A new formula for evaluating the truncation error coefficient

Hagiwara, Yukio

doi:10.1007/bf02522312

Cited by 36 publications

(7 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(A.1) or applying Paul's (1973) algorithm. Alternatively, they can be computed recurrently (cf., Hagiwara, 1976). We note that Green's integrals can be readily reformulated for the ellipsoidal approximation of the geoidal surface according to the approach described in Vaníček et al (1995).…”

Section: Far-zone Contributions To the Gravity Field Quantitiesmentioning

confidence: 99%

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

et al. 2009

View full text Add to dashboard Cite

show abstract

Section: Far-zone Contributions To the Gravity Field Quantitiesmentioning

confidence: 99%

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

et al. 2009

View full text Add to dashboard Cite

show abstract

“…7) is derived in the Appendices of Jekeli (1979), and recursions for e nk (ψ 0 ) (Eq. 28) are given in Paul (1973) or Hagiwara (1972Hagiwara ( , 1976 …”

Section: Deterministic Hybrid (Modification D4)mentioning

confidence: 99%

Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral

Featherstone

2013

J Geod

View full text Add to dashboard Cite

show abstract

“…where S is the Stokes function. The coefficients Q n are computed recurrently according to formulae provided by Hagiwara (1975). Alternatively, they can be computed using the algorithm developed by Paul (1973).…”

Section: Spectral Approach For the Far-zone Contributionmentioning

confidence: 99%

Application of Möbius coordinate transformation in evaluating Newton's integral

Tenzer

Gladkikh

2011

Contributions to Geophysics and Geodesy

View full text Add to dashboard Cite

Application of Möbius coordinate transformation in evaluating Newton's integralWe propose a numerical scheme which efficiently combines various existing methods of solving the Newton's volume integral. It utilises the analytical solution of Newton's integral for tesseroid in computing the near-zone contribution to gravitational field quantities (potential and its first radial derivative). The far-zone gravitational contribution is computed using the expressions derived based on applying Molodensky's truncation coefficients to a spectral representation of Newton's integral. The weak singularity of Newton's integral is treated analytically using formulas for the gravitational contribution of the cylindrical mass volume centered with respect to the observation point. All three solutions are defined and evaluated in the system of polar spherical coordinates. A conversion of the geographical to polar spherical coordinates of input data sets (digital terrain and density models) is based on the Möbius transformation with an enhanced integration grid resolution at vicinity of the observation point.

show abstract

A new formula for evaluating the truncation error coefficient

Cited by 36 publications

References 3 publications

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

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

Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral

Application of Möbius coordinate transformation in evaluating Newton's integral

Contact Info

Product

Resources

About