix recovery and compressive sensing literature are difficult to achieve by standard industry hardware. For practical purposes, a compromise between stochastic and realizable samples is needed. In this paper, we propose a deterministic and computationally cheap tool to alleviate randomized acquisition design, prior to survey deployment and large-scale optimization. We consider universal and deterministic matrix completion results in the context of seismology, where a bipartite graph representation of the source-receiver layout allows for the respective spectral gap to act as a quality metric for wavefield reconstruction. We provide realistic survey design scenarios to demonstrate the utility of the spectral gap for successful seismic data acquisition via low-rank and sparse signal recovery.