Beating the aliasing limit with aperiodic monotile arrays

TL;DR

This paper demonstrates that aperiodic monotile arrays, specifically the Hat tiling family, can surpass the traditional aliasing limit in wave sampling, offering a new approach for seismic and wavefield applications.

Contribution

It introduces MAS arrays based on aperiodic monotile tilings as a novel method to overcome the WNS aliasing limit in wave sampling, outperforming regular and other aperiodic arrays.

Findings

MAS arrays surpass the WNS aliasing limit in wave sampling.

MAS arrays outperform regular and other aperiodic arrays in beamforming scenarios.

MAS arrays are robust to station-position noise.

Abstract

Finding optimal wave sampling methods has far-reaching implications in wave physics, such as seismology, acoustics, and telecommunications. A key challenge is surpassing the Whittaker-Nyquist-Shannon (WNS) aliasing limit, establishing a frequency below which the signal cannot be faithfully reconstructed. However, the WNS limit applies only to periodic sampling, opening the door to bypass aliasing by aperiodic sampling. In this work, we investigate the efficiency of a recently discovered family of aperiodic monotile tilings, the Hat family, in overcoming the aliasing limit when spatially sampling a wavefield. By analyzing their spectral properties, we show that monotile aperiodic seismic (MAS) arrays, based on a subset of the Hat tiling family, are efficient in surpassing the WNS sampling limit. Our investigation leads us to propose MAS arrays as a novel design principle for seismic arrays. We show that MAS arrays can outperform regular and other aperiodic arrays in realistic beamforming scenarios using single and distributed sources, including station-position noise. While current seismic arrays optimize beamforming or imaging applications using spiral or regular arrays, MAS arrays can accommodate both, as they share properties with both periodic and aperiodic arrays. More generally, our work suggests that aperiodic monotiles can be an efficient design principle in various fields requiring wave sampling.