Local Gravity Field Research Articles

Crustal Apparent Density Variations in the Middle Segment of the North Tianshan Mountains and Their Tectonic Significance

In this study, we collected mobile gravity observations in the middle segment of the North Tianshan Mountains from August 2016 to July 2022 and carried out classical adjustment calculations under the constraint of the absolute gravity datum to obtain the spatiotemporal variation pattern of the local gravity field. We used equivalent source inversion to obtain the spatiotemporal variation characteristics of crustal apparent density. We also extracted the coseismic deformation field from SAR data, using the 2016 Hutubi earthquake as an example, and constructed a model of the seismogenic fault. The gravity monitoring network in the study area performed well in resolving the earthquake source parameters. Both the time-varying gravity field and equivalent apparent density variation pattern show prominent zoning characteristics with a smoothly evolving spatial distribution over time. The variation trends of the gravity field and equivalent apparent density are in line with the orientation of tectonic structures, and their anomalous signals can be detected before and after an earthquake. The constructed seismogenic structure of the 2016 Hutubi earthquake indicates a typical thrust earthquake, probably occurring on a north-dipping blind fault beneath a region with intense crustal deformation. The subsurface tectonic system reflected by this earthquake can be informatively extended to the entire middle segment of the North Tianshan Mountains by subsurface configuration. Our findings can serve as a reference for analyzing the source characteristics of the time-varying gravity field and interpreting anomalous pre-seismic signals, and aid in understanding earthquake preparation zones and the mode of crustal tectonic movements.

Parallel Multiple Methods with Adaptative Decision Making for Gravity-Aided Navigation

Gravity-aided navigation is an effective navigation method for underwater vehicles. However, the distribution of the gravity field may affect the measurement errors of gravity anomalies and the precision of gravity-aided navigation. In this paper, the upper and lower thresholds of the gravity field standard deviation are computed by the statistical properties of the local gravity field to classify each grid in the gravity map into different levels. A parallel multiple methods with adaptive decision making (PMMADM) for gravity-aided navigation is proposed which incorporates the gravity anomaly measurements, particle filtering, and maximum correlation method into the observation equation of the extended Kalman filter. The algorithm autonomously selects the observation variables in the filter by combining the gravity field standard deviation at the current position of the carrier with a decision tree. This approach can combine the characteristics of different gravity matching algorithms, reduce the impact of random noise in the measurements, and improve the positioning accuracy of gravity-aided navigation. Physical simulation experiments demonstrated that the proposed gravity matching algorithm achieves the high navigation accuracy and long-term stability in different gravity fields, and the mean value of positioning error is 620.72 m.

Gravity field modelling in mountainous areas by solving the nonlinear satellite-fixed geodetic boundary value problem with the finite element method

The paper concerns a novel concept based on the iterative approach applied for solving the nonlinear satellite-fixed geodetic boundary value problem (NSFGBVP) using the finite element method (FEM). We formulate the NSFGBVP that consists of the Laplace equation defined in the 3D bounded domain outside the Earth, the nonlinear boundary condition (BC) prescribed on the disretized Earth’s surface, and the Dirichlet BC given on a spherical boundary placed approximately at the altitude of GOCE satellite mission and additional four side boundaries. The iterative approach is based on determining the direction of actual gravity vector together with the value of the disturbing potential. Such a concept leads to the first iteration where the oblique derivative boundary value problem is solved, and the last iteration represents the approximation of the actual disturbing potential and the direction of gravity vector. As a numerical method for our approach, we implement the FEM with triangular prisms. High-resolution numerical experiments deal with the local gravity field modelling in the Andean, Himalayan and Alpine mountain range, where we focus on the contribution to the disturbing potential solution by solving the nonlinear geodetic boundary value problem in comparison with the solution to the oblique derivative geodetic boundary value problem. The obtained results showed the maximal contribution of the presented approach 0.0571 [{text{m}}^{{text{2}}} {text{s}}^{{{text{ - 2}}}}] (Andes), 0.0702 [{text{m}}^{{text{2}}} {text{s}}^{{{text{ - 2}}}}] (Himalayas), 0.0066 [{text{m}}^{{text{2}}} {text{s}}^{{{text{ - 2}}}}] (Alps) in the disturbing potential, that is located in the areas of the highest values of the deflection of vertical.

Using a SPATIAL INS/GNSS MEMS Unit to Detect Local Gravity Variations in Static and Mobile Experiments: First Results.

In this study, we present the feasibility of using gravity measurements made with a small inertial navigation system (INS) during in situ experiments, and also mounted on an unmanned aerial vehicle (UAV), to recover local gravity field variations. The INS operated is the SPATIAL one developed by Advanced Navigation, which has three-axis accelerometers. When the temperature bias is corrected, these types of INS are powerful enough to present the periodic signal corresponding to the solid Earth tides. There is also a clear correlation with the data measured at different altitudes by a CG5 gravimeter. However, these data were recorded on static points, so we also studied the INS in a moving platform on a UAV. Because there are a lot of vibrations recorded by the INS (wind, motor, on-board computer), the GPS and accelerometric data need to be filtered extensively. Once the data are corrected so they do not show thermal bias and low-pass filtered, we take the second derivative of the altitude (GPS) data to find the radial accelerometry of the drone and compare it to the radial accelerometry measured directly by the INS, in order to isolate the accelerometric signal that is related to the area that is being studied and the altitude. With a high enough precision, this method could be used to obtain the gravity variations due to the topography and density variations in the ground.

Results from the Third QDaedalus Astrogeodetic System Observation Campaign in the Mountainous Terrain of the Surses Region in Switzerland

This study presents the results of an astrogeodetic survey campaign conducted in the mountainous terrain of the Surses region in Switzerland. In our third astrogeodetic campaign using the QDaedalus system, we observed new deflections of the vertical (DoV) using three astrogeodetic systems. These observations were used to validate DoV data derived from the Global Gravity Model GGMplus and the Swiss Geoid model CHGeo2004. Astrogeodetic observations were conducted at 15 benchmarks (BMs) along the astrogeodetic profile over five nights in June 2021 at elevations ranging from 1,185 to 1,800 m and a station spacing of about 1 km. This is the first time two TS60 total station-based QDaedalus systems and one zenith telescope-based COmpact DIgital Astrometric Camera (CODIAC) system were used together for an astrogeodetic observation campaign. The standard deviations (SDs) of the QDaedalus system data for each session were 0.04″–0.22″ and 0.01″–0.20″ for the N–S and E–W components, respectively, while the SDs of the CODIAC system for each session were 0.02″ for both components. These high quality data were compared to DoV data derived from GGMplus and CHGeo2004. The N–S components from GGMplus exhibited large residuals ranging from −2.31″ to 1.75″, while the E–W component residuals are from −0.27″ to 1.80″. The residuals from CHGeo2004 range from −0.60 to 1.21 for the N–S components and −1.01 to 0.32 for the E–W components. These results show that the derived DoV data from CHGeo2004 are closer to the observed DoV and more accurate than the global GGMplus model that does not incorporate local gravity field data. The first and second astrogeodetic observation campaigns were conducted in the coastal terrain of Istanbul, Turkey and in the flat terrain in the Munich region, Germany, respectively. In this study, we provide an overall comparison of these previous results to the GGMplus residuals. Our latest results show that the GGMplus model is of higher quality in the Surses mountainous terrain than in the coastal terrain of Istanbul, while it is of lower quality than in the flat terrain of the Munich region.

Insights into the Magmatic Feeding System of the 2021 Eruption at Cumbre Vieja (La Palma, Canary Islands) Inferred from Gravity Data Modeling

This study used spatiotemporal land gravity data to investigate the 2021 eruption that occurred in the Cumbre Vieja volcano (La Palma, Canary Islands). First, we produced a density model by inverting the local gravity field using data collected in July 2005 and July 2021. This model revealed a low-density body beneath the western flank of the volcano that explains a highly fractured and altered structure related to the active hydrothermal system. Then, we retrieved changes in gravity and GNSS vertical displacements from repeated measurements made in a local network before (July 2021) and after (January 2022) the eruption. After correcting the vertical surface displacements, the gravity changes produced by mass variation during the eruptive process were used to build a forward model of the magmatic feeding system consisting of dikes and sills based on an initial model defined by the paths of the earthquake hypocenters preceding the eruption. Our study provides a final model of the magma plumbing system, which establishes a spatiotemporal framework tracing the path of magma ascent from the crust–mantle boundary to the surface from 11–19 September 2021, where the shallowest magma path was strongly influenced by the low-density body identified in the inversion process.

Local gravity field modeling using gravity difference observations along the line of sight of the GRACE-FO satellites and adjusted spherical cap harmonic basis functions

Local gravity field modeling using gravity difference observations along the line of sight of the GRACE-FO satellites and adjusted spherical cap harmonic basis functions

The European GeoMetre project: developing enhanced large-scale dimensional metrology for geodesy

We provide a survey on the joint European research project “GeoMetre”, which explores novel technologies and their inclusion to existing surveying strategies to improve the traceability of geodetic reference frames to the SI definition of the metre. This work includes the development of novel distance meters with a range of up to 5 km, the realisation of optical multilateration systems for large structure monitoring at an operation distance of 50 m and beyond, and a novel strategy for GNSS-based distance determination. Different methods for refractivity compensation, based on classical sensors, on dispersion, on spectroscopic thermometry, and on the speed of sound to reduce the meteorological uncertainties in precise distance measurements, are developed further and characterised. These systems are validated at and applied to the novel European standard baseline EURO5000 at the Pieniny Kippen Belt, Poland, which was completely refurbished and intensely studied in this project. We use our novel instruments for a reduced uncertainty of the scale in the surveillance networks solutions for local tie measurements at space-geodetic co-location stations. We also investigate novel approaches like close-range photogrammetry to reference point determination of space-geodetic telescopes. Finally, we also investigate the inclusion of the local gravity field to consider the deviations of the vertical in the data analysis and to reduce the uncertainty of coordinate transformations in this complex problem.

A bubble-based demonstration of free-fall weightlessness

According to the equivalence principle, there is no local gravity field inside free-falling systems. Consequently, all gravity-related forces disappear. Among them is the buoyant force. The absence of the buoyant force in free-falling systems was previously shown in various published demonstrations.

Computationally Effective Gravity Inversion Allows for High-Resolution Regional Density Modeling of Earth's Crust with the Inclusion of the Topography Layer

The problem of inverting measured gravity data for large regions is of a great importance for planetary structure studies. Unfortunately, the usual methods of local gravity field inversion do not scale up well. There are three primary factors that start to play significant role: topography or terrain surface with large height differences, spherical geometry of the planet, and high computational complexity. In our previous work we were separately considering each of those problems in detail. In this paper however, we will address those issues simultaneously, offering a complete and computationally effective method of recovering spherical density model of Earth's crust with the upper topography layer. The method utilizes a closed form expression for the discretized model's gravity field which allows for great accuracy and speed without enforcing restrictions on model geometry or gravity field data grid. Inversion process is based on the conjugate gradient method. An example of inversion for a synthetic regional model is presented.

Gravity field changes during deep exploitation of the coal longwall and their relation to stress distribution and seismic activity

Mining operations cause volumetric deformations within the rock mass and changes in its density, to which the gravimetric method is sensitive. These changes are particularly well seen in periodic measurements of the local gravity field. The paper analyses the relationship between the movement of a longwall in a coal seam and the change in the distribution of the gravity field in time and space observed on the ground surface. Relative gravimetric measurements were carried out in six series between 2018 and 2020; before the start of coal extraction, with the progress of the longwall and after the cessation of mining. Collected data allowed differential maps of changes in gravity to be plotted. Differential anomalies between the subsequent measurement series, and the reference one were then analysed. The distribution and temporal variations of the anomalies suggest a relationship between changes in density distribution of the rock medium in the longwall overburden, and the change in the stress state in the rock mass caused by the passage of the longwall front. An attempt was made to relate the variability of the state of stresses in the longwall overburden to the intensity of seismic tremors with energy > 10E4 J accompanying longwall exploitation.

Patched Local Lunar Gravity Solutions Using GRAIL Data.

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka‐band range‐rate data with a short‐arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into 12 regions and 2 polar caps, with a resolution of 0.15°×0.15° (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small‐scale features clearly, and can be used in local studies of the structure of the lunar crust.

Simulation of earth gravity field using satellite constellation with variable inclination configuration

Based on a satellite constellation composed of two GRACE-type satellite formations with different inclinations (near polar orbit + low inclination) and the theory of repeat orbit cycle, we discuss the methods for selecting medium-low inclinations for global and local gravity fields. The effects of this constellation configuration on gravity field inversion are comparatively analyzed using a whole-course dynamics simulation. The results show that compared with the single GRACE-type satellite formation, the use of satellite constellations with different inclination configurations improves the gravity solution precision by 34%. The inclusion of multi-directional observations can improve the spatio-temporal resolution of the satellite missions, and yield gravity field solutions with higher isotropic sensitivity. Furthermore, it is necessary to select the optimal low inclination according to the study area, which will have a significant influence on the gravity field solution.

Refinement of Mean Dynamic Topography Over Island Areas Using Airborne Gravimetry and Satellite Altimetry Data in the Northwestern South China Sea

AbstractThe determination of high‐quality mean dynamic topography (MDT) over island areas faces multiple challenges, due to the error in a global geopotential model (GGM) as well as the contaminated waveforms of satellite altimetry data and scarcity of surveyed gravimetric observations. We study the potential to enhance regional quasi‐geoid/MDT over island areas by using recently released satellite altimetric gravity data and airborne gravimetric observations. Numerical experiments over the Paracel Islands in the northwestern South China Sea show that the combination of airborne gravity data enhances the local gravity field, and reduces the errors in the associated quasi‐geoid, in comparison to the result directly derived from a GGM. The results demonstrate that the direct application of a GGM may cause significant oscillations in MDT determination over island areas, by a magnitude exceeding 6 cm. The incorporation of altimetric gravity data slightly reduces these errors; however, the bubble‐like errors are prominent, suggesting that altimetry data alone may be insufficient for high‐accuracy MDT recovery. In contrast, combining airborne gravity data dramatically reduces these oscillations, by a magnitude of several centimeters, indicating that airborne gravimetric surveys may be necessary for MDT determination with centimeter‐level accuracy over coastal/island areas. Further comparison with independent ocean data shows that the geostrophic velocities computed by merging a high‐degree GGM and local airborne gravity data can reconstruct real surface ocean circulation; and the GOCE‐based (Gravity Field and Steady‐State Ocean Circulation Explorer) GGMs may be preferable as the reference models in MDT determination.

On the finite element method for solving the oblique derivative boundary value problems and its application in local gravity field modelling

On the finite element method for solving the oblique derivative boundary value problems and its application in local gravity field modelling

Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment

This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis Attitude Determination (TRIAD), the QUaternion ESTimator (QUEST), the Factored Quaternion Algorithm (FQA), and the Arc-TANgent (ATAN). For the purpose of the error analysis, constant biases in the accelerometer and magnetometer measurements are considered (encompassing, hence, the effect of hard-iron magnetism), in addition to systematic errors in the local gravity and Earth magnetic field models (flux density magnitude, declination angle, and inclination angle). The contributions of this paper are novel closed-form formulae for the residual errors (normality, orthogonality, and alignment errors) developed in the computed Direction Cosine Matrices (DCM). As a consequence, analytical insight is provided into the problem, allowing us to properly compare the performance of the investigated alignment formulations (in terms of ultimate accuracy), as well as to remove some misleading conclusions reported in previous works. The adequacy of the proposed error analysis is validated through simulation and experimental results.

Environmental Influence Analysis of Global Gravity Anomaly Gradient Basing on Neighbourhood Satistics in GIS

A series of abnormal environmental phenomena were found related with local earth gravity field anomaly through statistics and calculation analysis. Gravity anomaly gradient was used to describe gravity anomaly change in local extent. Total of 79% in earth surface gravity anomaly gradient express stable (<30 mGal/Degree), 7.37% area express major gravity anomaly gradient (> 50 mGal/Degree), of 3.43% area gravity anomaly gradient is very high (> 70 mGal/Degree). While gravity anomaly is over 30 mGal/Degree, there will may more easily appear sandstorm, tornadoes and haze weather, if thermodynamic conditions and material conditions are proper. Many natural disasters start from these areas, where gravity anomaly gradient is very high.

Improved measurement model for FG5/X gravimeters

Absolute gravimeters are instruments that realize reference measurements of the free-fall acceleration, at present by tracking the freelyfalling objects using interferometry. The functional model of measurements of absolute gravimeters contains parameters related to the model of the local gravity field as well as to the model of particular instrumental effects. In this paper, we show an improvement of the measurement model of absolute gravimeters based on laser interferometry, by an enhanced description of instrumental effects. Namely, a more precise description of the demodulation of the interferometric signal is presented as well as a newly discovered and explained parasitic signal due to the dropping mechanism of FG5 and FG5X (FG5/X) gravimeters. These improvements can be easily incorporated into the measurement model allowing to obtain more accurate and more stable results for g-values needed for various geophysical and metrological applications requiring the highest level of accuracy.

An Innovative 9-Parameter Magnetic Calibration Method Using Local Magnetic Inclination and Calibrated Acceleration Value

In this paper, an innovative algorithm for Tri-Axial Magnetometers calibration based on the magnetic inclination is proposed. The proposed “Inclination based Calibration method” uses the fact that the angle between the local gravity and magnetic field is invariant hence overcoming the limitations of most existing in-field calibration methods which require nonlinear optimization. This calibration algorithm is formulated as the solution to a linear least square problem. A commonly used 9-parameter model and its associated 12-observation Icosahedron experimental scheme were developed to evaluate its applicability to calibrated Tri-Axial Magnetometers based on measured acceleration and magnetic data. The results show that the algorithm can provide effective calibration results for the magnetic field in both simulation and experiments. In addition, the influence of accelerometers data applied in this algorithm is investigated by simulation and experiment to demonstrate the importance of accelerometers data accuracy. The acceleration value after effective calibration is demonstrated to make an improvement in the estimation results.

Effects of a scalar fifth force on the dynamics of a charged particle as a new experimental design to test chameleon theories

This article describes the dynamics of a charge particle in a electromagnetic field in presence of a scalar fifth force. Focusing to the fifth force that would be induced by a chameleon field, the profile of which can be designed properly in the laboratory, it draws its physical effects on the cyclotron motion of a particle in a static and uniform magnetic field. The fifth force induces a drift of the trajectory that is estimated analytically and compared to numerical computations for profiles motivated by the ones of a chameleon field within two nested cylinders. The magnitude of the effect and the detectability of this drift are discussed to argue that this may offer a new experimental design to test small fifth force in the laboratory. More important, at the macroscopic level it induces a current that can in principle also be measured, and would even allow one to access the transverse profile of the scalar field within the cavity. In both cases, aligning the magnetic field with the local gravity field suppresses the effects of Newtonian gravity that would be several order larger than the ones of the fifth force otherwise and the Newtonian gravity of the cavity on the particle is also argued to be negligible. Given this insight, this experimental set-up, with its two effects -- on a single particle and at the macroscopic level -- may require attention to demonstrate its actual feasability in the laboratory.