Measurement of the Earth Tides with a Diamagnetic-Levitated Micro-Oscillator at Room Temperature

The precise measurement of the gravity of Earth plays a pivotal role in various fundamental research and application fields. Although a few gravimeters have been reported to achieve this goal, miniaturization of high-precision gravimetry remains a challenge. In this work, we have proposed and demonstrated a miniaturized gravimetry operating at room temperature based on a diamagnetic levitated micro-oscillator with a proof mass of only 215 mg. Compared with the latest reported miniaturized gravimeters based on microelectromechanical systems, the performance of our gravimetry has substantial improvements in that an acceleration sensitivity of $15\mathrm{\mu }\mathrm{Gal}/\sqrt{\mathrm{Hz}}$ and a drift as low as $61\mathrm{\mu }\mathrm{Gal}$ per day have been reached. Based on this diamagnetic levitation gravimetry, we observed Earth tides, and the correlation coefficient between the experimental data and theoretical data reached 0.97. Some moderate foreseeable improvements can develop this diamagnetic levitation gravimetry into a chip size device, making it suitable for mobile platforms such as drones. Our advancement in gravimetry is expected to facilitate a multitude of applications, including underground density surveying and the forecasting of natural hazards.

Figure 1

Schematic of the diamagnetic levitation gravimeter. (a) The diamagnetic levitated micro-oscillator with a proof mass of 215 mg is placed in the aluminum frame. The thermometer and heater are fixed on the aluminum frame to stabilize the temperature of the permanent magnets with the PID controller. A vacuum chamber and thermal isolators are used to avoid ambient temperature disturbances. Magnetic shields are placed outside the aluminum frame to shield against external magnetic field. A 633-nm laser beam reaches the displacement sensor and is then sent to a photodetector through optical fibers. Piezoelectric positioners are used to control the position of displacement sensor to ensure that the copper wire is exactly at the focal point of the laser beam. Tilt adjusters are used to level the setup. A magnetometer is placed outside of the vacuum chamber to measure the external magnetic field. (b) Schematic of oscillator displacement detection. The laser beam is focused by a lens. The copper wire is placed on the focal point, where displacement sensitivity in the $Z$ direction is maximum. (c) The measured response curve of voltage to displacement in the $Z$ direction of (b). It can be seen that the response curve has very good linearity in the range of $-1\mathrm{\mu }\mathrm{m}$ to $1\mathrm{\mu }\mathrm{m}$, with the $R$ squared of linear fitting for this segment of the data reaching 0.999.

Figure 2

Measurement of Earth tides. (a) Data obtained from the diamagnetic levitated gravimeter. Each blue dot represents the mean value of measured data over a one-hour period. A drift of $61\mathrm{\mu }\mathrm{Gal}$ per day has been observed. (b) Comparison between theoretical and experimental data of Earth tides. The red line is a theoretical plot calculated with tsoft [30]. The blue dots represent the same data as in (a) but with the drift removed. The correlation coefficient between experimental data and theoretical calculation is 0.97.

Figure 3

Allan deviation. (a) Raw data with a sampling rate of 0.5 Hz. Points 1 and 2 are earthquake signals that occurred off the east coast of Honshu, Japan and in the Bali Sea, Indonesia, respectively. (b) Data from (a) corrected for external magnetic field and temperature. (c) Data from (b) with theoretical tide signal removed. (d) Data from (c) with drift removed. (e)–(h), represent the Allan deviation of the data in (a)–(d), respectively. The bias instability of this gravimeter is $5.1\mathrm{\mu }\mathrm{Gal}$ at an average time of 6000 s.