“It is not perfect for either but good enough to be useful within both areas, which means that we can now use more efficiently the data we collect for earthquake monitoring for subsurface imaging, and vice versa,” says Aurélien Mordret, Professor of Seismology at the Geological Survey of Denmark and Greenland (GEUS) about the use of aperiodic monotile tilings in earthquake monitoring and subsurface imaging.
Aurélien Mordret and Adolfo G. Grushin, a theoretical physicist at the Institut Néel of CNRS, have developed an innovative approach to seismic wave sampling that surpasses conventional limitations. Their study, published in Physical Review Applied, demonstrates how a new type of aperiodic seismic array can significantly improve signal reconstruction and wavefield imaging.
Seismic arrays often rely on periodic or regular geometries, constrained by something called the Whittaker-Nyquist-Shannon (WNS) limit, which dictates the minimum frequency required for accurate signal reconstruction. One of the issues researchers usually encounter if they try to use the data collected for earthquake monitoring purposes is aliasing. Most people will have witnessed aliasing, as it is a common occurrence, for instance when the wheels of a car in a stunt movie seem to move the wrong way or not move at all or someone’s patterned shirt seem to flicker in an image. In seismology, aliasing could mean locating an earthquake in the wrong place.
However, a mathematical finding that stunned the world of math a few years ago of a shape that allows for a non-repeating tiling, a so-called “einstein” tile, has found its way to applied research remarkably fast. The tiles in question are known as the ‘hat’ family because they are similar in shape to a fedora.
“My co-authour and I started talking about the possibilities the ‘hat’ family presented within physics and geophysics only two months after we heard of the mathematical discovery of the tile,” says Aurélien Mordret.
The researchers investigated the potential of aperiodic monotile tilings—specifically, the ‘hat’ tiling family—to overcome the constraints of the WNS limit.
“By applying this principle, we designed Aperiodic Monotile Seismic (AMS) arrays, which outperform both conventional regular grids and existing aperiodic configurations in realistic beamforming scenarios. This is beyond what we could expect,” explains Aurélien Mordret.
The study found that AMS arrays provide improved resilience to station failures and positioning errors while maintaining high-quality signal processing for seismic imaging and monitoring. This breakthrough could enhance applications not only in geophysics but also in acoustics, and telecommunications, offering a versatile new tool for wave sampling in complex environments.
At GEUS, this new array design will be helpful to efficiently use the pool of 1200 seismic nodes in various projects, from landslide area characterization to CCS reservoir monitoring.
“We have yet to see the full potential of this in practice,” sums up Aurélien Mordret.