Quantum sensing for gravity cartography

Nature 602, 590-594 (2022) · DOI: 10.1038/s41586-021-04315-3

License: CC BY 4.0.

Abstract

The sensing of gravity has emerged as a tool in geophysics applications such as engineering and climate research, including the monitoring of temporal variations in aquifers and geodesy. However, it is impractical to use gravity cartography to resolve metre-scale underground features because of the long measurement times needed for the removal of vibrational noise. Here we overcome this limitation by realizing a practical quantum gravity gradient sensor. Our design suppresses the effects of micro-seismic and laser noise, thermal and magnetic field variations, and instrument tilt. The instrument achieves a statistical uncertainty of 20 E (1 E = 10⁻⁹ s⁻²) and is used to perform a 0.5-metre-spatial-resolution survey across an 8.5-metre-long line, detecting a 2-metre tunnel with a signal-to-noise ratio of 8. Using a Bayesian inference method, we determine the centre to ±0.19 metres horizontally and the centre depth as (1.89 −0.59/+2.3) metres. The removal of vibrational noise enables improvements in instrument performance to directly translate into reduced measurement time in mapping. The sensor parameters are compatible with applications in mapping aquifers and evaluating impacts on the water table, archaeology, determination of soil properties and water content, and reducing the risk of unforeseen ground conditions in the construction of critical energy, transport and utilities infrastructure, providing a new window into the underground.

Figures

13 panels with data across 5 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (b-1): Temperature ($\mu$K) of the upper cloud (dashed) and the lower cloud (solid) against time (h). Lines are averages over bins of 50 measurements; shaded regions span $\pm\sigma$ of the averaged data. Top panel of (b). data.csv
• panel (b-2): Relative change of the 1 m cloud separation baseline (ppm) against time (h), from time of arrival. The line is the average over bins of 50 measurements; the shaded region spans $\pm\sigma$ of the averaged data. Bottom panel of (b). data.csv
• panel (c): Gravity gradient difference signal (E) for the test mass close to the sensor (open triangles) and displaced from it (filled triangles), against measurement time (s), increasing downwards. Error bars are the standard error of eight gradient readings; grey bands mark the close position; the red dashed line is the modelled change $\Delta G_{zz}$. The print labels this axis by measurement number. data.csv

Fig. 2

• panel (1): Allan deviation (E), with overlapping averages, of the gradiometer output during about 8.6 h of outdoor operation against averaging time (s), log-log axes. The shaded band is the stated error of the Allan deviation. data.csv
• panel (1-inset): Inset of Fig. 2: a typical subset of 300 ellipse points, upper interferometer output against lower interferometer output (Lissajous figure). data.csv

Fig. 3

• panel (a): Gravity gradient (E) against position (m) along the survey line: gradiometer data with standard error (black) and the total inferred uncertainty including model uncertainty (blue), the $1\sigma$ (dark) and $2\sigma$ (light) credible interval bands, and the site model (dashed). data.csv
• panel (c): Probability of excavation (POE) inferred from the gradiometer data against position (m) and depth (m), with its contours at 0.1 to 0.9 (blue) and the expected tunnel cross-section (dashed). Depth increases downwards as printed; the print shades the contour bands, hosted as a continuous colour map. data.csv
• panel (d): Probability density against anomaly density (g cm$^{-3}$): the prior (green) and the posterior (blue) of the soil density inferred with the tunnel geometry assumed known, with the 68% highest density interval (HDI) of the posterior as a black bar. data.csv

Fig. 4

• panel (a): Contours of the typical gravity gradient signal (E) of a buried object against depth from surface (m) and object radius (m), for a density contrast of 1.8 g cm$^{-3}$, at 10 to 600 E. The thick line is the sensor uncertainty at 10 min, the red dot the detected tunnel, and shaded boxes the ranges of four applications. data.csv

Ext. Data Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF.

Ext. Data Fig. 2

Illustrative figure, no extractable data. Shown in the paper PDF.

Ext. Data Fig. 3

Illustrative figure, no extractable data. Shown in the paper PDF.

Ext. Data Fig. 4

• panel (1): Bayesian posterior probability density of the tunnel model parameter $x$ length (m), with its 68% highest density interval (HDI) as a black bar; $x$ is horizontal and $z$ vertical. Top left panel. The median and HDI limits printed as text are not drawn. data.csv
• panel (2): Bayesian posterior probability density of the tunnel model parameter $z$ length (m), with its 68% highest density interval (HDI) as a black bar; $x$ is horizontal and $z$ vertical. Top right panel. The median and HDI limits printed as text are not drawn. data.csv
• panel (3): Bayesian posterior probability density of the tunnel model parameter $x$ centroid (m), with its 68% highest density interval (HDI) as a black bar; $x$ is horizontal and $z$ vertical. Bottom left panel. The median and HDI limits printed as text are not drawn. data.csv
• panel (4): Bayesian posterior probability density of the tunnel model parameter $z$ centroid (m), with its 68% highest density interval (HDI) as a black bar; $x$ is horizontal and $z$ vertical. Bottom right panel. The median and HDI limits printed as text are not drawn. data.csv

Cite

Ben Stray et al. (23 authors). Quantum sensing for gravity cartography. Nature 602, 590-594 (2022). https://doi.org/10.1038/s41586-021-04315-3

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