Applications In Geodesy Research Articles

The effect of topographic density variations on the geoid and orthometric heights in Hong Kong

Utilizing the adopted average topographic density of 2670 kg/m3 in the reduction of gravity anomalies introduces errors attributed to topographic density variations, which consequently affect geoid modeling accuracy. Furthermore, the mean gravity along the plumbline within the topography in the definition of Helmert orthometric heights is computed approximately by applying the Poincaré-Prey gravity reduction where the topographic density variations are disregarded. The Helmert orthometric heights of benchmarks are then affected by errors. These errors could be random or systematic depending on the specific geological setting of the region where the leveling network is physically established and/or the geoid model is determined. An example of systematic errors in orthometric heights can be given for large regions characterized by sediment or volcanic deposits, the density of which is substantially lower than the adopted topographic density used in Helmert's definition of heights. The same applies to geoid modeling errors. In this study, we investigate these errors in the Hong Kong territory, where topographic density is about 20% lower than the density of 2670 kg/m3. We use the digital rock density model to estimate the effect of topographic density variations on the geoid and orthometric heights. Our results show that this effect on the geoid and Helmert orthometric heights reach maxima of about 2.1 and 0.5 cm, respectively. Both results provide clear evidence that rock density models are essential in physical geodesy applications involving gravimetric geoid modeling and orthometric height determination despite some criticism that could be raised regarding the reliability of these density models. However, in regions dominated by sedimentary and igneous rocks, the geological information is essential in these applications because topographic densities are substantially lower than the average density of 2670 kg/m3, thus introducing large systematic errors in geoid and orthometric heights.

A data-adaptive network design for the regional gravity field modelling using spherical radial basis functions

A high-precision regional gravity field model is significant in various geodesy applications. In the field of modelling regional gravity fields, the spherical radial basis functions (SRBFs) approach has recently gained widespread attention, while the modelling precision is primarily influenced by the base function network. In this study, we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm, and the performance of the algorithm is verified by the observed gravity data in the Auvergne area. Furthermore, the turning point method is used to optimize the bandwidth of the basis function spectrum, which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously. Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model. Compared to the existing methods, the number of SRBFs used for modelling has been reduced by 15.8%, and the time cost to determine the centre positions of SRBFs has been saved by 12.5%. Hence, the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.

Colocation in Time and Space of High-Precision Two-Way Optical and Microwave Observations for Calibration of a Microwave Ranging Link—The ACES Mission Case

The ACES mission of the European Space Agency combines optical and microwave-based geodetic observation techniques with highly accurate atomic clocks to achieve a new level of accuracy for geodesy and fundamental physics applications. In addition, the combination of two high-precision measurement techniques provides an even more exciting insight into their errors. Fundamental physics is particularly interested in experiments that require high precision between the results of the successive passes of a satellite. An example of such an experiment is the determination of gravitational redshift. Geodesy applications, in contrast, require both high accuracy and precision. Especially for applications like precise ranging or time synchronization, all possible error influences must be characterized and determined with high precision. Therefore, electronic delays of microwave link terminals pose a challenge to achieving high accuracy. They must, therefore, be calibrated, and the stability of the electronic delays must be monitored. While optical observation techniques can be calibrated sufficiently on the ground, the calibration of microwave measurements before a launch is not precise enough, and continuous monitoring is also not possible. In this study, four calibration methods were tested, all based on colocating optical and microwave measurements onboard a satellite and on the ground. The results of two methods achieved the required accuracy of 100 ps for time synchronization, with a mean error and standard deviation of better than 4 ps and 55 picoseconds, respectively. Correlations between the measured parameters were identified, and the impact of the different approaches on accuracy was investigated. It will be shown that the satellite-based colocation of two different geodetic observation techniques has clear advantages, and the calibration results achieved the required accuracy for geodetic applications in this simulation study.

Time transfer and significance of vertical land motion in relativistic geodesy applications: a review paper

Determination of the Earth’s gravity field and geopotential value is one of the fundamental topics in physical geodesy. Traditional terrestrial gravity and precise leveling measurements can be used to determine the geopotential values at a local or regional scale. However, recent developments in optical atomic clocks have not only rapidly improved fundamental science but also contributed to applied research. The latest generation of optical clocks is approaching the accuracy level of 10−18 when facilitating atomic clock networks. These systems allow examining fundamental theories and many research applications, such as atomic clocks applications in relativistic geodesy, to precisely determine the Earth’s gravity field parameters (e.g., geopotential values). According to the theory of relativistic geodesy, the frequency difference measured by an optical clock network is related to the gravity potential anomaly, provided that the effects of disturbing signals (i.e., tidal and non-tidal contributions) are filtered out. The relativistic geodesy principle could be used for a practical realization of global geodetic infrastructure, most importantly, a vertical datum unification or realization of height systems. This paper aims to review the background of relativistic (clock-based) geodesy and study the variations of optical atomic clock measurements (e.g., due to hydrology loading and land motion).

External gravitational field of a homogeneous ellipsoidal shell: a reference for testing gravity modelling software

There are numerous applications in geodesy and other geo-sciences in which the gravitational potential effect or other functions of the potential are computed by forward modelling from a given mass distribution. Different volume discretisations, e.g. prisms, tesseroids or mass layers are used. In order to control the numerical realisation of the forward calculation in the practical application, e.g. in reduction tasks, these evaluation programs should be verified against rigorous analytical solutions. In this contribution, a closed analytical solution for the potential of an ellipsoidal shell as a test body is presented. Furthermore, we derive the respective closed formulae for the gravity vector and the gravity gradient tensor. Program implementations of the tesseroid approach are compared on the basis of this ellipsoidal mass arrangement. For the practical usage, fast-converging expansions in spherical harmonics are provided in addition. The derivation of the formulae is based on a closed solution of the potential of a homogeneous ellipsoid for computation points situated on the rotation axis, which then is extended to the external space.

DIRECTIONS OF APPLICATION OF ARTIFICIAL INTELLIGENCE IN GEODESIC MONITORING OF BUILDINGS AND STRUCTURES

The study determined the necessity of using artificial intelligence in solving the tasks of geodetic monitoring of buildings and structures. According to the results of the research, examples of the world experience of involving artificial intelligence in solving various issues of geodetic monitoring were found. The issues of using modern instrument equipment in conducting geodetic monitoring with the use of artificial intelligence are investigated. Therefore, the application of artificial intelligence in geodetic monitoring of buildings and structures can significantly increase the efficiency and accuracy of data collection and analysis, reduce risks and increase the safety of workers and the public, as well as reduce costs and increase the productivity of processes. There are various examples of the application of artificial intelligence in geodetic monitoring of buildings and structures, such as the use of machine learning to predict landslides, the use of autonomous drones to collect data, and automatic image processing systems to detect defects and damage to buildings. The use of artificial intelligence in geodetic monitoring of buildings and structures has great potential for improving the safety, efficiency and productivity of construction processes. In addition, the development of artificial intelligence and its application in geodesy can help solve complex tasks, such as predicting floods, earthquakes and other dangerous phenomena related to geodesy and construction. The application of artificial intelligence can also increase the accuracy and reliability of surveying and mapping, which can be useful for solving many different problems related to surveying and construction. In this regard, it can be argued that artificial intelligence has already found its application in geodesy and construction, and its capabilities are still being explored and developed. This opens up many opportunities to improve the efficiency and accuracy of construction processes, reduce risks and increase the safety of workers and the public, as well as to create new innovations and achievements in the field of surveying and construction. Keywords: artificial intelligence, geodetic monitoring, geoinformation system, automation, camera works, monitoring principles, building and construction monitoring data, geospatial analysis, construction objects.

A Multi-GNSS/IMU Data Fusion Algorithm Based on the Mixed Norms for Land Vehicle Applications

As a typical application of geodesy, the GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation technique was developed and has been applied for decades. For the integrated systems with multiple sensors, data fusion is one of the key problems. As a well-known data fusion algorithm, the Kalman filter can provide optimal estimates with known parameters of the models and noises. In the literature, however, the data fusion algorithm of the GNSS/INS integrated navigation and positioning systems is performed under a certain norm, and performance of the conventional filtering algorithms are improved only under this fixed and limited frame. The mixed norm-based data fusion algorithm is rarely discussed. In this paper, a mixed norm-based data fusion algorithm is proposed, and the hypothesis test statistics are constructed and adopted based on the chi-square distribution. Using the land vehicle data collected through the multi-GNSS and the IMU (Inertial Measurement Unit), the proposed algorithm is tested and compared with the conventional filtering algorithms. Results show that the influences of the outlying measurements and the uncertain noises are weakened with the proposed data fusion algorithm, and the precision of the estimates is further improved. Meanwhile, the proposed algorithm provides an open issue for geodetic applications with mixed norms.

Towards optical frequency geopotential difference measurements via a flying drone.

Geopotential and orthometric height differences between distant points can be measured via timescale comparisons between atomic clocks. Modern optical atomic clocks achieve statistical uncertainties on the order of 10-18, allowing height differences of around 1 cm to be measured. Frequency transfer via free-space optical links will be needed for measurements where linking the clocks via optical fiber is not possible, but requires line of sight between the clock locations, which is not always practical due to local terrain or over long distances. We present an active optical terminal, phase stabilization system, and phase compensation processing method robust enough to enable optical frequency transfer via a flying drone, greatly increasing the flexibility of free-space optical clock comparisons. We demonstrate a statistical uncertainty of 2.5×10-18 after 3 s of integration, corresponding to a height difference of 2.3 cm, suitable for applications in geodesy, geology, and fundamental physics experiments.

Investigation of an underwater clock and data transmission optical wireless link at 650 nm for robotic oriented geodesy applications

Underwater geodesy is important for marine studies and seafloor mapping. These studies typically make use of the time of flight, for example SONAR, and collect a lot of data. Furthermore, high map densities require big data collection and transportation, and therefore require high bandwidth underwater networks. In this article, we propose and demonstrate an underwater optical network based on a directly-modulated laser at 650 nm that enables the deployment of underwater robotic systems which are capable of transferring the captured data to a base station and allow the synchronization of the clocking signals. As proof of concept, we demonstrated a unipolar NRZ data transfer from an Arduino at 2 Mbps through an underwater channel measuring about 1 meter in length. A bit error rate value of about 10 − 5 for underwater data transmission was realised by the designed optical network, showcasing its potential for use in underwater data transfer during robotic geodesy surveys. Recovery of the clock signal from the signal generator at 2 kHz was also shown. Phase noise floor values below −90 dBc/Hz were attained for the underwater clock signal transmission.

Rigorous spherical bearing with Soldner coordinates and azimuth angles on sphere

Meridian systems, called Soldner coordinates (parallel coordinate) systems, have found wide application in geodesy. In particular, the meridian system constitutes a suitable base for the Gauss-Kruger projection of the ellipsoid and the sphere. Soldner coordinates can be used in Cassini-Soldner projection without any processing. As it is known, the directions of the edges are shown with azimuth angles in the geographic coordinate system and the bearing angles in the Soldner coordinate system. Bearing or azimuth angles are frequently used in geodetic calculations. These angles give the direction of sides in the clockwise direction from a certain initial direction. Both angle values range from 0 to 360 degrees and are usually calculated from the arctan function. But the arctan function returns an angle value between -90 and +90 degrees. Therefore, it is necessary to analyze the quarter for the angle found. For practical computations, the quadrants of the arctangents are determined by the signs of the numerator and denominator in the tangent formulas. Determining the quarter of the angles is done with if…, then…, end..., blocks on the computer. It should be noted that each comparison requires a separate processing time. This study will be given how to calculate both bearing and azimuth angles with direct formulas without any need to examine them. In addition, a solution proposal will be given against the division by zero errors in the bearing and azimuth angles calculations.

Improved GNSS Water Vapor Tomography With Modified Mapping Functions

AbstractThe use of optimized GNSS mapping functions is here shown to lead to significant improvements in the performance of a water vapor tomographic model, totally driven by GNSS observations. The method improves a recent proposal for unconstrained tomographic inversions and is developed and validated with data from the Manaus dense GNSS network and in‐situ radiosondes, covering different seasons and synoptic conditions. The optimization uses a Monte Carlo technique to find the minimum root‐mean‐square error in a two‐dimensional parameter space. A set of fixed parameters, computed by optimizing over a small subset of cases, is found to lead to results that are overall significantly better than those produced by the three more common mapping functions used for geodesy applications. The quality of inversions is, however, found to have significant spread, an indication of the impact of varying GNSS data quality and a reminder of the need of further improvements in the method.

Determination of the orthometric height difference based on optical fiber frequency transfer technique

The development of remote frequency transfer techniques, especially the appearance of optical clocks with unprecedented stability, has prompted geoscientists to study their applications in geodesy. Using remote frequency transfer technique, by frequency comparison of two optical clocks at two points P and Q connected by optical fibers, one can measure the signal's frequency shift between them, and the geopotential difference between them can be determined based on the gravity frequency shift equation. Given the orthometric height of P, the orthometric height of Q can be determined. Since the present stability of the optical clock has achieved 1 × 10−18 or better and comparing the frequency transfer via optical fiber provides stability at 10−19 level, the optical clock network enables determining the orthometric height at centimeter-level. This study provides a formulation to determine the height difference at one-centimeter level between two points on the ground based on the optical fiber frequency transfer technique.

Methodological and On-Site Applied Construction Layout Plan with Batter Boards Stake-Out Methods Comparison: A Case Study of Romania

The layout or stake-out is one of the most important assignments of the surveying engineer, and it is of vital importance in the building process, as the designed geometries of the structure ensure the verticality and the correct positioning inside the terrain. The mission of the surveying engineer involves both legal and technical aspects, and the correct planning of the layout process must take into consideration aspects regarding the site conditions, instrumentation used, the required and achievable accuracies, network design and survey methods used. Given the vast applications of geodesy and topography in different domains and industries, the study incorporates general notions and technical aspects regarding the workflow in cadastre and construction surveying, guidelines for an efficient design of site layout plan with on-site applicability, as well as a novel comparison between four methods of construction lines geometry layout on batter boards. The results of this study aim to further consolidate the importance of accurate and efficient construction layout projects, with comprehensive design plans, methods and instrumentation selection, as well as recommendations. The presented discussions and conclusions are of interest to the geodetic community as well as the construction industry, and due to the pragmatic and experimental nature of the research, incorporates technical notes and original results of professional and academic importance.

Analysis of phase noise effects in a coupled Mach\u2013Zehnder interferometer for a much stabilized free-space optical link

Recently, new physics for unconditional security in a classical key distribution (USCKD) has been proposed and demonstrated in a frame of a double Mach–Zehnder interferometer (MZI) as a proof of principle, where the unconditional security is rooted in MZI channel superposition. Due to environmental phase noise caused by temperature variations, atmospheric turbulences, and mechanical vibrations, free-space optical links have been severely challenged for both classical and quantum communications. Here, the double MZI scheme of USCKD is analyzed for greatly subdued environment-caused phase noise via double unitary transformation, resulting in potential applications of free-space optical links, where the free-space optical link has been a major research area from fundamental physics of atomic clock and quantum key distribution to potential applications of geodesy, navigation, and MIMO technologies in mobile communications systems.

Spatial Data Performance Test of Mid-cost UAS with Direct Georeferencing

Recent development of lightweight and small size multi-frequency GNSS receivers allows determination of the precise position of the moving platform and spatial data acquisition without the need for setting up and measuring of ground control points. The main advantage of this approach is a higher operational capacity with reduced time and cost of field measurement. This relates to fieldwork in inaccessible areas with demanding terrain configuration. In this paper development and use of a UAS with direct georeferencing of camera sensor for spatial data acquisition is described, and the possibility of 3D scene reconstruction based on the precise position of the camera with predetermined interior parameters is examined. Modern computer vision-based SfM photogrammetry algorithms are used for determining attitude parameters and reconstruction of the scene. For that purpose, several tests on two different test fields were performed using various system parameters for collecting and analysis of several spatial data sets. The presented results demonstrate a satisfactory accuracy (3.1 cm planar and 6.4 cm spatial) of the system for various applications in geodesy.

Implementing Marine Gravimetry Test Using Strapdown Gravimeter in the South China Sea

Yu, R.; Xu, X.; Zhao, L.; Wang, M.; Cai, S.; Cao, J.; Wu, M., and Lu, S., 2020. Implementing marine gravimetry test using strapdown gravimeter in the South China Sea. In: Zheng, C.W.; Wang, Q.; Zhan, C., and Yang, S.B. (eds.), Air-Sea Interaction and Coastal Environments of the Maritime and Polar Silk Roads. Journal of Coastal Research, Special Issue No. 99, pp. 382–388. Coconut Creek (Florida), ISSN 0749-0208.As one of the major kinematic ways for surveying purpose in the sea region, shipborne marine gravimetry is important to get high accuracy and resolution gravity information. Until today, after decades of development and innovation, marine gravimetry is still a main and important mean of obtaining gravity data from the vast ocean areas. Based on the former generation gravimeter, SGA-WZ02 designed by NUDT has a further development. With this gravimeter, a marine test in the South China Sea was implemented for 40 days. The purpose was assessing feasibility and accuracy of this gravimeter for marine gravimetry. Surveying region was near the Xidutan area and the East Island in the South China Sea and total area of the measuring region is about 442.55 km2 with a total of 884.7 km surveying distance. In this test, 15 east-west parallel lines separated by 1 km and 2 north-south inspection lines were measured. The average line distance is 14 km and the speed is about 10 kn. Since there were no repeated measurement lines, this paper used cross over differences among 17 lines to evaluate the performance. In marine gravity measurement experiments, it is particularly important to use GNSS precision point positioning (PPP) technology to measure the accurate position and velocity information of the carrier. Totally, 30 cross over points were obtained in the test and the average value of these points is -0.42 mGal using 300 s FIR filters which means the resolution was about 750 m. The root mean square value is 0.64 mGal that the result was at the same level of accuracy as the current mainstream marine gravimeters. It indicates that the SGA-WZ02 strapdown gravimeter can be used for marine gravimetry applications in geodesy and geophysical survey activities.

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures; spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid; while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N - ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

HIGH-RESOLUTION RESIDUAL TERRAIN MODEL AND TERRAIN CORRECTIONS FOR GRAVITY FIELD MODELLING AND GEOID COMPUTATION IN NIGER REPUBLIC

In this study, we computed and presented grid maps of high-resolution terrain corrections and residual terrain model (RTM) as short-wavelengths of the gravity field and the geoid in Niger. We constructed RTM elevations from mean elevation surfaces corresponding to ~100 km and ~9 km of spatial scales and 3 arc-seconds SRTM data. The computations are performed at gravity stations and 1.5 arc-minute regular grid, out to 10 and 200 km for inner and outer zones respectively with the standard density of 2670 kg/m-3. The study area is characterized by low values of terrain effects. The indirect effects are lower than 10 cm for ~9 km and reach 1.8 m for ~100 km. In Niger, 98.44% of indirect effects are lower than 1 cm and 98.2% of direct effect are lower than 5 mgal for ~9 km. For ~100 km, 85.87% of indirect effects are lower than 10 cm and 89.77% of direct effects are lower than 5 mgal for ~100 km, and 98.77% of terrain corrections are lower than 1 mgal. We found out that height discrepancies between gravity stations and SRTM influences the precision of terrain effects. The results are value for applications in geodesy and geophysics that require accurate interpretations.

Atmospheric delay for electromagnetic signals associated with space / time variations of the refractive index in the lower atmosphere: Applications in spatial geodesy

The feasibility quantifying atmospheric delay of electromagnetic signals using a mesoscale numerical model (WRF model) is explored. The experiment investigates a new alternative to reduce uncertainty sources in data exploitation for spatial geodesy applications. Our experiment was compared with GPS estimations of stations located in the South-America. The GPS estimations are consistent with values of our proposed methodology. This opens the possibility of using a mesoscale numerical model applied to spatial geodesy. However, these results, despite being promising, need further analysis and research, opening the opportunity to numerical modeling of atmospheric delays using mesoscale models.

Normal gravity field in relativistic geodesy

Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, VLBI, SLR, and GNSS have achieved an unprecedented level of accuracy in measuring coordinates of the reference points of the ITRF and the world height system. The main geodetic reference standard is a normal gravity field represented in the Newtonian gravity by the field of a Maclaurin ellipsoid. The present paper extends the concept of the normal gravity field to the realm of general relativity. We focus our attention on the calculation of the first post-Newtonian approximation of the normal field that is sufficient for applications. We show that in general relativity the level surface of the uniformly rotating fluid is no longer described by the Maclaurin ellipsoid but is an axisymmetric spheroid of the forth order. We parametrize the mass density distribution and derive the post-Newtonian normal gravity field of the rotating spheroid which is given in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce the post-Newtonian multipolar expansion of the metric tensor given in terms of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy. Finally, we derive the post-Newtonian generalization of the Somigliana formula for the gravity field on the reference ellipsoid.