Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients

Tenzer, Róbert; Novák, Pavel; Prutkin, I.; Ellmann, Artu; Vajda, P.

doi:10.1007/s11200-009-0010-1

Cited by 9 publications

(6 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Geod., 55 (2011) By analogy with Eq. (5), Tenzer et al (2009) defined the extended Stokes integral for computing the far-zone contribution to the disturbing potential fz T in the point   , r  above the geoid surface in the following form…”

Section: Green's Integrals By Means Of Molodensky's Truncation Coeffimentioning

confidence: 99%

“…2-17), Green's integral modified for computing the far-zone contribution to the gravity disturbance fz g  was found to be (cf. Tenzer et al, 2009) …”

Section: Green's Integrals By Means Of Molodensky's Truncation Coeffimentioning

confidence: 99%

“…In these studies, the form of truncation coefficients depends on the type of integral. A different concept for a definition of truncation coefficients was proposed in Tenzer et al (2009), where Stud. Geophys.…”

Section: Introductionmentioning

confidence: 99%

“…Geod., 55 (2011) Molodensky's truncation coefficients were applied uniformly to all types of Green's integrals used in solving the boundary-value problems. Tenzer et al (2009) introduced the far-zone modified spherical harmonics. The far-zone modified spherical harmonics are functionally related with the spherical harmonics by means of Molodensky's truncation coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…Following the methodology presented in Tenzer et al (2009), we introduce the far-zone modified spherical height functions. The far-zone modified spherical height functions are functionally related with the spherical height functions by means of Molodensky's truncation coefficients.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

et al. 2011

Self Cite

View full text Add to dashboard Cite

A spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients are applied to a spectral representation of Newton's integral. In this study we utilise Molodensky's truncation coefficients in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms of Molodensky's truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data.

show abstract

Section: Green's Integrals By Means Of Molodensky's Truncation Coeffimentioning

confidence: 99%

“…2-17), Green's integral modified for computing the far-zone contribution to the gravity disturbance fz g  was found to be (cf. Tenzer et al, 2009) …”

Section: Green's Integrals By Means Of Molodensky's Truncation Coeffimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

et al. 2011

Self Cite

View full text Add to dashboard Cite

show abstract

Uncertainties associated with integral-based solutions to geodetic boundary-value problems

Novák,

Eshagh,

Pitoňák

2024

J Geod

View full text Add to dashboard Cite

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 for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

show abstract

An accurate and lightweight calculation for the high degree truncation coefficient via asymptotic expansion with applications to spectral gravity forward modeling

Zhong,

Li,

2024

J Geod

View full text Add to dashboard Cite

Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients

Abstract: To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid

Cited by 9 publications

References 11 publications

Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

Uncertainties associated with integral-based solutions to geodetic boundary-value problems

An accurate and lightweight calculation for the high degree truncation coefficient via asymptotic expansion with applications to spectral gravity forward modeling

Contact Info

Product

Resources

About