Optical clocks for gravity field observation and further geodetic applications

2020 ◽  
Author(s):  
Hu Wu ◽  
Jürgen Müller ◽  
Annike Knabe
Keyword(s):  
Gravity Field ◽  
Rapid Development ◽  
Satellite Orbit ◽  
Equipotential Surface ◽  
Gravity Potential ◽  
Height Difference ◽  
The Earth ◽  
Temporal Gravity ◽  
Reference Clock

<p>In the past three decades, optical clocks and frequency transfer techniques have experienced a rapid development. They are approaching a fractional frequency uncertainty of 1.0x10<sup>-18</sup>, corresponding to about 1.0 cm in height. This makes them promising to realize “relativistic geodesy”, and it opens a new door to directly obtain gravity potential values by the comparison of clock frequencies. Clocks are thus considered as a novel candidate for determining the Earth’s gravity field. We propose to use a spaceborne clock to obtain gravity potential values along a satellite orbit through its comparison with reference clocks on ground or with a co-orbital clock. The sensitivity of clock measurements is mapped to gravity field coefficients through closed-loop simulations.</p><p>In addition, clocks are investigated for other geodetic applications. Since they are powerful in providing the height difference between distant sites, clocks can be applied for the unification of local/regional height systems, by estimating the offsets between different height datums and the systematic errors within levelling networks. In some regions like Greenland, clocks might be a complementary tool to GRACE(-FO) for detecting temporal gravity signals. They can be operated at locations of interest and continuously track changes w.r.t. reference clock stations. The resulting time-series of gravity potential values reveal the temporal gravity signals at these points. Moreover, as the equipotential surface at a high satellite altitude is more regular than that on the Earth’s surface, a couple of clocks in geostationary orbits can realize a space-based reference for the determination of physical heights at any point on the Earth through clock comparisons.</p><p>We gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy EXC-2123/1 (Project-ID: 390837967).</p>

scholarly journals Indoor height determination of the new absolute gravimetric station of L'Aquila

2020 ◽  
Vol 63 (Vol 63 (2020)) ◽  
Author(s):  
Marco Fortunato ◽  
Augusto Mazzoni ◽  
Giovanna Berrino ◽  
Filippo Greco ◽  
Federica Riguzzi ◽  
...  
Keyword(s):  
Gravity Field ◽  
Equipotential Surface ◽  
Absolute Gravity ◽  
Post Processing ◽  
Height Difference ◽  
Geoidal Undulation ◽  
Height Determination ◽  
Topographic Survey ◽  
Gravity Measurements

In this paper we describe all the field operations and the robust post-processing proceduresto determine the height of the new absolute gravimetric station purposely selected to belong to a new absolute gravimetric network and located in the Science Faculty of the L’Aquila University. This site has been realized indoor in the Geomagnetism laboratory, so that the height cannot be measured directly, but linking it to the GNSS antenna of AQUI benchmark located on the roof of the same building, by a classical topographic survey. After the topographic survey, the estimated height difference between AQUI and the absolute gravimetric site AQUIgis 14.9700.003 m. At the epoch of the 2018 gravimetric measures, the height of AQUI GNSS station was 712.9740.003 m, therefore the estimated ellipsoidalheight of the gravimetric site at the epoch of gravity measurements is 698.0040.005 m. Absolute gravity measurements are referred to the equipotential surface of gravity field, so that the knowledge of the geoidal undulation at AQUIg allows us to infer the orthometric height as 649.32 m.

scholarly journals Strategy for the realisation of the International Height Reference System (IHRS)

2021 ◽  
Vol 95 (3) ◽  
Author(s):  
Laura Sánchez ◽  
Jonas Ågren ◽  
Jianliang Huang ◽  
Yan Ming Wang ◽  
Jaakko Mäkinen ◽  
...  
Keyword(s):  
Gravity Field ◽  
Reference System ◽  
International Association ◽  
Accuracy Assessment ◽  
Equipotential Surface ◽  
Precise Determination ◽  
Gravity Models ◽  
Reference Network ◽  
Global Gravity Models

AbstractIn 2015, the International Association of Geodesy defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The IHRS is a geopotential reference system co-rotating with the Earth. Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbersC(P) referring to an equipotential surface defined by the conventional valueW0 = 62,636,853.4 m2 s−2, and geocentric Cartesian coordinatesXreferring to the International Terrestrial Reference System (ITRS). Current efforts concentrate on an accurate, consistent, and well-defined realisation of the IHRS to provide an international standard for the precise determination of physical coordinates worldwide. Accordingly, this study focuses on the strategy for the realisation of the IHRS; i.e. the establishment of the International Height Reference Frame (IHRF). Four main aspects are considered: (1) methods for the determination of IHRF physical coordinates; (2) standards and conventions needed to ensure consistency between the definition and the realisation of the reference system; (3) criteria for the IHRF reference network design and station selection; and (4) operational infrastructure to guarantee a reliable and long-term sustainability of the IHRF. A highlight of this work is the evaluation of different approaches for the determination and accuracy assessment of IHRF coordinates based on the existing resources, namely (1) global gravity models of high resolution, (2) precise regional gravity field modelling, and (3) vertical datum unification of the local height systems into the IHRF. After a detailed discussion of the advantages, current limitations, and possibilities of improvement in the coordinate determination using these options, we define a strategy for the establishment of the IHRF including data requirements, a set of minimum standards/conventions for the determination of potential coordinates, a first IHRF reference network configuration, and a proposal to create a component of the International Gravity Field Service (IGFS) dedicated to the maintenance and servicing of the IHRS/IHRF.

Subtleties in spherical harmonic synthesis of the gravity field

2020 ◽  
Author(s):  
Ropesh Goyal ◽  
Sten Claessens ◽  
Will Featherstone ◽  
Onkar Dikshit
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Gravitational Constant ◽  
Angular Rate ◽  
Physical Geodesy ◽  
Major Axis ◽  
Gravity Potential ◽  
Semi Major Axis ◽  
The Earth ◽  
Spherical Harmonic Synthesis

<p>Spherical harmonic synthesis (SHS) can be used to compute various gravity functions (e.g., geoid undulations, height anomalies, deflections of vertical, gravity disturbances, gravity anomalies, etc.) using the 4pi fully normalised Stokes coefficients from the many freely available Global Geopotential Models (GGMs).  This requires a normal ellipsoid and its gravity field, which are defined by four parameters comprising (i) the second-degree even zonal Stokes coefficient (J2) (aka dynamic form factor), (ii) the product of the mass of the Earth and universal gravitational constant (GM) (aka geocentric gravitational constant), (iii) the Earth’s angular rate of rotation (ω), and (iv) the length of the semi-major axis (a). GGMs are also accompanied by numerical values for GM and a, which are not necessarily identical to those of the normal ellipsoid.  In addition, the value of W<sub>0,</sub> the potential of the geoid from a GGM, needs to be defined for the SHS of many gravity functions. W<sub>0</sub> may not be identical to U<sub>0</sub>, the potential on the surface of the normal ellipsoid, which follows from the four defining parameters of the normal ellipsoid.  If W<sub>0</sub> and U<sub>0</sub> are equal and if the normal ellipsoid and GGM use the same value for GM, then some terms cancel when computing the disturbing gravity potential.  However, this is not always the case, which results in a zero-degree term (bias) when the masses and potentials are different.  There is also a latitude-dependent term when the geometries of the GGM and normal ellipsoids differ.  We demonstrate these effects for some GGMs, some values of W<sub>0</sub>, and the GRS80, WGS84 and TOPEX/Poseidon ellipsoids and comment on its omission from some public domain codes and services (isGraflab.m, harmonic_synth.f and ICGEM).  In terms of geoid heights, the effect of neglecting these parameters can reach nearly one metre, which is significant when one goal of modern physical geodesy is to compute the geoid with centimetric accuracy.  It is also important to clarify these effects for all (non-specialist) users of GGMs.</p>

scholarly journals Effects of New Level-1B Data on GRACE Temporal Gravity Field Models and Precise Orbit Determination Solutions

2021 ◽  
Vol 13 (20) ◽  
pp. 4119
Author(s):  
Nannan Guo ◽  
Xuhua Zhou ◽  
Kai Li
Keyword(s):  
Gravity Field ◽  
Orbit Determination ◽  
Field Model ◽  
Precise Orbit Determination ◽  
Satellite Orbit ◽  
Data Types ◽  
Gravity Field Model ◽  
Precise Orbit ◽  
Temporal Gravity ◽  
Gravity Field Models

The quality of Gravity Recovery and Climate Experiment (GRACE) observation is the prerequisite for obtaining the high-precision GRACE temporal gravity field model. To study the influence of new-generation GRACE Level-1B Release 03 (RL03) data and the new atmosphere and ocean de-aliasing (AOD1B) products on recovering temporal gravity field models and precise orbit determination (POD) solutions, we combined the global positioning system and K-band ranging-rate (KBRR) observations of GRACE satellites to estimate the effect of different data types on these solutions. The POD and monthly gravity field solutions are obtained from 2005 to 2010 by SHORDE software developed by the Shanghai Astronomical Observatory. The post-fit residuals of the KBRR data were decreased by approximately 10%, the precision of three-direction positions of the GRACE POD was improved by approximately 5%, and the signal-to-noise ratio of the monthly gravity field model was enhanced. The improvements in the new release of monthly gravity field model and POD solutions can be attributed to the enhanced Level-1B KBRR data and the AOD1B model. These improvements were primarily due to the enhanced of KBRR data; the effect of the AOD1B model was not significant. The results also showed that KBRR data slightly improve the satellite orbit precision, and obviously enhance the precision of the gravity field model.

scholarly journals A global vertical datum defined by the conventional geoid potential and the Earth ellipsoid parameters

2020 ◽  
Author(s):  
Hadi Amin ◽  
Lars E. Sjöberg ◽  
Mohammad Bagherbandi
Keyword(s):  
Gravity Field ◽  
Satellite Altimetry ◽  
Input Data ◽  
Equipotential Surface ◽  
Sea Surface ◽  
Dynamic Topography ◽  
The Earth ◽  
Degree Harmonic ◽  
Mean Sea Surface ◽  
Zero Degree

<p>According to the classical Gauss–Listing definition, the geoid is the equipotential surface of the Earth’s gravity field that in a least-squares sense best fits the undisturbed mean sea level. This equipotential surface, except for its zero-degree harmonic, can be characterized using the Earth’s Global Gravity Models (GGM). Although nowadays, the satellite altimetry technique provides the absolute geoid height over oceans that can be used to calibrate the unknown zero-degree harmonic of the gravimetric geoid models, this technique cannot be utilized to estimate the geometric parameters of the Mean Earth Ellipsoid (MEE). In this study, we perform joint estimation of W<sub>0</sub>, which defines the zero datum of vertical coordinates, and the MEE parameters relying on a new approach and on the newest gravity field, mean sea surface, and mean dynamic topography models. As our approach utilizes both satellite altimetry observations and a GGM model, we consider different aspects of the input data to evaluate the sensitivity of our estimations to the input data. Unlike previous studies, our results show that it is not sufficient to use only the satellite-component of a quasi-stationary GGM to estimate W<sub>0</sub>. In addition, our results confirm a high sensitivity of the applied approach to the altimetry-based geoid heights, i.e. mean sea surface and mean dynamic topography models. Moreover, as W<sub>0</sub> should be considered a quasi-stationary parameter, we quantify the effect of time-dependent Earth’s gravity field changes as well as the time-dependent sea-level changes on the estimation of W<sub>0</sub>. Our computations resulted in the geoid potential W<sub>0 </sub>= 62636848.102 ± 0.004 m<sup>2</sup>s<sup>-2</sup> and the semi-major and –minor axes of the MEE, a = 6378137.678 ± 0.0003 m and b = 6356752.964 ± 0.0005 m, which are 0.678 and 0.650 m larger than those axes of the GRS80 reference ellipsoid, respectively. Moreover, a new estimation for the geocentric gravitational constant was obtained as GM = (398600460.55 ± 0.03) × 10<sup>6</sup> m<sup>3</sup>s<sup>-2</sup>.</p>

The Effect of the Disturbing Potential for the Gravity Field

2015 ◽  
Vol 220-221 ◽  
pp. 257-263
Author(s):  
Petras Petroškevičius ◽  
Rosita Birvydiene ◽  
Darius Popovas
Keyword(s):  
Gravity Field ◽  
Surface Deformation ◽  
Equipotential Surface ◽  
Material Point ◽  
Gravity Potential ◽  
The Moon ◽  
Disturbing Potential ◽  
Normal Height ◽  
Earth’S Gravity Field ◽  
Accuracy Of Measurements

The Earth’s gravity field tends to change due to various reasons. These are diverse processes occurring inside the Earth or changes initiated by human activity. The increasing accuracy of measurements has enabled to take into consideration fluctuations in the gravity field. The article presents research study on the effect of gravity potential describing variations in the gravity field affecting gravity field elements related to the performed measurements. Due to the effect of the disturbing potential, a change in gravity and the deviation of vertical and equipotential surface deformation have been determined. The paper has analyzed the disturbing effect of the material point or homogeneous sphere and has specified the possibilities of assessing the disturbing effect of any form of the homogeneous body. Based on the tidal potential induced by the celestial body, the disturbing effect of the Moon and Sun onto the Earth’s gravity field has been assessed. The carried out research indicates that the range of deformation changes in the equipotential surface of the Earth’s gravity field induced by the effect of the Moon is equal to 0.4824 m, whereas that of the Sun makes 0.1861 m. The conducted studies prove that, due to the effect of the Moon, the direction of the vertical, in terms of the Earth’s surface, tends to change up to 0.0541", and as a result of the Sun’s effect it could reach 0.0204". Having assessed the Lunisolar effect in the first order vertical network measurements in Lithuania, in a polygon with the perimeter of 451 km, it has been determined that the closing error of normal height difference has decreased by the factor of 1.3.

TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

2020 ◽  
Author(s):  
Meng Yang ◽  
Christian Hirt ◽  
Roland Pail
Keyword(s):  
Gravity Field ◽  
Adaptive Algorithm ◽  
Computation Time ◽  
Spherical Approximation ◽  
Constant Density ◽  
The Earth ◽  
Digital Elevation ◽  
Gravity Effects ◽  
Residual Terrain Modelling

<p>With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation models (DEM) in the evaluation of Newtonian integration. This paper presents a new MATLAB-based program, terrain gravity field (TGF), for the accurate and efficient determination of the terrain-related gravity field based on an adaptive algorithm. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries and DEMs with different spatial resolutions. The most accurate but least efficient polyhedron together with the finest DEM are only considered for the innermost zone, while prism approximation for the second zone, the third zone with the more efficient tesseroid and a coarse DEM, and the most efficient but least accurate point-mass with the coarsest DEM for distant masses. Compared to some publicly available algorithms depending on one type of geometric approximation, the TGF achieves accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent elements of gravity field, supports two types of density inputs (constant density value and digital density map), and considers the sphericity of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. Results from internal and external numerical validation experiments of TGF confirmed its accuracy of sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms TGF the capability of dealing with large datasets.</p>

A discussion on orbital analysis - A brief survey of satellite orbit determination

1967 ◽  
Vol 262 (1124) ◽  
pp. 71-78
Keyword(s):  
Orbit Determination ◽  
Accurate Determination ◽  
Solar Radiation Pressure ◽  
Satellite Orbit ◽  
Dynamical Theory ◽  
Satellite Orbits ◽  
Perturbation Techniques ◽  
The Earth ◽  
Orbital Analysis

The accurate determination of satellite orbits depends on an adequate accumulation of observations, a sound dynamical theory and a fairly sophisticated sequence of numerical computations. The particular patterns of observation, theory and computation are considered in relation to the objectives of orbit determination. Factors to be taken into account are the type, accuracy and spread of observations; perturbations of the orbit due to air drag, attraction of the Earth, Moon, and Sun, and solar radiation pressure; and the speed and cost of available computers. These factors, together with the overall objectives, determine the main features of the computation; whether to use special or general perturbation techniques, what length of orbit arc to use, what parameters to determine and how to present the results.

Determination of upper-atmosphere air-density profile from satellite observations

1959 ◽  
Vol 252 (1268) ◽  
pp. 28-34 ◽  
Keyword(s):  
Density Profile ◽  
Satellite Orbit ◽  
Major Axis ◽  
Scale Height ◽  
Semi Major Axis ◽  
Relative Variation ◽  
Air Density ◽  
The Earth ◽  
Point Data

The theory previously developed for the changes in the perigee distance and semi-major axis of a satellite orbit due to air drag is extended to enable the air-density profile (i. e. its relative variation with height) to be derived from the motion of the orbit’s perigee. The solution is first obtained in terms of the change in perigee distance and then in terms of the change in the radius of the earth at the sub-perigee point. Data are analyzed by the two methods, leading to 39 (± 9) and 36 (± 15) km for the scale height in the 180 and 220 km altitude regions.

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