Perspective Chapter: Application of Gyroscopes in Geophysics

Abstract

More researchers have gradually realized that gyroscopes are powerful rotational measurement sensors, and the use of high-performance gyroscopes in geophysics began in the last decade and continues to deepen. This chapter will present the applications of gyroscopes in geophysics. In rotational seismology, large gyroscopes are used in the observation and analysis of natural earthquakes; miniaturized and portable fiber-optic gyroscopes are used in practical applications, including high-speed-railway seismology, natural earthquake observation, and subsurface structure imaging. In the study of the Earth’s rotation, the angular velocity of the Earth’s rotation is observed with large optical gyroscopes. In gravimetry, high-performance fiber-optic gyroscopes are used to measure the rotational motion generated by the gravitational field and, hence, the gravity gradient.

1. Introduction

Gyroscopes are sensors that measure rotational motion and can be used to measure the rotational parameters of an object, such as angle, angular velocity, and angular acceleration. In the field of geophysics, there are many phenomena related to rotational motion, such as the Earth’s rotation, the rotational component of seismic waves, etc.; thus, gyroscopes can play a vital role in geophysics.

In fact, the first well-known application of gyroscopes was in the field of geophysics. In 1852, J. Foucault used the directional stability of a high-speed rotating rigid body to design the first gyroscope for verifying the Earth’s rotation [1]. The phenomenon caused by the Earth’s rotation can only be seen for about 10 minutes due to the friction of the mechanical rotor. This is also known as the basis for electro-mechanical gyroscopes based on classical mechanics.

With the development of Einstein’s theory of relativity, G. Sagnac proposed the Sagnac effect in 1913 [2], that is, the phase difference between two light waves traveling opposite each other along the closed optical path is proportional to the angular velocity of the normal direction of the closed optical path. This has become the sensing principle of the current optoelectronic gyroscopes. In 1925, A. A. Michelson and H. G. Gale used a large ring interferometer with a circumference of about 2 km to increase sensitivity and were able to measure the Earth’s rotation [3]. After the advent of the He-Ne gas laser, Macek and Davis validated the ring laser gyroscope in 1963 [4]. Fiber-optic gyroscope (FOG) is developed on the basis of the fiber-optic communication device. In 1966, K. C. Kao proposed that the high loss of optical fiber material is caused by its impurities, and the loss can be reduced to 20 dB/km by reducing the impurities in the material [5]. This became the beginning of the practical use of optical fibers. In 1967, G. Pincher and G. Hepner first proposed the idea of making FOG by enhancing the Sagnac effect with multi-turn fiber-optic coils [6]. In 1976, Victor Vali and Richard W. Shorthill successfully demonstrated the first FOG in the laboratory, marking the birth of the FOG [7].

Due to the fact that rotational phenomena in geophysics are usually small, the requirements for the performance of gyroscopes are very high. With the development of optical devices such as optical cavities, lasers, and optical fibers, optical gyroscopes based on the Sagnac effect have gradually become the first choice for high-performance applications. Furthermore, as the performance of gyroscopes has improved, new branches of geophysics have been born in the last two decades, such as rotational seismology and high-speed-railway seismology. The following sections show applications of high-performance gyroscopes in seismology, Earth’s rotation, and gravimetry.

2. Applications in seismology

2.1 Rotational component of seismic wave

In seismology, the classical linear elastic theory is commonly used to describe the distortion of a medium. With the assumption of infinitesimal deformations, a function of the space $\mathbf{u}=\mathbf{u}\left(\mathbf{x}\right)$ is used to denote the translational displacement of the points $\mathbf{x}$. For a point $\mathbf{x}+\delta \mathbf{x}$ in its vicinity, the displacement $\mathbf{u}\left(\mathbf{x}+\delta \mathbf{x}\right)$ can be written as [8]:

$$\mathbf{u}\left(\mathbf{x}+\delta \mathbf{x}\right)=\mathbf{u}\left(\mathbf{x}\right)+\mathit{\epsilon }\delta \mathbf{x}+\mathit{\omega }\times \delta \mathbf{x},$$E1

where $\mathit{\epsilon }$ denotes the strain tensor, and $\mathit{\omega }$ represents the rotation vector. Under the assumption of small and linear deformations, the rotation vector $\mathit{\omega }$ is neglected. On the one hand, this is due to the small amplitude of the rotation relative to the translational motion. On the other hand, this is also because the rotational phenomena in seismic waves are not obvious, and the performance of the measurement sensors is not sufficient.

But the fact is that the rotational properties of seismic waves do exist and cannot be neglected. The earliest recorded rotation of buildings and tombstones caused by an earthquake was the shifting of two obelisk-shaped pillars during an earthquake in Calabria in 1783 [9]. This record attracted the attention of many researchers, and seismologists set out to find and design the sensors for observing the rotational component of seismic waves.

The introduction of gyroscopes into the field of view of seismologists and the measurement of the rotational component of seismic waves dates back to 1968. W. E. Farrell developed a gyroscope with two counter-rotating pendulums. During the Borrego earthquake of April 9, 1968 (M 6.5), static dislocations of less than 1 cm and rotations of less than $5\times {10}^{-4}$ rad were observed at La Jolla, California, 115 km from the source [10].

With the development of optical devices, optical gyroscopes have replaced electro-mechanical gyroscopes in geophysical applications due to their high sensitivity. Built on October 5, 2001, the Ring Laser Gyroscope G is located at the Wettzell Geodetic Observatory in Bavaria, Germany. It observed the Tokachi-Oki earthquake (M 8.1) which occurred in Hokkaido, Japan on September 25, 2003. In this work, the translational and rotational components of the earthquake are compared. This is the first reported observational record of rotational motion about a vertical axis induced by a large distant earthquake consistent with the shape of translational motion [11]. An FOG placed at the National Time Service Center in Xi’an, China, obtained the rotational motion record of an earthquake (M 4.9) that occurred in Yingcheng, Hubei Province, China, at 18:36:34 on December 26, 2019 (UTC + 8) [12]. The distance from the FOG to the epicenter of the earthquake is about 580 km.

2.2 Rotational seismology

Rotational seismology, a branch of seismology that studies the rotational ground motion induced by earthquakes, has seen significant advances over the years. It has emerged as an essential component of earthquake studies, providing valuable insights into the complex dynamics of seismic events [13].

The development of rotational seismology dates back to the mid-twentieth century, when scientists began to recognize the importance of rotational ground motion. Early observations were primarily made through the use of simple pendulum-type rotational sensors [14]. As seismology has expanded, it has become clear that the rotational component of seismic waves carries valuable information that cannot be adequately captured by traditional translational seismometers alone. Advances in technology and instrumentation in recent decades have led to the establishment of dedicated rotational seismology networks, facilitating the systematic study of these complex rotational signals.

To promote the research of rotational seismology, an international working group on rotational seismology (IWGoRS) was organized to promote investigations of rotational motions and their implications and to share experience, data, software, and results in an open web-based environment. Researchers can join IWGoRS at http://www.rotational-seismology.org, subscribe to mailing lists, and contribute to the content (publications, data, links, etc.). Nowadays, rotational seismology has gained considerable momentum in earthquake research. Seismologists have come to appreciate the significance of rotational ground motions in understanding the rupture process, seismic focal mechanisms, and seismic wave propagation [15, 16]. The rotational components of ground motion have been observed and analyzed in various seismic events worldwide, enhancing our understanding of seismic source processes and their associated complexities.

2.3 Gyroscopes as rotational seismometers

The successful implementation of rotational seismology relies on high-performance rotational seismometers. Rotational seismometers are critical in capturing and analyzing the rotational components of ground motion during seismic events. The core of a rotational seismometer lies in its angular velocity sensor (i.e., gyroscope), which comes in various types, such as mechanical gyroscopes [17], MEMS (Micro-Electro-Mechanical System) gyroscopes [18], electrochemical gyroscopes [19], laser gyroscopes [20], and FOGs [21, 22, 23]. Based on actual observation cases, researchers at Ludwig-Maximilians University specified the following a priori requirements of seismic rotational sensors [24]:

1. The sensor needs to be effectively insensitive to linear motion, or at any rate, distinct measurement of linear and rotational motions must be possible.

2. For installing networks of temporary stations, the instrument needs to be small and stable with respect to ambient conditions, including changes in temperature.

3. The electrical power supply should be easily managed with batteries, at least in combination with solar panels or fuel cells.

4. A useful instrument for weak motion seismology needs to be able to measure amplitudes in the order of ${10}^{-7}$ rad/s at periods from 10 to 100 s.

Mechanical and MEMS gyroscopes use the principle of angular momentum conservation to measure rotational motion. They are simple and reliable; however, they have relatively low sensitivity and are susceptible to the influence of vibrations and shocks, leading to potential measurement errors. Electrochemical gyroscopes measure the change in capacitance of charged particles to measure the angular velocity. They are cost-effective but suffer from low sensitivity and limited frequency response as well as dynamic range. Both laser gyroscopes and FOGs are high-precision rotational sensors that employ the Sagnac effect to measure angular rotation. However, the larger size and complexity of laser gyroscopes limit their portability, and they are also more expensive compared to other gyroscopes. The FOG-based rotational seismometer is an all-solid-state device without any moving parts, enabling the design of compact, lightweight, and energy-efficient rotational seismometers. This makes FOG-based rotational seismometers highly suited for easy deployment and integration into existing seismic networks. Besides, FOG exhibits a wide dynamic range, allowing it to probe a wide range of rotational motions, from large-scale seismic events to microseismic events. This capability ensures that FOG-based rotational seismometers can capture and analyze a wide spectrum of rotational ground motions, providing comprehensive data for seismic research. In the following content, we choose two representative FOG-based rotational seismometers to introduce, the BlueSeis-3A and the Three-component Dual-Polarization Fiber-Optic Rotational Seismometer (DP-Rot3C) (Figure 1).

Figure 1.

The pictures of (a) BlueSeis-3A and (b) DP-Rot3C.

2.3.1 BlueSeis-3A

BlueSeis-3A is the first commercially available FOG-based rotational seismometer. This rotational seismometer has gained widespread recognition for its high sensitivity and stable performance in measuring ground rotational motions. It utilizes three closed-loop FOGs, each with a 5 km long fiber-optic coil, assembled in mutually orthogonal orientations, forming a three-component rotational seismometer.

Specifically, the self-noise of the rotational seismometer determines the minimum detectable angular rate and is typically represented by the power spectral density (PSD) or the square root of the power spectral density (root PSD) obtained from static tests. Currently, BlueSeis-3A exhibits a root PSD of $20\mathit{\text{nrad}}/s/\sqrt{\mathit{Hz}}$ within the frequency range of 0.001–100 Hz [22], as shown in Figure 2(a).

Figure 2.

(a) The self-noise and (b) scale factor nonlinearity of BlueSeis-3A [22].

The nonlinearity of the scale factor is an indicator of the nonlinear error between the input and output angular velocities of the rotational seismometer. Typically, the entire measurement range is tested, and the maximum error is compared to the measured range to calculate the ratio. Displayed in Figure 2(b), in the angular rate range from 0.035 to 0.873 rad/s, the nonlinearity level of the scale factor is maintained within 50 ppm (parts per million) [22], meeting the performance requirements in seismology.

2.3.2 DP-Rot3C

DP-Rot3C, proposed and implemented by Peking University, is another high-precision FOG-based rotational seismometer. DP-Rot3C consists of three orthogonal open-loop FOGs, each with a fiber-optic coil of length 6 km. Notably, each FOG component in DP-Rot3C adopts a dual-polarization configuration [25], enabling the multiplexing of two orthogonal polarization states originating from the same light source, thus allowing enhanced simultaneous measurement of rotational ground motions.

Essentially, each component consists of two sets of highly consistent gyroscopes that act as mutual reference signals. Through the implementation of cooperative processing of two polarization states, the relative intensity noise (RIN), which is the most significant factor affecting the self-noise of FOG, is substantially suppressed. As shown in Figure 3(a), the root PSD of three components of DP-Rot3C reaches $20\mathit{\text{nrad}}/s/\sqrt{\mathit{Hz}}$ from 0.01 to 125 Hz. The fluctuations observed in the high-frequency segments of the root PSD are mainly attributed to environmental vibrations.

Figure 3.

(a) Self-noise and (b) scale factor nonlinearity of DP-Rot3C.

DP-Rot3C utilizes an open-loop configuration, where the nonlinearity of the scale factor has been a limiting factor in achieving high-precision measurements and applications in seismic wave observations. The primary source of nonlinearity errors stems from the nonlinear characteristics of components in optoelectronic detection systems, including photodetectors, amplifiers, analog-to-digital converters, and piezoelectric phase modulators. To address this issue, a simple and effective compensation algorithm named the k-value compensation algorithm has been proposed [26]. This algorithm models the nonlinear response error of the detection system and effectively compensates for the output angular velocity in real time within the demodulation system. Experimental results demonstrate that even after expanding the measurement range from $\pm {30}^{\circ }/s$ to $\pm {300}^{\circ }/s$, the k-value compensation algorithm successfully achieves a scale factor nonlinearity of only 2.5 ppm. This makes DP-Rot3C the open-loop FOG with an ultra-small scale factor nonlinearity. This enhancement ensures an accurate and linear response over a wide range of ground motion amplitudes, contributing to improved accuracy in seismic event characterization.

Table 1 gives the key performance indicators of current portable rotational seismometers.

Name	Self-noise	Bandwidth	Scale factor nonlinearity	Size
	(nrad/s/$\sqrt{\mathrm{Hz}}$)	(Hz)	(ppm)	($\mathrm{mm}\times \mathrm{mm}\times \mathrm{mm}$)
BlueSeis-3A	20	0.001–100	<50	$318\text{diameter}\times 335$
DP-Rot3C	20	0.01–125	<10	$200\times 200\times 200$
RotSensor3C [23]	120	0.005–125	<10	$190\times 190\times 165$
DP-Rot1C [27]	9	0.01–125	<3	$330\text{diameter}\times 100$
FOSREM-BB [28]	32	0.1a–328.12	No data	$360\times 360\times 160$
FOSREM-SS [28]	49	0.01a–328.12	No data	$470\times 360\times 230$
R-2 [29]	60	0.03–50	No data	$120\times 120\times 102$

Table 1.

Key performance indicators of current portable rotational seismometers.

^a

Estimated from Allan variance curve.

2.4 Applications cases

Gyroscopes have emerged as crucial tools in rotational seismology, providing significant advances in various fields. In this section, three typical examples are presented, including high-speed-railway seismology, natural earthquake observation, and subsurface structure imaging.

2.4.1 High-speed-railway seismology

High-speed railway, as a critical transportation infrastructure, is characterized by its stable, punctual, and high-speed operation. In seismology, high-speed railways also generate vibration signals at different frequencies during their operation. While previous studies of high-speed railway vibrations have focused on their interference with seismic station monitoring and damage to buildings near the railway, train vibrations have rarely been considered as a source for studies of underground structure detection. Zhang et al. have proved that this signal can be regarded as a passive source signal that is generated regularly, which can provide new methods for geological exploration, structure detection, resource prospecting, etc. [30]. FOG-based rotational seismometers play a crucial role in accurately measuring the rotational ground motion induced by a high-speed train along a railway.

Signals from high-speed trains have been observed using FOG-based seismometers in the vicinity of high-speed railways and viaducts near Dingxing, Hebei Province, China. Vibrational signals excited by different trains were analyzed in both time and frequency domains. Additionally, a comparison was made with the signals recorded simultaneously and at the same location using a separate set of three-component translational seismometer [31].

As shown in Figure 4, in the time domain, both the rotational and translational signals of the ground vibration induced by the moving high-speed train show periodic phenomena caused by the grouping of 16 carriages. The period of 16 consecutive stable periodic waveforms is 0.31 s. It is deduced that the actual travel speed of the train recorded is 281 km/h. In Figure 5, the amplitude spectra of the signal received by the rotational seismometer and translational seismometer have 16 obvious discrete spectral lines, and the amplitude spectra energy is basically concentrated between 20 and 60 Hz, and the spacing between the discrete spectral lines is mostly 3.3 Hz. This is most likely related to the wave nature of the high-speed railway signals, which is worthy of further study.

Figure 4.

Three-component waveforms recorded by a (a) rotational seismometer and (b) translational seismometer as the high-speed train passes by.

Figure 5.

Amplitude spectra of the waveforms recorded by a (a) rotational seismometer and (b) translational seismometer as the high-speed train passes by.

2.4.2 Natural earthquake observation

Observations and characterization of natural earthquake events are fundamental to understanding seismic mechanisms and earthquake hazards. In addition to the examples presented in Section 2.1, a high-precision FOG-based seismic seismometer located in Wuhan successfully detected the earthquake signal of a M 6.4 earthquake in Yangbi, Yunnan province, China, which occurred at a distance of 1510 km from the observation station [32]. Using the relationship between the translational and rotational components of the seismic wave fields, the Love wave phase velocity and incident angle beneath the station are estimated (Figure 6). The estimated phase velocity values are comparable to those obtained through model analysis and array processing, revealing distinct dispersion characteristics. The back-azimuth estimation suggests that the Love wave deviates slightly from the great circle path but significantly from the tail wave portion. These findings demonstrate the potential of single-point, multicomponent seismic rotation and translational wave field records in related seismological research.

Figure 6.

(a) Vertical rotation rate and converted rotation rate from theoretical transverse accelerations. (b) back-azimuths (BAzs) estimation [32].

2.4.3 Subsurface structure imaging

As seismic waves pass through subsurface structures, their wave fields undergo changes such as refraction, reflection, scattering, and other phenomena, which provide information about the underground structure. According to the characteristics of the seismic wave propagation, the observed seismic wave velocity, amplitude attenuation, and other information can be used to infer the underground structure, so as to complete the underground structure imaging. With the application of gyroscopes in rotational seismology, the rotational component of the seismic wave field is supplemented, and more complete information about the seismic wave field can be obtained for the study of subsurface structures.

Keil et al. conducted a single station test near the geothermal well SWMHK and BRUD station in Munich [33]. In this test, a BlueSeis-3A rotational seismometer and a Nanometrics Trillium Compact translational seismometer were used. They calculated the dispersion curves of the Love wave and Rayleigh wave, combined with the horizontal and vertical component spectral ratio (HVSR or H/V) technology of the translational component. These dispersion curves and H/V ratio are used in joint inversion, and the inversion is constrained to a three-layer model to obtain the most reliable P-wave and S-wave velocity profiles, as shown in Figure 7. As an application, the resulting 1D velocity profile will be used in future studies to estimate the local shaking characteristics in Munich.

Figure 7.

Estimation of (a) Love and (b) Rayleigh wave dispersion curves with BlueSeis-3A and a translational seismometer, and the resulting (c) three-layer P- and S-wave velocity profiles and (d) lithologic profile [33].

3. Applications in the Earth’s rotation

As a rotational motion sensor, the earliest application of gyroscopes was to measure the Earth’s rotation. However, due to the overall stability of the Earth’s rotation, variations in rotation are small. Therefore, quantitative studies of the Earth’s rotation rely on high-precision gyroscopes. With the development of laser technology and optical devices, high-precision real-time measurements of the Earth’s rotation using large optical gyroscopes have become the first choice.

Optical gyroscopes can directly measure the Sagnac effect caused by the Earth’s rotation. Its configuration is a Sagnac interferometer, consisting of two symmetric optical paths. Inside, a path of light emitted by the light source travels in one direction, passing through the loop and returning to the starting point. The other path of light is also emitted from the source but travels in the opposite direction, also passing through the loop and returning to the starting point. When light passes through an optical loop, it creates a phase difference caused by rotation due to the projection of the Earth’s angular velocity in the plane where the loop is located. The interference phase difference ${\varphi }_{\mathrm{s}}$ between the two paths is

$${\varphi }_{\mathrm{s}}=\frac{8\pi }{\mathit{\lambda c}}\mathbf{S}\cdot \mathit{\omega },$$E2

where $\lambda$ is the central wavelength of the light, $c$ denotes the speed of light in vacuum, $\mathbf{S}$ represents the area vector of the closed optical loop, and $\mathit{\omega }$ is the rotation velocity vector of the Earth.

At present, the technology for measuring universal time is mainly based on Very Long Baseline Interferometry (VLBI). Measurements of the Earth’s rotation using this method are indirect and require observations of reference objects such as satellites beyond the Earth, the Moon, stars, or extragalactic radio sources. In contrast to VLBI, measurements using optical gyroscopes have high real-time performance and do not require the observation of a reference target source outside the Earth.

Since the end of the last century, the team led by G. E. Stedman began to build a ring laser gyroscope in New Zealand to study the Earth’s tides and lunar nutations [34]. After that, the team successively built a series of large-scale laser ring gyroscopes with higher precision. A laser gyroscope named “G” for continuous Earth rotation monitoring was built by K. U. Schreiber and located at the Geodetic Observatory Wettzell, Germany [35]. As shown in Figure 8, the ring laser body forms a square with a side length of 4 m. The average noise level at subdaily frequencies is less than 1 part in ${10}^9$ after an integration time of about ${10}^4$s [36]. This puts the detection limit for subdaily signals to 2 nrad for polar motion and 0.15 ms for length of day. In 2016, a large-scale laser gyroscope called “ROMY” (Rotational Motions in Seismology) was built and funded by the European Research Council. Figure 9 illustrates the sensor layout in the construction. The gyroscope has four triangular square rings. It has the advantage of being able to measure the angular velocity of the Earth’s rotation in different directions simultaneously. Thus, the change of the Earth’s angular velocity vector is obtained, and reconstruction of the full Earth rotation vector can be achieved with sub-arcsecond resolution over more than 6 weeks [37].

Figure 8.

The construction of the G ring laser [35].

Figure 9.

The construction of ROMY [37].

With the continuous development and maturity of fiber-optic technology, FOGs, using optical fibers instead of ring resonators, can also approach the accuracy of laser gyroscopes. With advances in fiber winding technology, researchers are able to wind larger and longer fiber-optic coils. A reference level FOG was reported in 2016 by Honeywell. The sensing area of the fiber-optic coil is about $1000m^2$, and the corresponding sensitivity is $4.6\times {10}^{-9}\mathit{rad}/s/\sqrt{\mathit{Hz}}$. During a one-month test, the bias instability reached $3\times {10}^{-5\circ }/h$ [38]. The research group at Peking University has developed a FOG for the monitoring of the Earth’s rotation. As shown in Figure 10, a large FOG with a fiber length of 20 km and a diameter of 0.5 m has been implemented for precision measurement of universal time. It has a sensitivity of $3\times {10}^{-9}\mathit{rad}/s/\sqrt{\mathit{Hz}}$ and a bias instability of $5\times {10}^{-6\circ }/h$ [12, 39]. This FOG has also captured a series of seismic events during continuous operation, demonstrating its long-term capability and reliability.

Figure 10.

Photograph of the large fiber-optic gyroscope and the test environment.

4. Applications in gravimetry

The gravity field of the Earth is an important physical field in geophysical research, which is mainly determined by the density distribution of the Earth. Due to the inhomogeneous distribution of matter density on the Earth, the Earth’s gravity field is inhomogeneous. The strength and direction of the gravity field will vary at different locations on the Earth. It is precisely because of this fact that through the use of gravity measuring instruments, changes in the Earth’s gravity field can be measured, and thus, information can be obtained about the crustal movement, groundwater resources, and so on. The study of the Earth’s gravity field is also widely used in satellite navigation, geological exploration, mapping, and other fields. In gravimetry, the parameters of the gravity field that are often measured include gravity acceleration and gravity gradient. The former is the first spatial derivative of gravity potential, while the latter is the second spatial derivative of gravity potential.

Existing gravity measurement instruments usually employ atomic interferometry [40, 41, 42] or superconducting technology [43] to achieve higher sensitivity. Among them, instruments with atomic interferometry use cold atoms as test masses to sense the gravity field. However, in the use of atomic interferometry, vacuum tubes are required to achieve a vacuum environment, and seismic isolation platforms are required to reduce the impact of ground vibrations. Besides, there are obstacles to miniaturization. Instrument with superconducting technology uses mechanical test mass as a component of sensitive gravity field, and uses a superconducting quantum interference device (SQUID) to sense changes in superconducting current caused by the displacement of test mass. SQUID converts the external motion into a displacement change, which is converted into a current response by means of inductance modulation, and finally converts it into a voltage signal by an amplifier. However, the implementation of superconducting technology relies on the construction of a stable low-temperature environment, which also requires the large environmental control equipment of magnetic shields, vacuum tubes, and cryogenic systems.

Optical fibers are generally made of quartz, which means that external electromagnetic interference (EMI) will not affect the fiber as it affects electrical wires. This allows the optical fiber to operate normally, even in a strong EMI environment. In addition, the Sagnac effect is not sensitive to the translational motion in the detection plane but only to the rotational motion of the plane [21]. This makes a FOG, which is based on the Sagnac effect and uses optical fibers as a medium, a rotational motion sensor with strong environmental adaptability. If FOG can be used in gravimetry, a new solution to the problem of environmental adaptability in existing gravity measurement instruments will be yielded.

As the first attempt to apply gyroscopes to gravimetry, the research group in Peking University designed a structure based on two test masses. It used FOG to detect rotational motion due to gravity gradients [44]. As shown in Figure 11, the spatial distribution of the gravity field is inhomogeneous due to the existence of gravity gradient, which generates torque on the rotor by changing the gravity of the test masses at two different positions in space. This torque generates the rotational motion of the rotor and is detected by the FOG. The gravity gradient can be obtained by the relationship between the angular acceleration of rotation and the gravity gradient [44].

Figure 11.

Schematic diagram of the gravity gradient sensitive structure based on the fiber-optic gyroscope.

As shown in Figure 12, without the installation of a seismic isolation platform, magnetic shield, vacuum chamber, and other environmental control equipment, the self-noise level of the proposed system is estimated to be $1\times {10}^{-2}\mathrm{E}/\sqrt{\mathrm{Hz}}$ [$1\mathrm{E}\equiv {10}^{-9}{\mathrm{s}}^{-2}$, where E (Eötvös) is a unit of gravity gradient]. Moreover, the self-noise of this system decreases at smaller frequencies, suggesting that long-term observations will have lower self-noise. Considering that the experimental results were observed in the nonideal experimental environment of room temperature, nonvibrational isolation, and nonmagnetic isolation, the proposed scheme has an optimistic prospect of performance improvement. For seismic isolation, the method of differential-mode measurement can be used, using two rotors with FOG to suppress vibration in the environment [45]. At the same time, the self-noise in FOGs can be further suppressed by means of differential-mode measurements. For the temperature and magnetic field variation in the surrounding environment, on the one hand, high-order modulation can be used to reduce the temperature sensitivity of the FOG [46]; on the other hand, dual-polarization configuration can be used to improve the adaptability of the FOG to temperature and magnetic field [47, 48].

Figure 12.

Noise root power spectral density of static observations of FOG-based gravity gradient measurement system.

5. Conclusions

Gyroscopes have had an indissoluble relationship with geophysics since they were manufactured. With the development of gyroscopes, high-precision gyroscopes, especially optical ones, have become powerful tools for geophysical applications. In summary, the role of gyroscopes can be divided into two categories: direct and indirect measurements. In terms of direct measurements, such as the acquisition of the rotational component of seismic waves, observations of Earth’s rotation, etc., it relies on the high-precision and high sensitivity properties of gyroscopes. In indirect measurements, such as the measurement of the rotational motion of a sensing probe for gravity field, the high sensitivity with strong environmental adaptability of gyroscopes is required. In the future, in terms of direct measurements, continued progress in reducing noise and improving the performance of gyroscopes will enable more precise measurements of geophysical parameters; in indirect measurements, new sensing principles based on gyroscope should continue to be explored, bringing the advantages of gyroscope, especially the strong environmental adaptability, into play in geophysical applications.