Gravity Measurements Research Articles

A long-term charge/discharge cycle at Mt. Etna volcano revealed through absolute gravity and GPS measurements

We present results of repeated absolute gravity and GPS measurements, carried out at Mt. Etna volcano between 2009 and 2018. Absolute gravity measurements are rarely performed along arrays of stations on active volcanoes and, through our unprecedented dataset, we highlight the possibilities of this method to track underground mass changes over long time-scales. Analysis of the residual absolute gravity data and ground deformation reveals a cycle of gravity increase and uplift during 2009 to 2011, followed by gravity decrease and subsidence during 2011 to 2014. Data inversion points to a common mass and pressure source, lying beneath the summit area of the volcano, at depth of ~ 5 km b.s.l. The bulk volume change inferred by the inversion of the deformation data can account for only a small portion of the mass change needed to explain the correspondent gravity variations. We propose that the observed relationship between gravity and vertical deformation was mostly due to the compressibility of the magma in the inferred reservoir, which, in turn, was enhanced by the presence of exsolved gas. Overall, the gravity and deformation data we present reveal a cycle of magma recharge (2009–2011) and discharge (2011–2014) to/from the inferred storage zone. During the recharge phase only degassing occurred from the summit craters of Mt. Etna. During the following phase of discharge, the magma lost from the reservoir at ~ 5 km b.s.l. fed the exceptional phase of volcanic activity during 2011–2014, when tens of lava fountaining episodes took place.

Delineating a volcanic aquifer using groundwater-induced gravity changes in the Tatun Volcano Group, Taiwan

The Tatun Volcanic Group (TVG) is an active volcanic system that poses potential volcanic hazards to northern Taiwan. Groundwater migration can be sensitive to volcanic activities and can induce temporal gravity changes. Here we conducted four gravity measurement campaigns in 2012 with two CG5 relative gravimeters at a total of 31 gravity monitoring sites to probe the spatiotemporal groundwater variability in the TVG area. With careful adjustments to the gravity measurements, the standard point gravity error was approximately 8 μGal on average. The observed gravity changes were compared with the groundwater-induced gravity variations derived from two hydrological models: the continuous flow model that consisted of one permeable layer (Model A) and a dynamic groundwater flow model that used the hydrological solver MODFLOW (Model B). The results show that only gravity observations in the central TVG match the simulated gravity pattern, i.e., the hydrology in the central TVG follows free groundwater flows within the interconnected and porous strata. On the other hand, inconsistencies between simulated and observed gravity changes range from + 40 to – 80 μGal. The discrepancies were located at the eastern and western areas in the TVG and showed opposite variations over time. This pattern of temporal variability cannot be attributed to the use of shallow aquifer models that merely reflect the surface recharges and discharges. We infer that the pattern stems from deep flows, such as hydrothermal fluids alternately replenishing aquifers to the east and west of the TVG, i.e., deep fluid conduits may have developed to the east and west of the TVG and bypassed the central area.

Apparatuses for verifying the precision of gravimeters with lifting spherical source masses.

Two apparatuses with lifting spherical source masses are built and used to verify the precision of gravimeters. The 333-kg source mass produces a maximum acceleration of 200 nm/s2 with an uncertainty of 0.31 nm/s2, which corresponds to a relative uncertainty of 0.16%. After evaluating the temperature effect, drift of the gravimeter, the atmospheric effect, and the tidal effect, a combined uncertainty of 1 nm/s2 is obtained. One CG6 gravimeter is tested using two apparatuses, the measured accelerations agree with the theoretical values within the error range. Differential measurement with two CG6 gravimeters on one apparatus is performed, which provides a common-mode rejection of the effects due to ambient noise, such as the gravity tide, atmospheric effect, and drift. The difference in acceleration measured by the two gravimeters is determined to be 199 ± 6 nm/s2, which agrees well with the value 200 ± 1 nm/s2 obtained by using apparatus II. Our apparatuses provide a verification of the precision of gravimeters with an uncertainty of 1 nm/s2, which is one of the lowest uncertainties reached so far. The determination of geometrical metrology and mass distribution and detailed error analysis are presented. The methods on error analysis as well as differential measurement used in our work are helpful for gravity measurement.

A review of high-performance MEMS sensors for resource exploration and geophysical applications

MEMS sensors have the advantages of small volume, lightweight, and low cost, therefore, have been widely used in the fields of consumer electronics, industry, health, defence, and aerospace. With their ever-improving performance, MEMS sensors have also started to be used in resource exploration and geophysical applications. However, the requirements of high-precision MEMS sensors for geophysical applications have not been specified in detail. Therefore, this paper systematically analyzes the requirements of high-performance MEMS sensors for prospecting and geophysical applications, including seismic surveillance, Earth tide, volcanic activity monitoring for natural disasters; seismic, gravity, and magnetic resource prospecting; drilling process monitoring and local gravity measurement for gravity aided navigation. Focusing on the above applications, this paper summarizes the state-of-the-art of research on high-performance MEMS sensors for resource exploration and geophysical applications. Several off-the-shelf MEMS sensors have been used for earthquake monitoring, seismic exploration and drilling process monitoring, and a range of MEMS research prototype sensors have successfully been employed for Earth tides measurement and are promising to be used for gravity exploration. MEMS magnetometers should have a lower noise floor to meet the demand for magnetic exploration. MEMS gravity gradiometers are still under early development and will not be deployable in short-term. High-performance MEMS sensors hold the advantages of low-cost, high integration, and capability of working in extreme environments; therefore, they are likely to gradually replace some conventional geophysical instruments in some application areas.

Effect of Magnetic Shielding on Levitation Characteristics of Superconducting Gravimeter

The superconducting gravimeter is currently the most accurate instrument in relative gravity measurement, so the high-precision calculation and analysis of superconducting magnetic levitation system is crucial to the development work of superconducting gravimeter. Shielding material can weaken the influence of external magnetic field source fluctuation on the internal levitation magnetic field and provide a stable electromagnetic environment for the magnetic levitation system. But at the same time, shielding material will also have an impact on the internal suspended magnetic field itself, which will lead to large deviations in the study of electromagnetic characteristics of the magnetic levitation system. This article establishes and optimizes the simulation calculation model of a superconducting gravimeter magnetic levitation system based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> method, and studies the effect of magnetic shielding on the magnetic field, levitation force, and magnetic force gradient of the internal levitation system. After that, the simulation calculation results are compared with the experimental results, and the simulation calculation error of superconducting levitation force and magnetic gradient is less than 1%, which verifies the correctness of the optimized simulation model. This study is an important guide for the accurate calculation of the electromagnetic properties of all superconducting systems containing magnetic shielding materials, such as superconducting gravimeter, superconducting gravity gradiometer, etc.

A review of the 19th International Symposium on geodynamics and earth tide, Wuhan 2021

Modern geodetic technologies such as high-precision ground gravity measurements, satellite gravity measurements, the global navigation satellite system, remote sensing methods, etc. provide rich observation data for monitoring various geodynamic processes of the global Earth and its surface. The 19th International Symposium on Geodynamics and Earth Tides brought together scientific researchers from 26 countries around the world, shared the application of various measurements in different geoscience issues, covering Earth tidal deformation, oceanic and atmospheric loading effects, earthquake cycle, hydrology, Earth rotation changes, etc., and provided a precious exchange platform for global peers.

Minimal and maximal lengths of quantum gravity from non-hermitian position-dependent noncommutativity

A minimum length scale of the order of Planck length is a feature of many models of quantum gravity that seek to unify quantum mechanics and gravitation. Recently, Perivolaropoulos in his seminal work (Perivolaropoulos in Phys. Rev. D 95:103523, 2017) predicted the simultaneous existence of minimal and maximal length measurements of quantum gravity. More recently, we have shown that both measurable lengths can be obtained from position-dependent noncommutativity (Lawson in J. Phys. A Math.Theor. 53:115303, 2020). In this paper, we present an alternative derivation of these lengths from non-Hermitian position-dependent noncommutativity. We show that a simultaneous measurement of both lengths form a family of discrete spaces. In one hand, we show the similarities between the maximal uncertainty measurement and the classical properties of gravity. On the other hand, the connection between the minimal uncertainties and the non-Hermicity quantum mechanic scenarios. The existence of minimal uncertainties are the consequences of non-Hermicities of some operators that are generators of this noncommutativity. With an appropriate Dyson map, we demonstrate by a similarity transformation that the physically meaningfulness of dynamical quantum systems is generated by a hidden Hermitian position-dependent noncommutativity. This transformation preserves the properties of quantum gravity but removes the fuzziness induced by minimal uncertainty measurements at this scale. Finally, we study the eigenvalue problem of a free particle in a square-well potential in these new Hermitian variables.

Calculation method for deflection of the vertical based on path gravity anomaly compensation

To solverole inefficiency and complete autonomy issues for deflection of the vertical (DOV) determination in geomatics, navigation, and military weapon launching fields, a calculation method based on path compensation has been proposed. After conducting the discretization of the Vening-Meinesz formula in the spherical surface, a novel path gravity anomaly compensation based on the ‘remove–restore’ algorithm was formulated to satisfy the requirement of regional high-precision gravity anomaly data. Meanwhile, utilizing the European Improved Gravity model of Earth by New techniques (EIGEN-6c4), the DOV was calculated using the Vening-Meinesz formula based on the ‘remove–restore’ method, unlike the previous regional direct integral calculations. Finally, to verify the reliability and feasibility of the algorithm, the gravity measurement system, consisting of the high-precision gravimeter and strapdown inertial navigation system, was constructed to conduct the simulation and shipborne experiments. The simulation and experiment results of the proposed method show that the root mean squares, relative to the real values, of DOV calculation components, are 0.89″ and 1.67″, while standard deviation values of the DOV components are the same within 2″ in experiments, which satisfies the precision requirement of the DOV.

Gravity Without Newton’s Gravitational Constant and No Knowledge of the Mass Size

In this paper, we show that the Schwarzschild radius can be extracted easily from any gravitationally-linked phenomena without having knowledge of Newton’s gravitational constant or the mass size of the gravitational object. Further, the Schwarzschild radius can be used to predict a long series of gravity phenomena accurately, again without knowledge of Newton’s gravitational constant and also without knowledge of the size of the mass, although this may seem surprising at first. Hidden within the Schwarzschild radius are the more fundamental mass of the gravitational object, the Planck length, which we will assert contain the secret essence related to gravity, in addition to the speed of light (the speed of gravity). This seems to support that gravity is quantized, even at the cosmological scale, and this quantization is directly linked to the Planck units. This also supports our view that Newton’s gravitational constant is a universal composite constant of the form G = l2pc3/h , rather than relying on the Planck units as a function of G. This does not mean that Newton’s gravitational constant is not a universal constant, but rather that it is a composite universal constant, which depends on the Planck length, the speed of light, and the Planck constant. This is, to our knowledge, the first paper1 that shows how a long series of major gravity predictions and measurements can be completed without any knowledge of the mass size of the object, or Newton’s gravitational constant. At minimum, we think it provides an interesting new angle for evaluating existing theories of gravitation.

A gravimetric assessment of the Gotthard Base Tunnel geological model: insights from a novel gravity terrain-adaptation correction and rock physics data

The Gotthard Base Tunnel (GBT) is a 57 km long railway tunnel, constructed in the Central Alps in Switzerland and extending mainly North–South across numerous geological units. We acquired 80 new gravity data points at the surface along the GBT profile and used 77 gravity measurements in the tunnel to test and constrain the shallow crustal, km-scale geological model established during the tunnel construction. To this end, we developed a novel processing scheme, which computes a fully 3D, density-dependent gravity terrain-adaptation correction (TAC), to consistently compare the gravity observations with the 2D geological model structure; the latter converted into a density model. This approach allowed to explore and quantify candidate rock density distributions along the GBT modelled profile in a computationally-efficient manner, and to test whether a reasonable fit can be found without structural modification of the geological model. The tested density data for the various lithologies were compiled from the SAPHYR rock physical property database. The tested models were evaluated both in terms of misfit between observed and synthetic gravity data, and also in terms of correlation between misfit trend and topography of the target profile. The results indicate that the locally sampled densities provide a better fit to the data for the considered lithologies, rather than density data averaged over a wider set of Alpine rock samples for the same lithology. Furthermore, using one homogeneous and constant density value for all the topographic corrections does not provide an optimal fit to the data, which instead confirms density variations along the profile. Structurally, a satisfactory fit could be found without modifying the 2D geological model, which thus can be considered gravimetry-proof. From a more general perspective, the gravity data processing routines and the density-dependent corrections developed in this case study represent a remarkable potential for further high-resolution gravity investigations of geological structures.

The formation of the 8˚20’ N seamount chain, east pacific rise

Near-axis seamounts provide a unique setting to investigate three-dimensional mantle processes associated with the formation of new oceanic crust and lithosphere. Here, we investigate the characteristics and evolution of the 8˚20’N Seamount Chain, a lineament of seamounts that extends ~ 175 km west of the East Pacific Rise (EPR) axis, just north of the fracture zone of the Siqueiros Transform Fault. Shipboard gravity, magnetic, and bathymetric data acquired in 2016 are utilized to constrain models of seamount emplacement and evolution. Geophysical observations indicate that these seamounts formed during four distinct episodes of volcanism coinciding with changes in regional plate motion that are also reflected in the development of intra-transform spreading centers (ITSCs) along the Siqueiros transform fault (Fornari et al. 1989; Pockalny et al. 1997). Although volcanism is divided into distinct segments, the magnetic data indicate continuous volcanic construction over long portions of the chain. Crustal thickness variations along the chain up to 0.75 km increase eastward, inferred from gravity measurements, suggest that plate reorganization has considerably impacted melt distribution in the area surrounding the Siqueiros-EPR ridge transform intersection. This appears to have resulted in increased volcanism and the formation of the 8˚20’N Seamounts. These findings indicate that melting processes in the mantle and subsequently the formation of new oceanic crust and lithosphere are highly sensitive to tectonic stress changes in the vicinity of fast-spreading transform fault offsets.

The absolute gravity measurements from A10 along the 1240 km route in East Antarctica

The absolute gravity measurements from A10 along the 1240 km route in East Antarctica

All-fiber heterodyne velocity and displacement interferometer based on DPLL Doppler tracking with sub-nanometer per second and picometer sensitivity.

Velocity and displacement measurements play an important role not only in the process of industrial production and metrology on the ground but also in satellite gravity measurement in space. A high-precision all-fiber heterodyne velocity and displacement interferometer based on digital phase-locked loop (DPLL) Doppler tracking is proposed in this paper. The target velocity is measured by tracking the heterodyne frequency changes of the beat-note signal, and the displacement is obtained by the integrated phase of the Doppler frequency change. A dual-signal differential optical-path scheme combined with DPLL signal tracking technology enables high-precision and high-linearity measurement of velocity and displacement simultaneously. For integration and compactness, the interferometer uses all-fiber optics that are packaged in a small box with dimensions of 150×150×70m m 3, except for an externally fiber-connected collimator as the sensor head. The experimental results show a velocity sensitivity below 30p m/s/H z 1/2 in the 0.03-2Hz band and a displacement sensitivity below 10p m/H z 1/2 above 0.4Hz.

Modeling the gravitational effects of ocean tide loading at coastal stations in the China earthquake gravity network based on GOTL software

Abstract The gravitational effects of ocean tide loading, which are one of the main factors affecting gravity measurements, consist of three components: (1) direct attraction from the tidal water masses, (2) radial displacement of the observing station due to the tidal load, and (3) internal redistribution of masses due to crustal deformation. In this study, software for gravitational effects of ocean tide loading was developed by evaluating a convolution integral between the ocean tide model and Green’s functions that describe the response of the Earth to tide loading. The effects of three-dimensional station coordinates, computational grid patterns, ocean tide models, Green’s functions, coastline, and local tide gauge were comprehensively considered in the programming process. Using a larger number of high-precision coastlines, ocean tide models, and Green’s functions, the reliability and applicability of the software were analyzed at coastal stations in the China Earthquake Gravity Network. The software can provide the amplitude and phase for ocean tide loading and produce a predicted gravity time series. The results can effectively reveal the variation characteristics of ocean tide loading in space and time. The computational gravitational effects of ocean tide loading were compared and analyzed for different ocean tide models and Green’s functions. The results show that different ocean tide models and Green’s functions have certain effects on the calculated values of loading gravity effects. Furthermore, a higher-precision local ocean tide model, digital elevation model, and local tidal gauge record can be further imported into our software to improve the accuracy of loading gravity effects in the global and local zones. The software is easy to operate and can provide a comprehensive platform for correcting the gravitational effects of ocean tide loading at stations in the China Earthquake Gravity Network.

Long time series of absolute gravity observations in Kulusuk, southeast Greenland

AbstractThis report contains terrestrial absolute gravity measurements performed near the village of Kulusuk in southeast Greenland. It represents an exceptionally long time series of nearly two decades. The measurements began in July 1996 until July 2015. The station is located a few meters beside a permanent GNSS station. The final gravity values (g‐values), more precisely the accelerations due to gravity, are listed along their associated uncertainties. A description of the station, a short explanation on the absolute gravimeter, and the data processing are presented.

Zonal winds in the gas planets driven by convection above a stably stratified layer

ABSTRACT The analysis of the recent gravity measurements of Jupiter and Saturn reveal that the zonal winds observed on their surfaces reach several thousand kilometres deep into their atmospheres. However, it remains unclear which mechanism prevents them from penetrating deeper. Recent models suggest that a stably stratified region would yield the desired effect. In this numerical study we systematically explore the dynamics of flow in a rotating spherical shell where the lower third is stably stratified while convection in the outer region drives multiple zonal winds, similar to those observed on Jupiter or Saturn. When using a rigid lower boundary condition, only an equatorial jet pair is formed without an underlying stable layer. When including a stable layer, fierce multiple jets also develop at mid to high latitudes, once the stable stratification is strong enough to effectively decouple the jet dynamics from the lower boundary. We find that the decay of the jet amplitude near the stable layer boundary is controlled by Ω/N, where Ω is the rotation rate and N the Brunt-Väisälä frequency that quantifies the degree of stable stratification. Furthermore, the penetration distance of the jets is proportional to the jet width. In the convective region, the winds are invariant along the axis of rotation, whereas their extension in the stable layer tends to become radially aligned.

Compact single-seed, module-based laser system on a transportable high-precision atomic gravimeter

A single-seed, module-based compact laser system is demonstrated on a transportable 87Rb-based high-precision atomic gravimeter. All the required laser frequencies for the atom interferometry are provided by free-space acousto-optic modulators (AOMs) and resonant electro-optic phase modulators (EOMs). The optical phase-locked loop between the two optical paths derived from the same laser provides an easy frequency manipulation between two laser frequencies separated by the hyperfine frequency of 6.835 GHz using an AOM and an EOM, respectively. Our scheme avoids parasite Raman transitions present in the direct EOM modulation scheme (modulating directly at the frequency of the hyperfine splitting), which have detrimental effects on the accuracy of the gravity measurements. The optical phase-locked loop also provides a convenient way for vibration compensation through the Raman lasers' phase offset. Furthermore, the modular design approach allows plug-and-play nature on each individual optic module and also increases the mechanical stability of the optical systems. We demonstrate high-precision gravity measurements with 17.8 μGal stability over 250 s averaging time and 2.5 μGal stability over 2 h averaging time.

An atomic gravimeter dynamic measurement method based on Kalman filter

The atomic gravimeter is an innovative quantum sensor featuring high precision, great sensitivity, and lasting stability. Currently, one research focus is on the combination of the atomic gravimeter with an accelerometer to implement dynamic measurements and gather gravity information in a real-time and highly precise manner. The Kalman filter framework was utilized with gravity and accelerometer drift as its states to observe the outputs of the atomic gravimeter and accelerometer, and the fusion of their data is realized. It can restrain the influence of dynamic vibration noise and obtain high precision gravity information in real time. Moreover, the accelerometer drift was estimated and compensated for, so as to enhance the lasting stability of the system. Laboratory static, swing platform and lake navigation tests were carried out to verify the effectiveness and feasibility of the proposed method. As revealed in the static test, the proposed method could effectively inhibit the effect of noise, and enhance the precision of gravity measurement. After making a compensation for drift, the noise coefficients of the accelerometer, including the bias stability (B), acceleration random walk (K), and rate ramp (R) decreased noticeably. The swing platform test further verified the applicability of the proposed method in dynamic conditions. As proved in the lake test, better results were obtained at a maximum velocity of 8.5 km h−1. The gravity from the high-precision strap-down gravimeter on the same boat was taken as the reference, and processed to obtain the residual error of 2.03 ± 7.12 mGal, so that the proposed method was superior to the offline 300 s smooth filter. The proposed method offers a new approach for the study of atomic gravimeter dynamic measurement.

Решение задачи Молоденского по чистым аномалиям силы тяжести с относительной ошибкой порядка квадрата сжатия

The solution of the geodetic boundary value problem for determining the anomalous potential from gravity measurements in the spherical approximation, taking into account the relief and compression, was developed in sufficient detail in 1960 and is also based on the results of G. G. Stokes. Flattening of the reference surface was taken into account by D. V. Zagrebin in several works dated 1940–1970; in 1956 M. S. Molodensky proposed a simpler method for an oblate ellipsoid, based on the already known one for a sphere. It turned out that at the very beginning of developing the mentioned solution, an error was made when obtaining the derivative of the reciprocal distance between two points on the ellipsoid in the direction of the outward normal; later it was repeated in issue 131 of the Proceedings of the TsNIIGAiK. That inaccuracy did not influence the conclusions of V. V. Brovar in 1996 and 1999, where the relief was added to the consideration of compression. This solution of Molodensky’s problem, taking the compression into account, was seldom used, and that is probably why the mistake went unnoticed. V. V. Popadyev saw it and found the correct expression for the mentioned derivative, I. I. Mezhenova adapted subsequent conclusions for the gravity disturbances.

Methods for Underwater Gravity Measurement Error Compensations Based on Correlation Analysis

The measurement of Earth’s gravitational field is important in geophysics, geodynamics, geodesy, oceanography, and space science. The ocean covers 71% of the earth’s surface; therefore, measuring the ocean’s gravitational field is crucial. Compared with shipborne gravimetry, underwater gravimetry near the seafloor is closer to gravity sources and can obtain short-wavelength gravity information that is useful for small-scale deposit detection and seawater intrusion monitoring. This article focuses on gravimetric errors caused by the poor dynamics of the carrier; an error compensation method for underwater gravimetry based on correlation analysis is proposed. By analyzing the error sources that affect the dynamics of the carrier, the relationship between the gravimetry error and impact factors related to the dynamics was established, and the model’s parameters were estimated by the least-squares fitting method. The experimental data show that this method can effectively compensate for gravimetric errors caused by carrier dynamics and provide the theoretical basis and algorithm model for underwater gravimetry in the bottom-tracking mode.