Martin Pitoňák
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View article: On the Accurate Determination of the Orthometric Correction to Levelled Height Differences—A Case Study in Hong Kong
On the Accurate Determination of the Orthometric Correction to Levelled Height Differences—A Case Study in Hong Kong Open
Orthometric heights are practically determined from levelling and gravity measurements by applying orthometric corrections to levelled height differences. Currently, Helmert’s definition of orthometric heights is mostly used, with the mean…
View article: Uncertainty propagation through integral inversion of satellite gradient data in regional gravity field recovery
Uncertainty propagation through integral inversion of satellite gradient data in regional gravity field recovery Open
View article: Far-Zone Effects for Spherical Integral Transformations II: Formulas for Horizontal Boundary Value Problems and Their Derivatives
Far-Zone Effects for Spherical Integral Transformations II: Formulas for Horizontal Boundary Value Problems and Their Derivatives Open
Integral formulas represent a methodological basis for the determination of gravitational fields generated by planetary bodies. In particular, spherical integral transformations are preferred for their symmetrical properties with the integ…
View article: Uncertainties associated with integral-based solutions to geodetic boundary-value problems
Uncertainties associated with integral-based solutions to geodetic boundary-value problems Open
Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular fo…
View article: Uncertainties associated with integral-based transforms of measured potential gradients
Uncertainties associated with integral-based transforms of measured potential gradients Open
The geoid model over dry land areas is determined from data observed at or above the Earth’s surface. Observable quantities include various functional of the disturbing potential defined as the difference between the real and model (…
View article: Estimation of the Global Root Mean Square Error of Selected Gravitational Field Functionals Calculated by Integral Transforms
Estimation of the Global Root Mean Square Error of Selected Gravitational Field Functionals Calculated by Integral Transforms Open
Integral transformations of the gravitational field gradients are defined over the entire solid angle on the surface of the sphere. Despite the indisputable progress in satellite gravimetry and gradiometry, gravity field focused satellite …
View article: FarZone4IT: A new software for the calculation of far–zone effects for spherical integral
FarZone4IT: A new software for the calculation of far–zone effects for spherical integral Open
Integral transformations are a useful mathematical apparatus for modelling the gravitational field. They represent the mathematical basis for the formulation of integral estimators of gravity field values, including error propagation. The …
View article: Regional gravitational field modelling by the spectral combination of satellite higher-order radial derivatives of the gravitational potential and a global geopotential model
Regional gravitational field modelling by the spectral combination of satellite higher-order radial derivatives of the gravitational potential and a global geopotential model Open
In this contribution, we will discuss a problem of regional gravitational field modelling by the spectral combination of spaceborne first-, second- and third-order radial derivatives of the gravitational potential at the mean altitude of 2…
View article: Evaluation of external spherical harmonic series inside the minimum Brillouin sphere: examples for the lunar gravitational field
Evaluation of external spherical harmonic series inside the minimum Brillouin sphere: examples for the lunar gravitational field Open
Spherical harmonic expansions are routinely used to represent the gravitational potential and its higher-order spatial derivatives in global geodetic, geophysical, and planetary science applications. The convergence domain of external sphe…
View article: Merania družicovej misie GRAIL a senzoru LOLA riešia otázku konvergencie/divergencie analytického pokračovania vonkajších rozvojov do radu sférických harmonických funkcií
Merania družicovej misie GRAIL a senzoru LOLA riešia otázku konvergencie/divergencie analytického pokračovania vonkajších rozvojov do radu sférických harmonických funkcií Open
Rozvoje do radu sférických harmonických funkcií sa rutinne používajú pri reprezentácií gravitačného potenciálu a jeho priestorových derivácií v globálnych geodetických, geofyzikálnych a planetárnych aplikáciách. Oblasťou konvergencie tzv. …
View article: Vliv vzdálených zón pro integrální transformace: teorie a implementace
Vliv vzdálených zón pro integrální transformace: teorie a implementace Open
Integrální transformace jsou užitečný matematický aparát pro modelování gravitačního pole a vyžadují formulaci integrálních odhadů včetně chybových charakteristik. Pro klasické integrální transformace byla již tato problematika prozkoumána…
View article: Validácia gridov gravitačných gradientov pomocou výškových anomálií v Nórsku, Česku a na Slovensku
Validácia gridov gravitačných gradientov pomocou výškových anomálií v Nórsku, Česku a na Slovensku Open
Vypustenie družicových misií zameraných na tiažové pole Zeme na začiatku nového tisícročia viedlo k zlepšeniu presnosti globálnych gravitačných modelov (GGM). Jednou z týchto misií bola družica GOCE vypustená v roku 2009. Ako prvá niesla n…
View article: Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method
Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method Open
In this study, we apply a spectral combination method for estimation of height anomalies from gradients of the gravitational potential measured by satellites. The spectral combination method is used for solving over-determined problems wit…
View article: Combination of integral transforms by spectral weighting – an overview  
Combination of integral transforms by spectral weighting – an overview   Open
<p>Geodetic boundary-value problems (BVPs) and their solutions represent an important tool for describing and modelling potential fields such as the Earth’s gravitational field. Solutions to spherical geodetic BVPs lead to …
View article: Odhad hrúbky litosféry z vertikálnych gradientov meraných družicou GOCE a modelu CRUST 1.0
Odhad hrúbky litosféry z vertikálnych gradientov meraných družicou GOCE a modelu CRUST 1.0 Open
Elastická hrúbka litosféry (Te) je parameter predstavujúci litosférickú pevnosť vzhľadom na zaťaženie. Tieto miesta s veľkými hodnotami elastickej hrúbky sa ohýbajú menej. V tomto príspevku sa na určenie hrúbky litosféry v Afrike používajú…
View article: Odhad hustoty kůry a globálního gravitačního pole Měsíce z dat družicové mise GRAIL a senzoru LOLA
Odhad hustoty kůry a globálního gravitačního pole Měsíce z dat družicové mise GRAIL a senzoru LOLA Open
V tejto štúdií používame Newtonov integrál v spektrálnej oblasti na riešenie dvoch geodetických/geofyzikálnych úloh pre Mesiac, viď [1]. V prvej úlohe odhadneme hustotu mesačnej kôry (inverzný problém). Využívame model gravitačného poľa GL…
View article: Colorado geoid computation experiment: overview and summary
Colorado geoid computation experiment: overview and summary Open
View article: Contribution of GRAV-D airborne gravity to improvement of regional gravimetric geoid modelling in Colorado, USA
Contribution of GRAV-D airborne gravity to improvement of regional gravimetric geoid modelling in Colorado, USA Open
This paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, th…
View article: Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting &#160;&#160;
Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting    Open
<p>The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational poten…
View article: Calculation of Agro-Climatic Factors from Global Climatic Data
Calculation of Agro-Climatic Factors from Global Climatic Data Open
This manuscript aims to create large-scale calculations of agro-climatic factors from global climatic data with high granularity-climatic ERA5-Land dataset from the Copernicus Climate Change Service in particular. First, we analyze existin…
View article: Overview on the spectral combination of integral transformations
Overview on the spectral combination of integral transformations Open
<p>Geodetic boundary-value problems (BVPs) and their solutions are important tools for describing and modelling the Earth’s gravitational field. Many geodetic BVPs have been formulated based on gravitational observables mea…
View article: Lithospheric elastic thickness estimates in central Eurasia
Lithospheric elastic thickness estimates in central Eurasia Open
View article: Elastic Thickness Determination from on-orbit GOCE Data and CRUST1.0
Elastic Thickness Determination from on-orbit GOCE Data and CRUST1.0 Open
View article: Definition of Physical Height Systems for Telluric Planets and Moons
Definition of Physical Height Systems for Telluric Planets and Moons Open
View article: Local gravitational field modelling through spectral combination of satellite higher-order radial derivatives of the disturbing gravitational potential and a global gravitational model
Local gravitational field modelling through spectral combination of satellite higher-order radial derivatives of the disturbing gravitational potential and a global gravitational model Open
View article: Regional recovery of the disturbing gravitational potential by inverting satellite gravitational gradients
Regional recovery of the disturbing gravitational potential by inverting satellite gravitational gradients Open
Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surfac…
View article: Regional recovery of the disturbing gravitational potential from satellite observations of first-, second- and third-order radial derivatives of the disturbing gravitational potential
Regional recovery of the disturbing gravitational potential from satellite observations of first-, second- and third-order radial derivatives of the disturbing gravitational potential Open