Aperiodic Seismic Arrays
The recent discovery of a family of aperiodic monotiles has profoundly impacted the mathematical community, capturing significant attention from specialized and non-specialized audiences. This discovery resolves a long-standing mathematical problem regarding the existence of such monotiles. This monotile family, called Tile(p), with p ∈ [0 - 1] can tile the Euclidean plane through translation and rotation without exhibiting periodicity. With their simplicity, these 14-sided polygons reside at the boundary between order and disorder, potentially giving rise to novel physical properties yet to be explored.
In this study, we investigate the characteristics of seismic arrays constructed using Tile(p) as individual 14-station seismic arrays or as combinations of multiple tiles. Our findings demonstrate that for a 14-station array consisting of a single Tile(p), an optimal range of p-values exists whereTile(p) outperforms regular seismic arrays. Remarkably, the Specter, aka Tile(1,1) or Tile(0.5), represents one such optimal configuration that surpasses the spatial aliasing limitations of regular arrays. Arrays made of Specter tiles could also be optimal for ambient noise tomography as they produce more even ray paths than regular arrays.
