Gravity surveys using a mobile atom interferometer

It appears to still approximate with a lot background calcs. Maybe a way to better look at the ranges of gravity across the earth. They should do a full Pyramid test per Miles'

The pyramid by Miles Mathis

http://milesmathis.com/pyramid.html


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Gravity surveys using a mobile atom interferometer

[list=contributor-list]
[*]View ORCID ProfileXuejian Wu¹,
[*]Zachary Pagel¹,
[*]View ORCID ProfileBola S. Malek¹,
[*]Timothy H. Nguyen¹,
[*]Fei Zi¹,
[*]View ORCID ProfileDaniel S. Scheirer² and
[*]View ORCID ProfileHolger Müller¹,³,*

[/list]

See all authors and affiliations


Science Advances  06 Sep 2019:
Vol. 5, no. 9, eaax0800
DOI: 10.1126/sciadv.aax0800

https://advances.sciencemag.org/content/5/9/eaax0800.full

Abstract

Mobile gravimetry is important in metrology, navigation, geodesy, and geophysics. Atomic gravimeters could be among the most accurate mobile gravimeters but are currently constrained by being complex and fragile. Here, we demonstrate a mobile atomic gravimeter, measuring tidal gravity variations in the laboratory and surveying gravity in the field. The tidal gravity measurements achieve a sensitivity of 37 μGal/Hz−−−√


(1 μGal = 10 nm/s²) and a long-term stability of better than 2 μGal, revealing ocean tidal loading effects and recording several distant earthquakes. We survey gravity in the Berkeley Hills with an uncertainty of around 0.04 mGal and determine the density of the subsurface rocks from the vertical gravity gradient. With simplicity and sensitivity, our instrument paves the way for bringing atomic gravimeters to field applications.      

INTRODUCTION

Light-pulse atom interferometers (1) have been used to measure inertial forces (2–6) and fundamental constants (7, 8), test fundamental laws of physics (9), and search for physics beyond the standard model (10). Gravimeters based on atom interferometry are among the most accurate and sensitive tools for measuring gravity (11, 12). By contrast to instruments based on springs (13), superconducting coils (14), microelectromechanical devices (15), or falling corner cubes (16), atomic gravimeters rely on matter-wave interferometry with a freely falling atomic cloud. Matter waves are directed into two interferometer arms by the momentum of photons, extremely well defined through the laser wavelength. Transportable atomic gravimeters are being developed toward metrology (17–22), airborne sensing (23), shipborne surveys (24), and field applications (25–29). They typically reach sensitivities around 5 to 100 μGalileo (μGal)/Hz−−−√(1 μGal = 10 nm/s²) in the laboratory (17–21, 25, 27), but the only atomic gravimeter used in gravity surveys achieves a precision of only ~1 mGal on a ship (24). Meanwhile, precise mobile gravimetry is valuable in broad areas. Gravity measurements with an uncertainty of a few microGalileos are required for using the Watt balance to realize the definition of the kilogram (30). The use of gravity reference maps to aid inertial marine navigation requires onboard gravimeters with at least milliGalileo accuracy (31). Seasonal aquifer fluctuations can be monitored by sensing microGalileo-scale gravity changes (32). These examples illustrate that atomic gravimeters must be not only sensitive but also mobile and reliable in field conditions.

Here, we demonstrate laboratory and field operation of a mobile atomic gravimeter. We achieve a sensitivity of 37 μGal/Hz−−−√
and a stability of better than 2 μGal in half an hour. Comparing the measured gravity with a solid Earth tide model, the atomic gravimeter is sensitive enough to reveal ocean tidal loading effects and to measure seismic waves of distant earthquakes. The atomic gravimeter measures absolute gravity in the laboratory with an uncertainty of 0.02 mGal, confirmed by a spring-based relative gravimeter referencing to a site with known absolute gravity. Furthermore, the mobility allows us to measure gravity in the field with a resolution of around 0.5 mGal/Hz−−−√
, depending on environmental noise. We implement gravity surveys in the Berkeley Hills along a route of ~7.6 km and an elevation change of ~400 m. At each static measurement location, it takes about 15 min to set up the gravimeter and a few minutes to measure gravity with an uncertainty of around 0.04 mGal. From the measured vertical gravity gradient (VGG), the density of subsurface rocks is estimated to be 2.0(2) g/cm³. Geodetic and geophysical studies—such as refining the geoid, resource exploration, hydrological studies, and hazard monitoring—can benefit from precise absolute gravity measurements using field-operating atomic gravimeters.

RESULTS

Mobile atom interferometer

The mobile atomic gravimeter is based on an atom interferometer, schematically shown in Fig. 1A. It features a magneto-optical trap (MOT) inside a pyramid mirror with a through-hole. This novel geometry offers many advantages. First, it acts as a differential pumping stage between the MOT and atom interferometry regions. A vapor pressure ratio of more than 10:1 (see fig. S1) accelerates atom-loading speed and decreases background noise in atom detection. We achieve a signal-to-noise ratio of 200:1 (see fig. S1) and reduce systematic effects from the refractive index of background atoms, particularly important when the laser is at a small detuning (see Materials and Methods). Second, it allows the MOT and interferometer laser beams to have different waists such that we can obtain both a large MOT volume and a high Raman beam intensity with the available laser power. Third, the atomic gravimeter takes advantage of retroreflection from a vibration-isolated mirror and is insensitive to vibrations of the pyramid mirror. Thus, the vibration isolation is simpler and more effective than in traditional pyramidal atomic gravimeters (26–28). Last, using a flat mirror as the retroreflector eliminates the systematic effects from imperfections in the pyramidal top angle and wavefront aberration due to the pyramid edges.

DISCUSSION

We have developed a mobile atomic gravimeter and performed tidal gravity measurements and gravity surveys. Our instrument uses a novel pyramidal MOT that takes advantage of single-beam atom interferometry and offers differential pumping, simple laser-to-gravity alignment, and enhanced vibration isolation. Our atomic gravimeter is mobile, compact, and robust over transport in the field while maintaining comparable sensitivity to other transportable atomic gravimeters (17–29). These features make it a candidate for geodetic and geophysical applications requiring precise mobile gravimetry (38).

Although spring-based gravimeters and falling corner cube gravimeters are popular transportable instruments, atomic ones are developing rapidly. 

Atomic and classical gravimeters have been compared in the laboratory (17, 18, 20, 27). Spring-based gravimeters can measure gravity variations with a sensitivity of tens of μGal/Hz−−−√, but their accuracy depends on the compensation of spring drifts and reference to gravity stations with known absolute gravity. Falling corner cube gravimeters can measure the absolute value of the local gravity, but their mechanical dropping and lifting system may not be suitable for continuous long-term operations. By contrast, atomic gravimeters can continuously measure absolute gravity with sensitivity and accuracy that are comparable to classical gravimeters. In the future, a field campaign of different types of gravimeters would provide more perspectives on the strengths and weaknesses of different gravimeter technologies with regard to particular applications.

The sensitivity of our atomic gravimeter is currently limited by vibrational noise. However, the sensitivity as a function of the pulse separation time indicates that we can further improve the sensitivity by dropping the atomic cloud longer (see fig. S4). To increase the gravity measurement rate, we can sample the fringes with fewer points, such as by alternating the laser phase around the rising and falling slopes. Because the local gravity is affected by the tidal effects, the inaccurate tide model at our location constrains the accuracy of the long-term stability measurement and the systematic effect evaluation. A gravity comparison at a geophysical observatory would allow us to characterize them more accurately (39). With these improvements, a more accurate measurement of the ocean tidal loading effect may be useful for investigating Earth’s mass structure and its variation with time at levels beyond current precision (35, 38). In addition, atomic gravimeters with mobility, sensitivity, and accuracy may find more applications in detecting tunnels, sensing underground water storage, and monitoring earthquake and volcano activity.

https://advances.sciencemag.org/content/5/9/eaax0800.full

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High-precision gravity measurements using atom interferometry

A Peters¹,  K Y Chung¹ and  S Chu¹
Published under licence by IOP Publishing Ltd
  Metrologia,  Volume 38, Number 1 Citation A Peters et al 2001 Metrologia 38 25
https://iopscience.iop.org/article/10.1088/0026-1394/38/1/4

https://iopscience.iop.org/article/10.1088/0026-1394/38/1/4/pdf

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Graphics on the Pyramid:

Posted on 18/01/2017 by Vexman


Calculus Simplified:
http://milesmathis.com/calcsimp.html