MEMS gravimeter takes underground mapping to the masses
With its resonant frequency of 2.3Hz, an acceleration sensitivity of 40μGal Hz-1/2 and a stability guaranteed for days or even weeks thanks to very accurate servo control loops that maintain the system’s temperature to within 1mK, the device can be used to monitor minute variations in gravity over long time spans, making it applicable to many fields of geology and underground exploration.
In a paper titled ‘Measurement of the Earth tides with a MEMS gravimeter’ published in Nature, the researchers detail the unique geometry of their 15x15mm MEMS die featuring an anti-spring flexure pair at the bottom (constraining the motion of the proof mass) and a curved cantilever at the top.
The proof mass motion is measured using an optical shadow sensor (a photodiode placed on one side measures the proof mass’ shadow variations as the MEMS is illuminated from the other side by a LED – see figure 1). This sensor setup achieves a high sensitivity, equating to an acceleration noise floor of under 10μGal at the sampling frequency of 0.03Hz, while allowing a large dynamic range of up to 50mm, explain the researchers. Key to the MEMS’ long term stability is the precise temperature control mechanism, achieved through the use of four small platinum resistors (one on the outer frame of the MEMS and three placed equidistantly around the copper shield of the full device).

Limiting temperature variations to within 1mK is necessary to stabilize the MEMS’ mechanical characteristics (through minimized thermal expansion fluctuations) and spring constant. A change in temperature of 1mK would give an uncertainty in the gravity reading of about 25μGal, the paper explains.
Although this MEMS-based gravimeter is a technological feat, in terms of compactness and sensitivity, it would look rather bulky compared to the typical MEMS accelerometers found in consumer electronics (these are in fact much more rigidly designed, with smaller proof mass to cantilever aspect ratios).
But as co-author Dr Richard Middlemiss explained, the sensitivity and the softness of the springs necessary for a very low resonant frequency are only achieved thanks to very high aspect ratios in the design.
“All the flexures are only 7μm wide but 250μm deep, etched vertically through the silicon die”, Middlemiss told eeNews Europe.
“There is scope to miniaturize the full MEMS die and we could probably design a similar structure with flexure thinned down to 0.5μm while still keeping a clean high aspect ratio using photolithography. We’ve not got to that point yet with our models, but this is certainly something we’d like to explore”

Middlemiss says that although the gravimeter prototype is very much an R&D experiment at this stage, it could certainly be further integrated on silicon, with on-chip sensors, thermal control and better integrated optical detection.
“The Wee-g system will not displace accelerometers any time soon”, admits Middlemiss when asked if such MEMS-based gravimeters could one day leverage crowdsourcing for gravity mapping, “but if we were to offer a solution only a few cubic centimetres in volume, then we could make this relative gravimeter widely accessible for new fields of application where money is often scarce”.
Today’s commercial solutions with that type of sensitivity typically sell for hundreds of thousands of dollars, are bulky assemblies and often weigh many kilos, they are mostly used for oil exploration (detecting underground oil reserves through density contrast).
But a low-cost and lightweight mass-produced alternative could be mounted on a drone instead of a low-flying aircraft, for simpler distributed land surveying and exploration through gravity mapping.
“To put things in perspective, 40μGalHz−1/2 is sufficient in 1s to detect a tunnel with a cross-sectional area of 2m2 and a length of 4m at a depth of 2m” the researcher wrote in his paper, so the gravimeter could be used to locate subterranean tunnels. Building contractors could find underground utilities.
“Unlike the electromagnetic spectrum, the gravity force can’t be blocked” notes Middlemiss, “hence we can also detect the absence of mass, this is another way of imaging that could have defence applications, say to secure shipping ports.
Gravity mapping could become affordable not only to geologists monitoring volcanos (detecting the evolution of magma reservoirs prior to volcanic eruptions) but also to archaeologists seeking remnant building foundations. You could even conceive a fleet of drones flying synchronously to form a wide area density-contrast imaging array.
The researchers are aiming at further miniaturization and looking for industrial partners via QuantIC, the UK centre of excellence for research, development and innovation in quantum enhanced imaging. From the beginning, the design options and materials were chosen to favour easy industrialization using established processes. “A spin-off may be on the agenda”, hinted Middlemiss.
Visit the University of Glasgow at www.glasgow.ac.uk
Visit QuantIC at https://quantic.ac.uk
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