Analysis of vibration correction performance of vibration sensor for absolute gravity measurement
Authors: Wen Yi , Wu Kang , Wang Li-Jun ,   State Key Laboratory of Precision Measurement Technology and Instrument, Department of Precision Instrument, Tsinghua University, Beijing 100084, China
Published: February 2022

Absolute gravity measurement refers to the measurement of the absolute value of gravitational acceleration (<i>g</i>, approximately 9.8 m/s<sup>2</sup>). The precision of absolute gravity measurement is limited mainly by vibration noises. Vibration correction is a simple and feasible way to deal with vibration noises, which corrects the measurement results by detecting vibration noises with a sensor. At present, the vibration correction performance of different sensors lacks systematic analysis and evaluation. In this paper, the theoretical analysis of how the sensor characteristics affect the correction performance is carried out. The vibration correction performances of three sensors, two different seismometers and one accelerometer, are evaluated experimentally in the three cases with different vibration noises. The experimental results show that the correction precision obtained by using low-noise seismometer is limited mainly by its bandwidth and range. In case I i.e. the quiet environment, the standard deviation of corrected results obtained by using both seismometers can reach tens of μGal (1 μGal = 10<sup>–8</sup> m/s<sup>2</sup>), which is close to that obtained by using an ultra-low-frequency vibration isolator. However, in case II i.e. the noisy environment, the standard deviation of corrected results obtained by both seismometers increase to hundreds of μGal due to the enhancement of high-frequency vibration components. This means that the correction performances of both seismometers deteriorate, and the performance of seismometer with narrower bandwidth turns even worse. Moreover, two seismometers cannot even work in case III with stronger vibration noises due to the range limitation. On the other hand, the correction precision obtained by using accelerometer is affected mainly by its resolution which is on the order of mGal (1mGal = 10<sup>–5</sup> m/s<sup>2</sup>). Its bandwidth can reach hundreds of or even thousands of hertz and its range is generally over ±2 g, which is large enough to meet the needs for noisy and dynamic applications. In case I, the standard deviation after correction with accelerometer is larger than that before correction. This is because the intensity of vibration noises in this case is close to or even smaller than the self-noise of accelerometer so that it could not be detected effectively by accelerometer. In case II, the resolution of accelerometer is sufficient to detect the vibration noises effectively. The standard deviation of the results is reduced from 2822 μGal to 1374 μGal after correction with accelerometer, and equal to a precision of 0.1 mGal after 100 drops. In case III where the amplitude of vibration noise rises to 0.1 m/s<sup>2</sup> and seismometer cannot work, the accelerometer could still achieve a precision of 0.3 mGal after 100 drops. The systematic deviation is corrected from –1158 mGal to –285 μGal and the standard deviation is reduced from 34 mGal to 3.3 mGal. Therefore, the low-noise seismometer is more suitable for vibration correction in a quiet environment with stable foundation, which could realize a standard deviation superior to hundreds of μGal, while the accelerometer is more appropriate for vibration correction in a complex or dynamic environment, which could achieve a standard deviation of mGal-level. Finally, the present results and analysis provide a theoretical guidance for selecting and designing the sensors in vibration correction applications.