Discrete solutions of the boundary value problem in physical geodesy
Open accessAbstract
Solutions of the discrete boundary value problem of physical geodesy are discussed. Dirac impulses, Wiener–Hopf predictions and “reflexive predictions” are compared. The dramatic computational gains with “reflexive filtering” are discussed.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The gravitational potential difference at points P and Q can be calculated using the general theory of relativity and frequency measurements obtained from atomic clocks.
“According to Bjerhammar, (1975) and Bjerhammar, (1985), the gravitational potential difference at points P and Q can be calculated using the general theory of relativity and frequency measurements obtained from atomic clocks, with the following formula [Sjöberg and Bagherbandi (2017), Chapter 7]:”
From Time transfer and significance of vertical land motion in relativistic geodesy applications: a review paper (2023) · cites this paper as Bjerhammar, (1975)
Cites
(1962) · Israel Program for Scientific Translations eBooks · Cited by 386 · see citing works
A Contribution to the Mathematical Foundation of Physical Geodesy
Borre, P. D. K. (2006) · Springer eBooks · doi:10.1007/3-540-33767-9_4 · Cited by 242 · see citing works
Hilbertsche Räume mit Kernfunktion
Meschkowski, H. (1962) · Springer eBooks · doi:10.1007/978-3-642-94848-0 · Cited by 171 · see citing works
Theory of errors and generalized matrix inverses
Bjerhmmar, A. (1974) · Bulletin Géodésique · doi:10.1007/bf02521826 · Cited by 144 · see citing works
Hilbertsche Räume mit Kernfunktion
Meschkowski, H., & Henney, D. R. (1963) · Physics Today · doi:10.1063/1.3051022 · Cited by 139 · see citing works
Determination of the Earth's gravitational field
Kaula, W. M. (1963) · Reviews of Geophysics · doi:10.1029/rg001i004p00507 · Cited by 78 · see citing works
Bjerhammar, A. (1958) · Elanders Boktryckeri Aktiebolag eBooks · Cited by 61 · see citing works
Self-citationSystèmes totaux de fonctions harmoniques
Deny, J. (1949) · Annales de l’institut Fourier · doi:10.5802/aif.9 · Cited by 55 · see citing works
A new theory of gravimetric geodesy
Bjerhammar, A. (1965) · Studia Geophysica et Geodaetica · doi:10.1007/bf02607317 · Cited by 34 · see citing works
Self-citationTheory of errors and generalized matrix inverses
Bjerhammar, A. (1973) · Cited by 25 · see citing works
Self-citationA study of covariance functions related to the earth's disturbing potential
Meissl, P. (1971) · The Knowledge Bank (The Ohio State University) · Cited by 19 · see citing works
On the boundary value problem of physical geodesy
Bjerhammar, A. (1969) · Tellus A Dynamic Meteorology and Oceanography · doi:10.3402/tellusa.v21i4.10103 · Cited by 14 · see citing works
Self-citationHeitz, S., & Tscherning, C. C. (1972) · Tellus A Dynamic Meteorology and Oceanography · doi:10.3402/tellusa.v24i3.10640 · Cited by 9 · see citing works
On the computation of spherical harmonics from satellite observations.
Moritz, H., & Schwarz, K. P. (1973) · Cited by 9 · see citing works
GRAVIMETRIC GEODESY FREE OF DENSITY ESTIMATES THROUGH ANALYSIS OF DISCRETE GRAVITY DATA
Bjerhammar, A. (1963) · Cited by 8 · see citing works
Self-citationBjerhammar, A. (1969) · Bulletin Géodésique · doi:10.1007/bf02521897 · Cited by 6 · see citing works
Self-citationOn the astrogeodetic determination of the geoid by least squares estimation
Heitz, S. (1971) · Bulletin Géodésique · doi:10.1007/bf02522008 · Cited by 4 · see citing works
On determination of shape of earth by using analytical continuation of function
Pick, M. (1965) · Studia Geophysica et Geodaetica · doi:10.1007/bf02607410 · Cited by 4 · see citing works
Bjerhammar, A. (1967) · Cited by 2 · see citing works
Self-citation
Flagged first, then by citations
3 of the 22 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Mehlstäubler, T. E., Grosche, G., Lisdat, C., Schmidt, P. O., & Denker, H. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab409 · Cited by 263 · see citing works
Moritz, H. (1978) · Reviews of Geophysics · doi:10.1029/rg016i003p00421 · Cited by 262 · see citing works
Bjerhammar, A. (1985) · Bulletin Géodésique · doi:10.1007/bf02520327 · Cited by 165 · see citing works
Self-citationThe topographic bias by analytical continuation in physical geodesy
Sjöberg, L. E. (2006) · Journal of Geodesy · doi:10.1007/s00190-006-0112-2 · Cited by 123 · see citing works
Huang, Y., Zhang, H., Zhang, B., Hao, Y., Guan, H., Zeng, M., Chen, Q., Lin, Y., Wang, Y., Cao, S., et al. (2020) · Physical Review A · doi:10.1103/physreva.102.050802 · Cited by 52 · see citing works
Geodetic applications of stochastic processes
Grafarend, E. W. (1976) · Physics of The Earth and Planetary Interiors · doi:10.1016/0031-9201(76)90045-5 · Cited by 50 · see citing works
The terrain correction in gravimetric geoid computation-is it needed?
Sjöberg, L. E. (2008) · Geophysical Journal International · doi:10.1111/j.1365-246x.2008.03851.x · Cited by 27 · see citing works
Archaean green-light environments drove the evolution of cyanobacteria’s light-harvesting system
Matsuo, T., Ito-Miwa, K., Hoshino, Y., Fujii, Y. I., Kanno, S., Fujimoto, K. J., Tsuji, R., Takeda, S., Onami, C., Arai, C., et al. (2025) · Nature Ecology & Evolution · doi:10.1038/s41559-025-02637-3 · Cited by 8 · see citing works
Planar, spherical and ellipsoidal approximations of Poisson's integral in near zone
Goli, M., & Najafi-Alamdari, M. (2010) · Journal of Geodetic Science · doi:10.2478/v10156-010-0003-6 · Cited by 8 · see citing works
Geoid model validation and topographic bias
Sjöberg, L. E. (2022) · Journal of Geodetic Science · doi:10.1515/jogs-2022-0133 · Cited by 4 · see citing works
History of the Method for Sourcewise Approximations of Geopotential Fields
Долгаль, А. С., Пугин, А. В., & Новикова, П. Н. (2022) · Izvestiya Physics of the Solid Earth · doi:10.1134/s1069351322020021 · Cited by 4 · see citing works
Stability investigations of various representations of the gravity field
Gerstl, M., & Rummel, R. (1981) · Reviews of Geophysics · doi:10.1029/rg019i003p00415 · Cited by 4 · see citing works
Bagherbandi, M., Shirazian, M., Amin, H., & Horemuz, M. (2023) · Frontiers in Earth Science · doi:10.3389/feart.2023.1139211 · Cited by 2 · see citing works
“This method was proposed for the first time by Bjerhammar, (1975). Later, he introduced the idea of relativistic geodesy (see Bjerhammar, 1985). Vermeer, (1983), who introduced chronometric leveling, also studied relativistic geodesy (see also Delva and Lodewyck, 2013). This novel approach helps determine the potentia…”
MethodInfluential
- Authors
- Bjerhammar, A.
- Affiliations
- KTH Royal Institute of Technology (SE)
- Corresponding author
- Bjerhammar, Arne
- Venue
- Tellus A: Dynamic Meteorology and Oceanography
- Publisher
- Stockholm University Press
- Published
- 1975-01-01
- Volume
- 27
- Issue
- 2
- Pages
- 97
- ISSN
- 0280-6495 (ISSN-L)
- 1600-0870
- OpenAlex
- W2041817758
- Cited by
- 13
- References
- 22
- Citations by year
- 2025: 1 · 2023: 1 · 2022: 2 · 2020: 1 · 2018: 1
- FWCI
- 1.23
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Tellus A Dynamic Meteorology and Oceanography (publishedVersion)
- Topics
- Physical Sciences › Earth and Planetary Sciences › Oceanography › Geophysics and Gravity Measurements
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Earth and Planetary Sciences › Oceanography › Oceanographic and Atmospheric Processes
- Keywords
- discrete boundary value problems, physical geodesy, computational efficiency
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
