Physical Geodesy

This research presents a quasi-geoid model for the Western part of Latvia based on parametric modelling of continuous polynomial surface by DFHRS (Digital Finite-element Height Reference Surface) software v.4.3 developed by Hochschule Karlsruhe – University of Applied Sciences. Apart from standard observations for quasi-geoid determination – GNSS/levelling points and Global Geopotential Models (GGMs), new kind of measurements – astrogeodetic vertical deflection (VD) observations provided by Digital Zenith Camera (DZC) are used. This instrument has been developed by the Institute of Geodesy and Geoinformatics, University of Latvia (GGI) and provides the accuracy of about 0.10 arcsec, what equivalent to 0.5 mm error in elevation for 1 km length and it gives two times better accuracy than 1st order levelling in Latvia respectively. 44 1st order GNSS/levelling points were observed by GGI staff and 27 1st order levelling points were provided by Latvian Geospatial Information Agency (LGIA...

The determination of gravimetric geoid models using gravity anomalies requires the computation of normal gravity on specific ellipsoids. For global models, the International Gravity Formula is applied to the WGS 84 ellipsoid, while local models use the ellipsoid adopted for geodetic computation in the region of study. In countries that use the Clarke 1880 ellipsoid, a theoretical gravity model is computed on this surface to establish a precise local geoid model. This paper formulates a local theoretical gravity model for calculation of theoretical gravity values on the Clarke 1880 spheroid using the Somiglinana's closed formula for normal gravity, angular velocity, gravitational constant, and the Clarke 1880 spheroid parameters. The model is presented in two forms (A and B) and compared to ensure accuracy. Both forms of the model are suitable for accurate normal gravity computation on the Clarke 1880 ellipsoid.

The prevailing scientific consensus attributes ocean tides to differential gravitational forces exerted by the Moon and Sun. Yet this gravitational model, despite its long-standing acceptance, suffers from unresolved explanatory problems: the far-side bulge paradox, phase lag of tidal peaks, and the disproportionate effectiveness of extremely small gravitational differentials. This paper argues that the Information Field (IΔF) model provides a more coherent framework for understanding tidal phenomena. Rooted in both modern physics' recognition of information as fundamental and in the biblical description of celestial bodies as "signs and seasons" (Genesis 1:14), the IΔF model views the Moon and Sun not as mechanical causes but as calendrical markers of pre-encoded tidal rhythms. This approach integrates scientific anomalies, quantum informational paradigms, and theological insights, presenting a holistic reinterpretation of tides consistent with both empirical evidence and a Logos-centered cosmology.

A large number of interacting particles that obey a classical Hamiltonian equation may exhibit hydrodynamic phenomena including turbulence. The equations describing the phenomena far from equilibrium are derived from Hamiltonian particle systems by formulating a simple perturbation theory with a scale separation parameter.

This research investigates the performance of six satellite-only GOCE-based Global Geopotential Models (GGMs) released between 2018 and 2023. They include the WHU-SWPU-GOGR2022S, GOSG2S, Tongji-GMMG2021S, GO_CONS_GCF_2_TIM_R6, IGGT_R1C, and GOSG01S models. The assessment has been carried out using 221 first-order observed gravity stations in Egypt where 16 of them are of absolute gravity measurements. In addition, the assessment comprises the World Gravity Map 2012 (WGM 2012) as another unique open-source of gravity information worldwide. The accomplished findings have demonstrated that the WHU-SWPU-GOGR2022S model produces the least standard deviation of ±11.272 mGal over the available absolute gravity stations. On relative gravity points, the GOSG2S is the accurate GGM a with standard deviation equals ±15.480 mGal. Even though the WGM 2012 is not a GOCE-based GGM it has produced standard deviations of ±7.598 and ± 12.296 mGal at absolute and relative gravity locations respectively. Thus based on the available datasets and attained results, it can be concluded that the WGM 2012 and the WHU-SWPU-GOGR2022S GGM precisely describe the Earth's gravitational field over Egypt in particular. Furthermore, it is recommended to utilize those two sources of free-air gravity anomalies in geodetic activities chiefly for local geoid modelling.

This research investigates the performance of six satellite-only GOCE-based Global Geopotential Models (GGMs) released between 2018 and 2023. They include the WHU-SWPU-GOGR2022S, GOSG2S, Tongji-GMMG2021S, GO_CONS_GCF_2_TIM_R6, IGGT_R1C, and GOSG01S models. The assessment has been carried out using 221 first-order observed gravity stations in Egypt where 16 of them are of absolute gravity measurements. In addition, the assessment comprises the World Gravity Map 2012 (WGM 2012) as another unique open-source of gravity information worldwide. The accomplished findings have demonstrated that the WHU-SWPU-GOGR2022S model produces the least standard deviation of ±11.272 mGal over the available absolute gravity stations. On relative gravity points, the GOSG2S is the accurate GGM a with standard deviation equals ±15.480 mGal. Even though the WGM 2012 is not a GOCE-based GGM it has produced standard deviations of ±7.598 and ± 12.296 mGal at absolute and relative gravity locations respectively. Thus based on the available datasets and attained results, it can be concluded that the WGM 2012 and the WHU-SWPU-GOGR2022S GGM precisely describe the Earth's gravitational field over Egypt in particular. Furthermore, it is recommended to utilize those two sources of free-air gravity anomalies in geodetic activities chiefly for local geoid modelling.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched by the European Space Agency (ESA) on March 17, 2009. Since then, several Global Geopotential Models (GGMs) have been released based on data collected by GOCE. This paper evaluates different GOCE-only and GOCE/GRACE GGMs using 567 available GPS/Levelling points and terrestrial free-air gravity anomalies in Argentina. EGM2008 and EIGEN-51C models are also included in the evaluation procedure, even though they are not based on GOCE data. The idea of using these models is to identify any improvements of the new GOCE-only or GOCE/GRACE GGMs in Argentina. The truncation of the Stokes coefficients at a certain spherical harmonic degree n1 produces an omission error. In order to reduce this omission error, synthetic GGMs are evaluated by adding signal from EGM2008 and topographic effects through a Residual Terrain Model (RTM) to the satellite GGMs models. The evaluati...

In the paradigm of Evolutionary Mechanics, the universe is described as a multidimensional structure composed of eight sub-universes, each with its own metric and local limit speed constant . In this context, the speed of light is not viewed as an absolute, impassable limit, but rather as a rhythmic structural constant regulating the emergent frequency of informational events.

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2007Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2007Bu çalışmada, GPS tekniğinden elde edilen elipsoidal yüksekliklerin bölgesel düşey datumdaki ortometrik yüksekliklere dönüştürülmesinde lokal geoit modeli çözümlerinin kullanımı araştırılmıştır. Araştırma iki kısımdan oluşmaktadır. Birinci kısımda Türkiye ulusal geoitleri TG99A ve TG03 ile Avrupa gravimetrik geoidi EGG97 beş adet lokal bölgedeki GPS/nivelman verileri kullanılarak test edilmiştir. Daha sonra bu modeller GPS/nivelman noktalarında geoit yükseklik farkları kullanılarak hesaplanan yüzey modelleri ile ulusal düşey datuma uydurulmuş ve bağımsız GPS/nivelman verileri yardımıyla sonuçlar test edilmiştir. Bölgesel geoit modelleri ile gerçekleştirilen bu testlerden başka lokal GPS/nivelman geoit modelleri hesaplanmış doğrulukları irdelenmiştir. Test edilen ve yeni hesaplanan geoit modellerinin doğrulukları karşılaşt...

Let us begin with describing what we mean by a Dual Domain Universe: We assume, at the beginning of the Universe, there was nothing but a huge Primordial homogeneous and isotropic Energy Field which was in an absolutely unperturbed state with Entropy 0. Gravity, Space Time, and everything we see in this world remain in an un manifest state. In this situation an operator (Hamiltonian) acts on this Field breaking it into two Domains. We conceptualize the 1 st Domain to consist of Matter, Radiation, Force,, Field etc, in effect, everything tangible we see in this world, and the 2 nd Domain consisting of Space-Time and other intangible things (like Dark Matter, Dark Energy, Dark Photons etc), known or unknown to us. Thus 1 st Domain represents Gross Matter and 2 nd Domain represents Subtle Matter. This split-up of the Primordial Energy Field broke the symmetry or balance creating a Force called Gravity and an Inflationary Force causing very quick expansion of the Universe. This also increased entropy of the system in the process, Gravity is supposed to be a bridge between these two domains, which works unhindered in both of these domains and is represented by a Tensor, while the Domain for Gross Matter is represented by a Ket Vector and the Domain for Subtle Matter is represented by a Bra Vector as per Dirac's notation, according to our postulation.

U radu su objasnjeni uzroci nastanka plime i oseke (morskih mijena), te opisani sila uzrocnica plimnih valova i nutacijsko razdoblje. Opisani su i geometrijski položaji Mjeseca i Sunca u odnosu na Zemlju, koji definiraju maksimalnu ili minimalnu visinu plimnog vala. Dan je kratki pregled mjerenja razine mora duž istocne obale Jadranskog mora s trenutacnim stanjem izgrađenih stalnih i privremenih mjernih postaja. Povezanost promjena Mjesecevih deklinacija s promjenama razine mora objasnjena je analizom izracunatih srednjih razina mora u nutacijskom razdoblju od 18, 61 godine za mareografe: Dubrovnik, Split, Bakar i Rovinj. Izracunate su srednje razine mora za 34 epohe (6794 dana) s ukupno 230 996 dnevnih srednjih vrijednosti razina mora.

A simultaneous adjustment of the National Gravimetric Network of Uruguay was performed in
1995, in the frame of an agreement between the Servicio Geográfico Militar of Uruguay – SGM
(now Instituto Geográfico Militar – IGM) and the Institut für Erdmessung, Leibniz University
Hannover (IfE-LUH), Germany. The history of the Uruguayan gravimetric network as well as all
the gravity instruments, procedures and results obtained is well documented in (1). The adjustment
made included several international gravity ties with Argentina and Brazil, 2376 relative gravity
stations, and 4 absolute stations, 3 of them in Uruguay and 1 in Argentina. All that gravity data were
collected between 1967 and 1993. The absolute stations were observed with the JILAG-3
gravimeter, a transportable free-fall apparatus, as part of the “IFE Absolute Gravity Program South
America 1989-1991” (2, 3, 4). Thus, the gravimetric datum in level and scale of the Uruguayan
gravity network is defined within the International Gravity Standardization Net 1971 (IGSN71), and
the Latin American Gravity Standardization Network 1977 (LAGSN77). In 2010 an offset of 0.09
μms-2 was applied to all JILAG-3 observations as a result of absolute campaign comparisons with
the state-of-the-art FG5 gravimeter systems (successor of JILAG) and a reprocessing of the station
values was performed (5). In 2022 new contacts were made by the IGM with IfE, to readjust the
gravity network, considering the new observations made since 1993, also including 4 new absolute
stations in Uruguay, and 1 in Brazil measured in 2023 with an A10 instrument operated by Centro
de Estudios de Geodesia, CENEGEO-USP (Brazil) (6) (see Annex 1 for A10 instrument details).
The results of this new cooperation project between IGM and IfE, including observations between
1967 and 2024 are presented here.

Historical gravity observations have been utilized to compute the gravimetric geoid for the kingdom of Saudi Arabia. Using the "remove and restore" techniques, the global geoid model (EGM2008) heights and free air anomaly have been computed using Moledensky formula. The gravimetric geoid model covers about 70 percent of the kingdom. Secondly, GNSS (GPS) space based observations along with the Bench Mark observations were also used to compute the geoid. Determination of GNSS/Benchmark geoid based on the vertical reference network of Saudi Arabia, which was built in early 1970's as first order vertical control network by spirit leveling based on tidal gauges along the Arabian Gulf and Red Sea. More than 5000 GPS/BM observations using the remove and restore techniques. The trend correction was applied using the least square method, and the high was implemented for high frequency correction. Analysis of the two geoids reveals some geoid biases, which is possibly due to th...

GPS (Global Positioning System) is a passive, all-weather satellite-based navigation and positioning system, which is designed to provide precise three dimensional position and velocity, as well as time information on a continuous worldwide basis. The ability of GPS for providing high-precision vertical component of relative coordinates could be exploited for monitoring, and hence mapping, the sea level. In this case, the local nature of GPS measurements could nicely supplement the temporal and spatial resolution of satellite altimetry measurements which has a more or less global nature. This paper would describe and discuss the concept and method of monitoring sea level using GPS, and the technical and operational aspects that should be taken into account in implementing this technique. The paper would also discuss the prospect of using this GPS-based approach for monitoring sea level in Indonesia, along with its potential related applications. The paper would be sum up with some concluding remarks and recommendations. I.

This study compares a series of global geopotential models (GGMs) using available terrestrial data from the territory of Libya. The anomalies of free air were determined in points of gravimetric survey of Libya by using the model of European Improved Gravity 6C2 (EIGEN-6C2), the model of the Earth Gravitational Model 2008 (EGM2008), as well as model of the Earth Gravitational Model 1996 (EGM96). The points of gravimetric survey of Libya are related to International Terrestrial Reference Frame (ITRF2000), Geodetic Reference System 1980 (GRS80), International Gravity Standardization Net 1971 (IGSN71) and the levelling network of Libya. Free air anomalies were evaluated at the points of gravimetric survey. Along with all mentioned above the results gained by using said models were separately compared with the data obtained by using the Earth Gravitational Model (EGM96).

Flexible pavement are exposed to various types of traffic axles during its service age and also to millions of affiliated applications to those axes as well as several values including the air pressure inside the tires; and because of that stresses and strains imposed on the asphalt pavement layers, and that the multiple consequential occurrence of such strains causes (Fatigue Cracking), permanent deformities and rutting on the pavement, This all of the aforesaid minimizes the service age of pavement.
The aim of this thesis is to study the performance of the flexible pavement under the condition of the wheel loads by using multipurpose program (ANSYS) and then inspecting the nature of stresses and strains distribution into the pavement.
Comparisons of pavement analysis using ANSYS, Ken Layer Program and flexible pavement design equations (close form equations).
By using (ANSYS) program which works on the basic of fundamental of finite element and Then determine of stresses and strains into the different pavement layers. The results were analyzed under the single and double wheel loads and the comparison between them with an analysis under both double wheel load. The result of the analysis was the finding of the point at which the tether of the load ends in both cases.

A new Earth Gravitational Model (EGM08) to degree 2160 has been released to IAG's EGM Evaluation Group. In this study, we evaluate EGM08 Tide Free Model by using regional gravity, quasi-geoid height and GPS/leveling data. The EGM08-derived quantities are compared with (1) the GPS/leveling quasi-geoid heights, (2) an existing GPS/leveling fitted regional quasi-geoid model (TG03), and (3) the surface gravity anomalies in Turkey. The differences between observed/computed and EGM08-derived quantities are investigated. The mean value and standard deviation of the differences between EGM08 derived and observed quantities are found to be -88.8 cm and 24.2 cm for GPS/leveling height anomalies, 27.1 cm and 75.3 cm for TG03 quasi-geoid heights, and 2.8 mGal and 17.1 mGal for surface gravity anomalies. As Turkish proprietary data were not used in EGM08 computations this work is believed to be an external check for EGM08.

Troposfera igra značajnu ulogu za geodetsku zajednicu, što se prije svega ogleda u njenom utjecaju na GNSS opažanja. Istovremeno, u troposferi se dešavaju skoro sve hirdometeorološke pojave, koje utječu na našu svakodnevnicu. Naučnici su pronašli način da iskoriste sistematski utjecaj koji troposfera ima na GNSS signal i pretvore ga u meteorološki pokazatelj, količinu vodene pare. U ovom radu opisan je pojam GNSS meteorologije i njena osnovna podjela i primjena.

Troposfera igra značajnu ulogu za geodetsku zajednicu, što se prije svega ogleda u njenom utjecaju na GNSS opažanja. Istovremeno, u troposferi se dešavaju skoro sve hirdometeorološke pojave, koje utječu na našu svakodnevnicu. Naučnici su pronašli način da iskoriste sistematski utjecaj koji troposfera ima na GNSS signal i pretvore ga u meteorološki pokazatelj, količinu vodene pare. U ovom radu opisan je pojam GNSS meteorologije i njena osnovna podjela i primjena.

We present the result of the spin-orbit interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to N 3 LO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. We apply canonical transformations to eliminate the non-physical divergences and spurious logarithmic behaviours of the Hamiltonian, and use the latter to derive the gauge-invariant binding energy and the scattering angle, in special kinematic regimes. 21 C.1 Non-spinning sector up to 3PN 21 C.2 Spin-orbit sector up to N 2 LO 22

The combined gravity field model EIGEN-6C4 (Förste et al., 2014) is the latest combined global gravity field model of GeoForschungsZentrum (GFZ) Potsdam and Groupe Recherches Geodesie Spatiale (GRGS) Toulouse. EIGEN-6C4 has been generated including the satellite gravity gradiometry data of the entire GOCE

This study investigates to use GPS/Levelling measurements of Kuwait and four heuristic regression methods including Least Square Support Vector Regression (LSSVR), Gaussian Process Regression (GPR), Kernel Ridge Regression (KRR), and Multivariate Adaptive Regression Splines (MARS) for modelling local geoid undulation. The accuracy of the models was compared by geoid undulation of gravitational observations and Global Geopotential Models (GGMs). The results show that the KRR model is suitable for Kuwait geoid model, its error of percentage is 0.018 and 0.124% relative to gravity and GPS/Levelling geoid undulation models, respectively. Furthermore, the comparison of KRR model with GGMs models signifies its accuracy.

In this study, a thorough validation of the recently released Global Geopotential Models (GGMs) has been carried out by comparing all models with both the free-air (FA) gravity anomaly observations and GPS/Levelling data in Kuwait. First, the gravity functional in terms of FA gravity anomalies and geoid heights that derived from GGMs and compared with the ground-based data before applying the Spectral Enhancement Method (SEM). The findings indicate that the combined GGMs, generally, fit the ground data better than the satellite-only GGMs due to the existing spectral gaps. Second, the FA gravity anomalies and geoid heights, obtained from GGMs at maximum Spherical Harmonics (SH) degree/order (d/o) for the combined models and from spherical harmonics d/o ranging from 100 to their maximum d/o, with a step of 10 d/o for the satellite only GGMs, were compared with the corresponding ones from terrestrial data using the SEM. For the FA gravity signal, the EIGEN-6C4 manifested the best results of combined GGMs with differences characterised with a mean of 0.967 mGal and a Standard Deviation (STD) of 2.845 mGal, while TIM_R5 at SH (d/o) 200 showed the best results with a mean of satellite only GGMs with a mean if 1.008 mGal and a STD of 2.657 mGal. In the case of the evaluation of the geoidal height with GPS/levelling, XGM2016 manifested the best results of combined GGMs with differences characterised with a STD of 0.234 m. For the satellite only GGMs, the best results have been obtained from SPW_R5 at SH d/o 250 with a STD 0.207 m.

Front Cover Foreground: These images show three different views of the Earth's geoid-a surface of equal gravitational potential that, over the ocean, closely follows the sea surface.The geoid was determined from data collected by previous satellite missions. Among these satellites is the Challenging Minisatellite Payload (CHAMP), the forerunner to GRACE, launched by the German Georesearch Center GeoForschungsZentrum Potsdam (GFZ). Similar products will be developed using data from GRACE with an expected improvement in accuracy of several orders of magnitude.These images were provided courtesy of GFZ. The illustration of the GRACE satellites was provided by Chris Meaney. Front Cover Background: This day/night image of the Earth was produced using a combination of data from the Moderate Resolution Imaging Spectrometer (MODIS) sensor aboard NASA's Terra satellite (daytime portion), and the city lights image produced using Operational Line Scan (OLS) data from the Defense Meteorological Satellite.The daytime side of the Earth in this image was made using surface reflectance data from MODIS.The data was composited over a period of several months during the Northern Hemisphere of summer 2001. (Image courtesy of Robert Simmon and the MODIS Science Team.) Back Cover: This is a photograph of the two identical spacecraft in the environmental test facility at Industrieanlagen-Betriebsgesellschaft GmbH (IABG) in Ottobrun, Germany. When deployed into space, the two craft will be upright inside the launch vehicle. After launch, they will fly 500 km above the Earth and will be separated by 220 km.The photograph was provided courtesy of Astrium GmbH.

We investigate analytically and numerically the orbits of spinning particles around black holes in the post Newtonian limit and in the presence of cosmic expansion. We show that orbits that are circular in the absence of spin, get deformed when the orbiting particle has spin. We show that the origin of this deformation is twofold: a. the background expansion rate which induces an attractive (repulsive) interaction due to the cosmic background fluid when the expansion is decelerating (accelerating) and b. a spin-orbit interaction which can be attractive or repulsive depending on the relative orientation between spin and orbital angular momentum and on the expansion rate.

Opisane su promjene koje su se dogodile u geodeziji u posljednjih cetrdeset godina, a vezane su uz razvoj elektronicke, satelitske i racunalne tehnologije. Navedeni su primjeri promjena naziva geodetskih udruga, casopisa, geodetskih ucilista pa i cijele struke. Analiziran je suvremeni razvoj matematicko- fizikalne i satelitske geodezije, prakticne i inženjerske geodezije, fotogrametrije i daljinskih istraživanja, kartografije te geoinformacijske tehnologije. Navedena su razlicita misljenja o buducnosti geodezije i na kraju su dane smjernice u skolovanju geodeta.

The gravity fi eld and steady-state ocean circulation explorer (GOCE) satellite, successfully concluded its mission in October 2013 after collecting unprecedented gravity gradient measurements. Such GOCE data made it possible to improve the determination of the geoid over the Red Sea region. The performance of GOCE-based satellite-only global geopotential models (GGMs), at the end of its mission, is evaluated via spectral analysis and by using shipborne free-air gravity anomalies collected over the study area, namely the Red Sea. Eight of the most recent GOCE-based satelliteonly GGMs, namely the DIR_R5, ITU_GGC16_2, SPW_R5, TIM_R5, NULP_02S, IfE_GOCE05s, IGGT_R1, and GGM05G, are validated. Firstly, the spectral analysis of these GGMs was performed. The DIR_R5 model showed a superior behaviour, in all terms, in comparison to all the investigated GGMs. Then, the GGMs were evaluated, from spherical harmonics degree/order (d/o) ranging from 100 to their maximum d/o, with respect to the ...

Digital Elevation Model (DEM) is crucial to a wide range of surveying and civil engineering applications worldwide. Some of the DEMs such as ASTER, SRTM1 and SRTM3 are freely available open source products. In order to evaluate the three DEMs, the contribution of EGM96 are removed and all DEMs heights are becoming ellipsoidal height. This step was done to avoid the errors occurred due to EGM96. 601 points of observed ellipsoidal heights compared with the three DEMs, the results show that the SRTM1 is the most accurate one, that produces mean height difference and standard deviations equal 2.89 and ±8.65 m respectively. In order to increase the accuracy of SRTM1 in EGYPT, a precise Global Geopotential Model (GGM) is needed to convert the SRTM1 ellipsoidal height to orthometric height, so that, we quantify the precision of most-recent released GGM (five models). The results show that, the GECO model is the best fit global models over Egypt, which produces a standard deviation of geoid undulation differences equals ±0.42 m over observed 17 HARN GPS/leveling stations. To confirm an enhanced DEM in EGYPT, the two orthometric height models (SRTM1 ellipsoidal height + EGM96) and (SRTM1 ellipsoidal height + GECO) are assessment with 17 GPS/leveling stations and 112 orthometric height stations, the results show that the estimated height differences between the SRTM1 before improvements and the enhanced model are at rate of 0.44 m and 0.06 m respectively.

According to the wide spread use of satellitebased positioning techniques, especially Global Navigation Satellite Systems (GNSS), a greater attention has been paid to the precise determination of geoid models. As it is known, leveling measurements require high cost and long time in observation process that make it not convenient for the practical geodetic purposes. Thus obtaining the orthometric heights by GNSS is the most conventional way of determining these heights. Verifying this goal was the main objective behind the current research. The current research introduces a numerical solution of geoid modeling by applying a surface fitting for a few sparse data points of geoid undulation using minimum curvature surface (MCS). The MCS is presented for deriving a system of linear equations from boundary integral equations. To emphasize the precise applicability of the MCS as a tool for modeling the geoid in an area using GPS/leveling data, a comparison study between EGM2008 and MCS geoid models, is performed. The obtained results showed that MCS technique is a precise tool for determining the geoid in Egypt either on regional and/ or local scale with law distortion at check points.

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in comparison to previous works on the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings which contribute to the breaking of the particle-antiparticle symmetry.

The LiDAR point clouds are usually processed in Universal Transvers Mercator projection. The transformation to a national coordinate system is frequently made with low accuracy with the help of the generic transformation implemented in the actual softwares. An accurate and precise transformation for LiDAR files in the national coordinate systems of Romania (planimetric system Stereographic 1970 and altimetric system Black Sea 1975) is not yet available. The National Center for Cartography (NCC) from Romania developed a software for precise transformation, but it works only for certain patterns of the text files and for a maximum number of points of about 1 million. Because of this, the use of point clouds in precision work was not possible, using only extracts of low-density grid points in text format. In this research we develop an algorithm which use the precise transformation of NCC to realise an accurate transformation of the LiDAR point clouds in the national coordinate systems. The algorithm is then implemented in an innovative software to transform the LiDAR *LAS files, using the common version 1.2. The software is a batch processing application, which it can process big LiDAR data without blocking. Moreover, the application is capable to apply with accuracy and precision the last published national quasigeoid to the LiDAR point files. In the end, the obtained LiDAR point cloud are more suitable to be used in any domain, because of the accurate and precise transformation in the Romanian coordinate systems.

The resolutions of current global altimetric gravity models and mean sea surface models are around 12 km wavelength resolving 6 km features, and for many years it has been difficult to improve the resolution further in a systematic way. For both Jason 1 and 2, a Geodetic Mission (GM) has been carried out as a part of the Extension-of-Life phase. The GM for Jason-1 lasted 406 days. The GM for Jason-2 was planned to provide ground-tracks with a systematic spacing of 4 km after 2 years and potentially 2 km after 4 years. Unfortunately, the satellite ceased operation in October 2019 after 2 years of Geodetic Mission but still provided a fantastic dataset for high resolution gravity recovery. We highlight the improvement to the gravity field which has been derived from the 2 years GM. When an Extension-of-Life phase is conducted, the satellite instruments will be old. Particularly Jason-2 suffered from several safe-holds and instrument outages during the GM. This leads to systematic gaps...

We introduce an action-angle formalism for bounded geodesic motion in Kerr black hole spacetime using canonical perturbation theory. Namely, we employ a Lie series technique to produce a series of canonical transformations on a Hamiltonian function describing geodesic motion in Kerr background written in Boyer-Lindquist coordinates to a Hamiltonian system written in action-angle variables. This technique allows us to produce a closed-form invertible relation between the Boyer-Lindquist variables and the action-angle ones, while it generates in analytical closed form all the characteristic functions of the system as well. The expressed in the action-angle variable Hamiltonian system is employed to model an extreme mass ratio inspiral (EMRI), i.e., a binary system where a stellar compact object inspirals into a supermassive black hole due to gravitational radiation reaction. We consider the adiabatic evolution of an EMRI, for which the energy and angular momentum fluxes are computed by solving the Teukolsky equation in the frequency domain. To achieve this a new Teukolsky equation solver code was developed.

In the earlier work Gen. Rel. Grav. 40, 2201-2212 (2008) an oscillating Universe in the linearized R 2 theory of gravity has been analyzed. In that paper the linearized Ricci curvature generated a high energy term which was identified as the Dark Energy of the Universe. The model was consistent with the Hubble Law and the cosmological redshift. After carefully reviewing previous results, in this work such a model is improved. We show that the line element of the linearized R 2 theory is solution of the exact theory too. The results of earlier linearized approach are therefore consistent with the new model analyzed in the exact R 2 theory. The high energy associated to the Ricci curvature enables the coupling constant of the R 2 term in the gravitational action to be very small with respect to the linear term R. Accordingly, the deviation from standard General Relativity results very weak and the theory can pass the Solar System tests. A quantitative analysis on this critical point is realized too. Other observations, like the anomalous acceleration of the Pioneer and the Dark Matter in the galaxy, are consistent with the model. The basic approach of this paper is that, in the exact R 2 gravity, a wave-solution of a Klein-Gordon equation for the Ricci curvature could solve some problems of the Dark Universe. The Ricci curvature represents a cosmological wave-packet with a wavelength longer than the Hubble radius. With this assumption the wave-packet is frozen with respect to the cosmological observations. Consequently, the theory results to be in the form of standard General Relativity "embedded " in an effective scalar gravity. General Relativity results dominant a small scales, while the effective scalar field, which is exactly the Ricci curvature, oscillates and results dominant at longer scales. Finally, a cosmological solution to the Einstein-Vlasov System is discussed. This solution shows reasonable results which are within the standard bounds predicted by the cosmological observations. The model is also consistent with a recent result which shows that the introduction of a non-linear electrodynamics Lagrangian in the framework of R 2 gravity permits to remove the Initial Singularity of the Universe and to obtain a bouncing with a power-law inflation where the Ricci curvature works like an inflaton field. An important point is that, at the present time, a unique Extended Theory of Gravity which is consistent with all the astronomical observations has not been found. The results of this paper suggest that the cosmological wave-packet could be a potential candidate.

The Italian official height system is defined through a high precision levelling network established and maintained by the Istituto Geografico Militare - IGM. During the last 20 years, IGM has performed levelling campaigns on almost the whole peninsular area of Italy with the aim of both densifying the existing network and updating the reference heights. This paper reports about the procedure applied to correct the levelling observations for the gravity effects and the assessment on the results. The needed gravity values were predicted from the Italian gravity dataset (IGD), and both from EGM2008 and XGM2019e high resolution global gravity models. A new formulation of the normal correction as well as the standard orthometric correction were applied. The IGD derived corrections proved to be effective by reducing the misclosure error of critical loops below the tolerance level. Gravity data derived from EGM2008 and XGM2019e proved to be too poor for the correction purposes, as it was ...

The ring-down phase of black-hole perturbations is governed by the quasi-normal modes (QNM) and offer valuable insight into the nature of the objects emitting them, raising an interesting question: whether QNMs can be used to distinguish between theories of gravity? We construct a consistency test of general relativity (GR) which enables one to distinguish between general relativity and a specific class of modified theories of gravity: f (R). We show that an energetic inequality between scalar (polar) and vector (axial) type gravitational perturbations will exist for Reissner-Nördstrom solutions of GR-using which we find a novel method of determining the charge of a non-spinning black hole in GR. We then show that there will be a further energetic difference for charged black holes in f (R). Finally, we utilize this extra difference to construct a parameter to quantify deviation from GR.

Spherical harmonic expansion is a commonly applied mathematical representation of the earth's gravity eld. This representation is implied by the potential coe cients determined by using elements/parameters of the eld observed on the surface of the earth and/or in space outside the earth in the spherical harmonic expansion of the eld. International Centre for Gravity Earth Models (ICGEM) publishes, from time to time, Global Gravity Field Models (GGMs) that have been developed. These GGMs need evaluation with terrestrial data of di erent locations to ascertain their accuracy for application in those locations. In this study, Bouguer gravity anomalies derived from a total of eleven (11) recent GGMs, using sixty sample points, were evaluated by means of Root-Mean-Square difference and correlation coe cient. The Root-Mean-Square di erences of the computed Bouguer anomalies from ICGEM website compared to their positionally corresponding terrestrial Bouguer anomalies range from 9.530 mgal to 37.113 mgal. Additionally, the correlation coe cients of the structure of the signal of the terrestrial and GGM-derived Bouguer anomalies range from 0.480 to 0.879. It was observed that GECO derived Bouguer gravity anomalies have the best signal structure relationship with the terrestrial data than the other ten GGMs. We also discovered that EIGEN-6C4 and GECO derived Bouguer anomalies have enormous potential to be used as supplements to the terrestrial Bouguer anomalies for Enugu State, Nigeria.

The geodetic and geophysical applications of Earth Gravity Field parameters computed from Global Geopotential Models (GGMs) are quite on the increase despite the inherent commission and omission errors of these models. In view of this, this study focuses on refining and quantifying terrain-induced effects on Bouguer gravity anomalies computed directly from a total of seven recent GGMs. In the study, the Residual Terrain Model (RTM) technique was used to estimate the residual terrain effects that were added to the GGM-computed Bouguer gravity anomalies at the sixty test points in Enugu State, Nigeria. The computed residual terrain effects range from −24.6 to 37.5 mgal while the percentage of the omission errors of the GGMs based on their Root-Mean-Square (RMS) differences ranges from 7.8% to 44.7%. It can be concluded that GGM-refined Bouguer gravity anomalies are better in accuracy than the unrefined GGM-computed Bouguer gravity anomalies and hence there is need for accurate height information in the development of GGMs. We, therefore, recommend that refined Bouguer gravity anomalies obtained from HUST-Grace2016s, EIGEN-6C4 and GECO that gave best improvement amongst the seven GGMs under consideration should be used to supplement the available terrestrial Bouguer anomalies for geodetic and geophysical applications within the study area.

Spherical harmonic expansion is a commonly applied mathematical representation of the earth’s gravity field. This representation is implied by the potential coeffcients determined by using elements/parameters of the field observed on the surface of the earth and/or in space outside the earth in the spherical harmonic expansion of the field. International Centre for Gravity Earth Models (ICGEM) publishes, from time to time, Global Gravity Field Models (GGMs) that have been developed. These GGMs need evaluation with terrestrial data of different locations to ascertain their accuracy for application in those locations. In this study, Bouguer gravity anomalies derived from a total of eleven (11) recent GGMs, using sixty sample points, were evaluated by means of Root-Mean-Square difference and correlation coeficient. The Root-Mean-Square differences of the computed Bouguer anomalies from ICGEMwebsite compared to their positionally corresponding terrestrial Bouguer anomalies range from 9....

We present the validation of sea level measurements taken over the eastern shelf of the Gulf of Cadiz (southwestern Iberian Peninsula) by the European Space Agency CryoSat-2 satellite's SIRAL altimeter in SAR mode. Time series of sea level anomaly (SLA) at 20-Hz posting rate (corresponding to approximately 350 m along the satellite track) are compared against sea level measurements from two tide gauge stations located along the Spanish coast of the study area. Due to the long repeat cycle of CryoSat-2 (369 days), data selection is performed by including all the tracks falling in a radius of 50 km from the location of the tide gauge stations. Then, time series of SLA are formed during the observational time period (August 2010-December 2014) by taking the altimeter measurements located at growing distances from the coast (1, 3, 5, 10, 15 and 20 km) as well as around four isobaths (10, 25, 50 and 75 m). The validation of AltiKa's SARAL altimeter 20-Hz data, using its two 35-day-repeat ground tracks available in the area is also presented. Overall, CryoSat-2 20-Hz SLAs selected in the coastal strip from 3 to 20 km agree well with data from the western station (Huelva) with rmse ranging from 11.4 to 6.4 cm. The analysis at the eastern station (Bonanza) yields rmse ranging from 16.8 to 14.6 cm. The comparisons made with CryoSat-2 20-Hz SLAs are in agreement with the rmse estimated using AltiKa 20-Hz SLAs at distances to the coast higher than 5 km, and much better in the 1-5 coastal band. The differences in quantity of SAR mode data observed at the two stations and in their agreement with the tide gauges can be explained by (1) the more complex coastal morphology around Bonanza station with the altimetry tracks almost parallel to the coast; (2) the noisier hydrodynamics around Bonanza station due to the presence of the estuary mouth of the Guadalquivir River; and (3) residual (uncorrected) tidal signals in the Bonanza gauge record. We conclude that the quality of SAR altimetry is comparable or even slightly better than conventional altimetry, thus qualifying SAR data for exploitation in oceanographic studies and sea level monitoring. An example is the analysis made of the surface signal due to a heavy Guadalquivir River discharge event.

Due to the increasingly advanced digital devices, high resolution cameras and utility of fast processing, Unmanned Aerial Vehicles (UAV) have become a prominent feature of the various remote sensing procedures. Because the benefits of the technology may justify the use of data in topographic mapping, cadastral mapping or even engineering geodesy, we have conducted studies to determine the accuracy that can be achieved using UAV as an integrated data acquisition tool. First, we developed a test field in rural area for investigations. The results of the test flights conducted there were determined that what conditions influence the accuracy of the survey.

Equations of motions and energy-momentum density tensors are obtained for a dispersive and dissipative medium sustaining electric and magnetic polarizations, using Lagrangian formalisms. A previous work on the subject by the authors has been simplified by reduction in the Lagrangian of the number of independent vector fields, with which the sink modes (associated with the dissipation) interact. The paper also formulates the dynamics of the electromagnetic field in the medium in a covariant (relativistic) manner. We discuss (and compare) the results, especially from the point of view of the positivity of the energy density.

GGMs GNSS/Levelling Geoid Statistical values This paper focuses on making a comparing of GNSS/Levelling data and data obtained from global geopotential models. For comparison, geoid undulations obtained by GNSS/Levelling method and geoid undulations obtained from global geopotential models have been used. As global geopotential models, SGG-UGM-2, XGM2019e_2159, GO_CONS_GCF_2_TIM_R6e, ITSG-Grace2018s, EIGEN-GRGS.RL04.MEAN-FIELD, GOCO06s, GO_CONS_GCF_2_TIM_R6, GO_CONS_GCF_2_DIR_R6 GGMs are used. The data sets used in the improvements of the models are altimetry, satellite, location data and topography. The disparities between the geoid undulations obtained from the GNSS/Levelling method and geoid undulations obtained from global geoid models have been taken. Some statistical criteria for these differences have been calculated. These criteria, such as smallest, biggest, average, standard deviation, Root Mean Square RMS statistical values of deviations between GNSS/Levelling geoid and global geopotential models, are taken into consideration when comparing the models. According to the comparison, the global gravity field model that best fits the GNSS/Levelling is selected.

A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction procedure to deal with them must be carried on. The reduction of the implicit control equations arising in these problems will be discussed in the slightly more general setting of implicit equations defined by invariant one-forms on Lie groups. As an instance, the first order differential equations describing the extremal solutions of an optimal control problem for a single spinning particle, obtained by using Pontryagin's Maximum Principle (PMP), will be found and shown to be completely integrable. Then, using again PMP, solutions for the problem of two coupled spinning particles will be characterised as solutions of a system of coupled non-linear matrix differential equations. The reduction of the implicit system will show that the reduced space for them is the product of the space of states for the independent systems, implying the absence of 'entanglement' in this instance. Finally it will be shown that, in the case of identical systems, the degree three matrix polynomial differential equations determined by the optimal feedback law, constitute a completely integrable Hamiltonian system and some of its solutions are described explicitly.

This paper investigates an accurate and efficient nonlinear method for propagating geostationary trajectory uncertainties under four dominant perturbations: solar radiation pressure, Earth's non-spherical gravity potential, and luni-solar gravitational attractions. A Jet Transport-based scheme (also known as Differential Algebra) is considered and implemented in several coordinate representations, and in two forms: Taylor and Chebyshev expansions. Taking into account the size of the uncertainty neighborhood, as well as the order and time

Doñana National Park is an area of approximately 500 km 2 located on the SW coast of Spain that shows one of the greatest geoid gradients on the entire Iberian Peninsula, due to its peculiar tectonic characteristics. So, it is necessary to elaborate an accurate geoid model that can be used with GPS for precise surveying, since the existing ones are insufficient, due to their poor resolution and their limited adaptation to a small area with such a strong gradient. The least squares prediction method was tested in order to obtain the undulation from GPS/orthometric points. The results obtained were unsatisfactory because of the strong geoid gradient. In order to improve accuracy the remove-restore technique was used. Global geopotential model EIGEN-CG01C and a Digital Elevation Model (DEM) with a 25 × 25 m resolution and an accuracy better than 3 m were used. Thus, the final geometrical geoid obtained reaches the precision required by other disciplines (3 cm in any point within the Park). Particularly, the geoid model has allowed for the acquisition of a precision DEM that is essential to formulate a hydrodynamic model for the Doñana marsh functions.