Disturbing Potential

2021 ◽  
pp. 99-124
Author(s):  
Willi Freeden
Keyword(s):  
Disturbing Potential

scholarly journals The surface layer integral method for the modelling of the radial gravity gradient component over sea surface

2019 ◽  
Vol 9 (1) ◽  
pp. 127-132
Author(s):  
D. Zhao ◽  
Z. Gong ◽  
J. Feng
Keyword(s):  
Surface Layer ◽  
Integral Method ◽  
Integral Formula ◽  
Radial Component ◽  
Second Order ◽  
Sea Surface ◽  
Gravity Potential ◽  
Gravity Gradient ◽  
Disturbing Potential ◽  
Gradient Component

Abstract For the modelling and determination of the Earth’s external gravity potential as well as its second-order radial derivatives in the space near sea surface, the surface layer integral method was discussed in the paper. The reasons for the applicability of the method over sea surface were discussed. From the original integral formula of disturbing potential based on the surface layer method, the expression of the radial component of the gravity gradient tensor was derived. Furthermore, an identity relation was introduced to modify the formula in order to reduce the singularity problem. Numerical experiments carried out over the marine area of China show that, the modi-fied surface layer integral method effectively improves the accuracy and reliability of the calculation of the second-order radial gradient component of the disturbing potential near sea surface.

scholarly journals Candidates for multiple impact craters: popigai and chicxulub as seen by EGM08, a global 5'×5' gravitational model

2010 ◽  
Vol 2 (1) ◽  
pp. 69-103 ◽  
Author(s):  
J. Klokočník ◽  
J. Kostelecký ◽  
I. Pešek ◽  
P. Novák ◽  
C. A. Wagner ◽  
...  
Keyword(s):  
High Spatial Resolution ◽  
Impact Craters ◽  
Stokes Parameters ◽  
Disturbing Potential ◽  
Gravitational Model ◽  
Secondary Crater ◽  
Complete Set ◽  
Multiple Impact ◽  
The Impact ◽  
Main Crater

Abstract. In 2008 the new Earth Gravitational Model (EGM08) was released. It contains a complete set of spherical harmonic coefficients of the Earth's gravitational potential (Stokes parameters) to degree 2190 and order 2159 that can be used for evaluation of various potential quantities with both the unprecedented accuracy and high spatial resolution. Two such quantities, the gravity anomaly and second-order radial derivative of the disturbing potential, were computed over selected areas with known impact craters. The displays of these derivatives for two such sites clearly show not only the strong circular-like features known to be associated with them but also other symmetrical structures which appear to make them multiple impact sites. At Popigai, Siberia, the secondary circular features fall in a line from the primary in the SE direction. At Chicxulub, Yucatán, there appears to be one secondary crater close to the primary in the NE direction, as well as possibly others in the vicinity of the main crater. Gravity information alone is not proof of the impact craters but it is useful in identifying candidate sites for further study, for future examination by geologists and geophysicists.

scholarly journals Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography

2020 ◽  
Vol 50 (3) ◽  
pp. 287-302
Author(s):  
Róbert ČUNDERLÍK ◽  
Matej MEDĽA ◽  
Karol MIKULA
Keyword(s):  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Scale ◽  
Horizontal Resolution ◽  
Geopotential Model ◽  
Computational Domain ◽  
Disturbing Potential ◽  
Volume Method ◽  
Upper Boundary

The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

Decorrelative Mollifier Gravimetry

2021 ◽  
Author(s):  
Willi Freeden
Keyword(s):  
Inverse Problems ◽  
Density Contrast ◽  
Disturbing Potential ◽  
Book Series ◽  
Inverse Gravimetry ◽  
Constructive Approximation ◽  
Vening Meinesz ◽  
Inverse Gravimetry Problem

<p>The lecture highlights arguments that, coming from multiscale mathematics, have fostered the advancement of gravimetry, as well as those that, generated by gravimetric problems, have contributed to the enhancement in constructive approximation and numerics. Inverse problems in gravimetry are delt with multiscale mollifier decorrelation strategies. Two examples are studied in more detail: (i) Vening Meinesz multiscale surface mollifier regularization to determine locally the Earth's disturbing potential from deflections of vertical, (ii) Newton multiscale volume mollifier regularization of the inverse gravimetry problem to derive locally the density contrast distribution from functionals of the Newton integral and to detect fine particulars of geological relevance. All in all, the Vening Meinesz medal  lecture is meant as an  \lq \lq appetizer'' served to enjoy the tasty meal "Mathematical Geoscience Today'' to be shared by geoscientists and mathematicians in the field of gravimetry. It provides innovative concepts and locally relevant applications presented in a monograph to be published by Birkhäuser in the book series “Geosystems Mathematics” (2021).</p>

Evaluation of the latest GOCE GGMs in support of regional geoid modeling over Greece

2021 ◽  
Author(s):  
Georgios S. Vergos ◽  
Ilias N. Tziavos ◽  
Dimitrios A. Natsiopoulos ◽  
Elisavet G. Mamagiannou ◽  
Eleftherios A. Pitenis
Keyword(s):  
Maximum Degree ◽  
Gravity Data ◽  
Ground Truth ◽  
Satellite Gravity ◽  
Disturbing Potential ◽  
Geopotential Models ◽  
Potential Functionals ◽  
Geoid Computation ◽  
Goce Satellite

<p>In the frame of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, GOCE Satellite Gravity Gradiometry (SGG) data are to be used for regional geoid and gravity field refinement as well as for potential determination in the frame of the International Height Reference Frame (IHRF). An inherent step in the geoid computation with either stochastic or spectral methods is the reduction of the related disturbing potential functionals within the well-known Remove-Compute-Restore (RCR) procedure. In this work we evaluate the latest, Release 6 (R6), satellite only and combined Global Geopotential Models (GGMs) which rely solely on GOCE and on land gravity data. The evaluation is performed over the established network of 1542 GPS/Levelling benchmarks over Greece mainland (BMs), which have been used in the past for the evaluation of GOCE GGMs. We employ the spectral enhancement approach, during which the GOCE-based GGMs are evaluated every one degree to the maximum degree of expansion coupled by EGM2008 and high-frequency RTM effects. This synthesis resolves wavelengths corresponding to maximum degree 216,000, hence the omission error is at the few mm-level. TIM-R6, DIR-R6, GOCO06s and XGM2019e are evaluated using EGM2008 residuals to the GPS/Levelling as the ground truth. From the results achieved, the optimal combination degree of a GOCE-only GGM augmented with EGM2008 is selected to be used in the sequel as reference field for the practical determination of the gravimetric geoid over Greece.</p>

scholarly journals Long Periodic Variation of Orbital Elements of A Satellite Perturbed by Discrete Gravity Anomalies

1978 ◽  
Vol 41 ◽  
pp. 240-240
Author(s):  
M.P. Ananda
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Large Data ◽  
Periodic Variation ◽  
Static Case ◽  
Orbital Elements ◽  
Disturbing Potential ◽  
Data Set ◽  
Simple Matrix ◽  
Derivatives Of

AbstractA method for generating long periodic variations in satellite orbital elements when perturbed by discrete gravity anomalies is presented. The method consists of developing a disturbing potential as a function of orbital and gravity anomaly parameters, and generating partial derivatives of the potential with respect to the orbital elements. The partials are averaged over the period of the satellite to eliminate the short periodic variations. The averaged partials are substituted into the variation of parameter equations to give the mean orbital rates. Classically orbital elements are used in generating gravity field and thus the method is dynamic in nature. The problem is extremely cumbersome and complex when multi-state parameters have to be estimated from a considerably large data set. However, when mean orbital rates are used, the problem reduces to a simple linear static case, where only the gravity parameters have to be estimated, and it is a simple matrix inversion problem. Thus the method developed here was utilized in reducing Appolo 15 and 16 subsatellite radio tracking data to produce a lunar gravity field represented by point masses.

scholarly journals Very-High-Eccentricity Librations at Some Higher Order Resonances

1992 ◽  
Vol 152 ◽  
pp. 153-158 ◽  
Author(s):  
J.C. Klafke ◽  
S. Ferraz-Mello ◽  
T. Michtchenko
Keyword(s):  
Phase Space ◽  
Numerical Integration ◽  
Higher Order ◽  
Planar Problem ◽  
High Eccentricity ◽  
Disturbing Potential ◽  
Numerical Exploration ◽  
Numerical Integrations ◽  
Short Period ◽  
Very High

Motions near the 3:1, 4:1 and 5:2 resonances with Jupiter are studied by means of numerical integrations of a semi-analytically averaged Sun-Jupiter-asteroid planar problem. In order to have a model including the very-high-eccentricity regions of the phase space, we adopted a set of local expansions of the disturbing potential, adequate to perform the numerical exploration of regions in the phase space with eccentricities higher than 0.9 (Ferraz-Mello and Klafke, 1991). Individual solutions and qualitative results thus obtained are completely reproduced by numerical integration of the complete equations by filtering off the short-period components of these solutions.

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