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Journal articles on the topic 'Molodensky'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Ziggah, Y. Y., I. Yakubu, and B. Kumi-Boateng. "Analysis of Methods for Ellipsoidal Height Estimation – The Case of a Local Geodetic Reference Network." Ghana Mining Journal 16, no. 2 (2016): 1–9. http://dx.doi.org/10.4314/gm.v16i2.1.

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Ghana’s local geodetic reference network is based on the War Office 1926 ellipsoid with data in latitude, longitude and orthometric height without the existence of ellipsoidal height. This situation makes it difficult to apply the standard forward transformation equation for direct conversion of curvilinear geodetic coordinates to its associated cartesian coordinates (X, Y, Z) in the Ghana local geodetic reference network. In order to overcome such a challenge, researchers resort to various techniques to obtain the ellipsoidal height for a local geodetic network. Therefore, this paper evaluate

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2

Kozenko, A. V. "Michael Sergeevich Molodensky (to the 100 anniversary)." Vestnik Otdelenia nauk o Zemle RAN 1, no. 2 (2009): 1–3. http://dx.doi.org/10.2205/2009nz000001.

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3

McCubbine, J. C., W. E. Featherstone, and N. J. Brown. "Error propagation for the Molodensky G1 term." Journal of Geodesy 93, no. 6 (2018): 889–98. http://dx.doi.org/10.1007/s00190-018-1211-6.

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4

Guimarães, Gabriel do Nascimento, and Denizar Blitzkow. "Problema de valor de contorno da Geodésia: uma abordagem conceitual." Boletim de Ciências Geodésicas 17, no. 4 (2011): 607–24. http://dx.doi.org/10.1590/s1982-21702011000400007.

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Um dos problemas da Geodésia é determinar o campo de gravidade externo às massas, além da superfície limitante, bem como a variação temporal do mesmo. Stokes propôs no século XVIII uma formulação para a solução desse problema, porém implicava em algumas dificuldades. A formulação proposta por Molodensky em meados do século XX abriu uma nova perspectiva para a solução do problema. Ao longo dos anos, na Geodésia, a relevância do Problema de Valor de Contorno da Geodésia (PVCG) tem sido reconhecida como base teórica para essa disciplina. Além disso, o PVCG ganhou novo impulso com a era espacial e

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5

Eteje, S. O., and V. N. Ugbelase. "Comparative Analysis of the Molodensky and Kotsakis Ellipsoidal Heights Transformation between Geocentric and Non-Geocentric Datums Models." Journal of Geography, Environment and Earth Science International 25, no. 10 (2021): 171–77. https://doi.org/10.9734/JGEESI/2021/v25i1030323.

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The non-availability of ellipsoidal heights of local geodetic Datums has made it necessary for the application of ellipsoidal heights transformation models to the available global ellipsoidal heights to obtain their respective theoretical heights in local Datums. It is required to know the accuracy, as well as reliability of any model of interest before its application. For that reason, this study comparatively analyses the Molodensky and Kotsakis models for the transformation of ellipsoidal heights between geocentric and non-geocentric Datums to determine the reliability of the Kotsakis model

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Banz, Lothar, Adrian Costea, Heiko Gimperlein, and Ernst P. Stephan. "Numerical simulations for the non-linear Molodensky problem." Studia Geophysica et Geodaetica 58, no. 4 (2014): 489–504. http://dx.doi.org/10.1007/s11200-013-0141-2.

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7

Klees, R., M. van Gelderen, C. Lage, and C. Schwab. "Fast numerical solution of the linearized Molodensky problem." Journal of Geodesy 75, no. 7-8 (2001): 349–62. http://dx.doi.org/10.1007/s001900100183.

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8

Günther, Matthias. "Ein einfacher Existenzbeweis für das nichtlineare MOLODENSKY-Problem." Mathematische Nachrichten 130, no. 1 (1987): 251–65. http://dx.doi.org/10.1002/mana.19871300124.

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9

Cheng, Luying, and Houze Xu. "General inverse of Stokes, Vening-Meinesz and Molodensky formulae." Science in China Series D 49, no. 5 (2006): 499–504. http://dx.doi.org/10.1007/s11430-006-0499-x.

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10

Mezhenova, I. I., and V. V. Popadyev. "Solution of Molodensky’s boundary-value problem for gravity disturbances with a relative error the Earth`s flattening square (second) order." Geodesy and Cartography 987, no. 9 (2022): 14–20. http://dx.doi.org/10.22389/0016-7126-2022-987-9-14-20.

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The solution of the geodetic boundary value problem for determining the anomalous potential from gravity measurements in the spherical approximation, taking into account the relief and compression, was developed in sufficient detail in 1960 and is also based on the results of G. G. Stokes. Flattening of the reference surface was taken into account by D. V. Zagrebin in several works dated 1940–1970; in 1956 M. S. Molodensky proposed a simpler method for an oblate ellipsoid, based on the already known one for a sphere. It turned out that at the very beginning of developing the mentioned solution

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11

Freeden, W., and C. Mayer. "Multiscale solution for the Molodensky problem on regular telluroidal surfaces." Acta Geodaetica et Geophysica Hungarica 41, no. 1 (2006): 55–86. http://dx.doi.org/10.1556/ageod.41.2006.1.6.

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12

Sideris, M. G., and K. P. Schwarz. "Advances in the numerical solution of the linear molodensky problem." Bulletin Géodésique 62, no. 1 (1988): 59–70. http://dx.doi.org/10.1007/bf02519325.

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13

Indriyani, Popy Dwi, Rina Dwi Indriana, and La Ode M. Sabri. "Semarang Subsurface Model Using Airborne Gravity Data." International Journal of Research and Review 10, no. 9 (2023): 271–80. http://dx.doi.org/10.52403/ijrr.20230929.

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The city of Semarang faults became active again in the Quaternary era. The gravity method has been widely used to identify subsurface conditions in Semarang City and its surroundings, especially the satellite gravity method and land gravity methods. Meanwhile, Semarang City and its surroundings have never used the airborne gravity method. Therefore, this study aims to identify subsurface conditions, especially faults, using airborne gravity data in Semarang and its surroundings. The airborne gravity value is the gravity value at a certain height. Therefore, in this study, the downward continua

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14

Costea, Adrian, Heiko Gimperlein, and Ernst P. Stephan. "A Nash–Hörmander iteration and boundary elements for the Molodensky problem." Numerische Mathematik 127, no. 1 (2013): 1–34. http://dx.doi.org/10.1007/s00211-013-0579-8.

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15

Abbey, D. A., and W. E. Featherstone. "Comparative Review of Molodensky–Badekas and Burša–Wolf Methods for Coordinate Transformation." Journal of Surveying Engineering 146, no. 3 (2020): 04020010. http://dx.doi.org/10.1061/(asce)su.1943-5428.0000319.

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16

Neiman, Yu M., L. S. Sugaipova, and V. B. Nepoklonov. "Numerical solution of the Molodensky boundary value problem with a fixed boundary." Geodesy and Cartography 1016, no. 2 (2025): 2–14. https://doi.org/10.22389/0016-7126-2025-1016-2-2-14.

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The functions of modern global navigation satellite systems (GNSS) allow us to consider the Earth’s surface as partially known at least. So, you can directly use the results of measurements on the real Earth surface, which significantly simplifies the entire theory of physical geodesy. The authors describe the theory of the Molodensky boundary value problem with a fixed boundary and its possible approximations briefly. It is proposed to look for a practical solution in the form of a deep neural network. Its choice represents a definite alternative to modern methods of physical geodesy and is o

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Majkráková, Miroslava, Juraj Papčo, Pavol Zahorec, Branislav Droščák, Ján Mikuška, and Ivan Marušiak. "An analysis of methods for gravity determination and their utilization for the calculation of geopotential numbers in the Slovak national levelling network." Contributions to Geophysics and Geodesy 46, no. 3 (2016): 179–202. http://dx.doi.org/10.1515/congeo-2016-0012.

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Abstract The vertical reference system in the Slovak Republic is realized by the National Levelling Network (NLN). The normal heights according to Molodensky have been introduced as reference heights in the NLN in 1957. Since then, the gravity correction, which is necessary to determine the reference heights in the NLN, has been obtained by an interpolation either from the simple or complete Bouguer anomalies. We refer to this method as the “original”. Currently, the method based on geopotential numbers is the preferred way to unify the European levelling networks. The core of this article is

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18

Ruffhead, A. C. "The SMITSWAM method of datum transformations consisting of Standard Molodensky in two stages with applied misclosures." Survey Review 48, no. 350 (2016): 376–84. http://dx.doi.org/10.1080/00396265.2016.1191748.

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Romeshkani, Mohsen, and Mehdi Eshagh. "DETERMINISTICALLY-MODIFIED INTEGRAL ESTIMATORS OF GRAVITATIONAL TENSOR." Boletim de Ciências Geodésicas 21, no. 1 (2015): 189–212. http://dx.doi.org/10.1590/s1982-217020150001000012.

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The Earth's global gravity field modelling is an important subject in Physical Geodesy. For this purpose different satellite gravimetry missions have been designed and launched. Satellite gravity gradiometry (SGG) is a technique to measure the second-order derivatives of the gravity field. The gravity field and steady state ocean circulation explorer (GOCE) is the first satellite mission which uses this technique and is dedicated to recover Earth's gravity models (EGMs) up to medium wavelengths. The existing terrestrial gravimetric data and EGM scan be used for validation of the GOCE data prio

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20

Siphiwe Mphuthi, Matthews, and Patroba Achola Odera. "Estimation of vertical datum offset for the South African vertical datum, in relation to the international height reference system." Geodetski vestnik 65, no. 02 (2021): 282–97. http://dx.doi.org/10.15292/geodetski-vestnik.2021.02.282-297.

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The vertical offset and the geopotential value over South Africa is estimated on the four fundamental benchmarks in relation to the international height reference system (IHRS). It is estimated to obtain discrepancies between the South African local vertical datum (W_P) and the global vertical datum (W_0). A single-point-based geodetic boundary value problem (GBVP) approach was used following Molodensky theory for estimating the height anomalies from the disturbing potential (T_P) using Bruns’s formula. The gravity potential at each tide gauge benchmark (TGBM) in South Africa deviates from the

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21

Annan, Richard Fiifi, Yao Yevenyo Ziggah, John Ayer, and Christian Amans Odutola. "Hybridized centroid technique for 3D Molodensky-Badekas coordinate transformation in the Ghana geodetic reference network using total least squares approach." South African Journal of Geomatics 5, no. 3 (2016): 269. http://dx.doi.org/10.4314/sajg.v5i3.1.

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22

Sidiq, Teguh P., Heri Purwanto, Irwan Gumilar, et al. "Localities of ID-74 to DGN95 Coordinate Transformation Parameters." IOP Conference Series: Earth and Environmental Science 1418, no. 1 (2024): 012024. https://doi.org/10.1088/1755-1315/1418/1/012024.

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Abstract As can be referred to almost all regulation in Ministry of Energy and Mineral Resources, all spatial information used in the oil and gas industry in Indonesia, should be referenced to DGN95. While it seems that the datum is now deprecated, the use of DGN95 in many data, especially seismic data collected in 1970 to 1990 are still used and maintain in many companies to avoid huge data transformation work if it is applied nationwide. Some work in finding coordinate transformation has been done since early 2000, but it produces a different set of parameters. In this paper, we collect some

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23

Ardalan, A. A., E. W. Grafarend, and J. Ihde. "Molodensky potential telluroid based on a minimum-distance map. Case study: the quasi-geoid of East Germany in the World Geodetic Datum 2000." Journal of Geodesy 76, no. 3 (2002): 127–38. http://dx.doi.org/10.1007/s00190-001-0238-1.

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24

Hassan, Abubakr, Dingfa Huang, Elhadi K. Mustafa, et al. "Statistical inference and residual analysis for the evaluation of datum transformation models developed on 3D coordinate data." Journal of Applied Geodesy 14, no. 1 (2020): 65–75. http://dx.doi.org/10.1515/jag-2019-0027.

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AbstractThe evaluation of geoscience data is a far-reaching topic which cannot be systematically covered. The purpose of inferential statistics is to harness useful information from data for making decisions. This paper conducts in-depth statistical study for the Bursa-Wolf and Molodensky Badekas models of the three-dimensional transformation parameters. We also considered the combined and observation equations scenarios of these methods for the comparative study. Four key indicators are conducted to evaluate the performance of the two transformation models according to the residual results. T

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25

Tenzer, Robert. "DISCUSSION ON THE ORTHOMETRIC HEIGHT REALIZATION." Geodesy and cartography 31, no. 1 (2012): 12–19. http://dx.doi.org/10.3846/13921541.2005.9636658.

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In the theory of the orthometric height, the mean value of gravity along the plumbline between the geoid and the earth's surface is defined as the integral mean. To determine the mean gravity from the gravity observations realized at the physical surface of the earth, the actual topographical density distribution and vertical change of gravity with depth have to be known. In Helmert's (1890) definition of the orthometric height, the assumption of the linear change of normal gravity is used adopting the constant topographical density distribution. The mean value of gravity is then approximately

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26

Tenzer, Robert, and Albertini Nsiah Ababio. "On the Consistency between a Classical Definition of the Geoid-to-Quasigeoid Separation and Helmert Orthometric Heights." Sensors 23, no. 11 (2023): 5185. http://dx.doi.org/10.3390/s23115185.

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It is acknowledged that a classical definition of the geoid-to-quasigeoid separation as a function of the simple planar Bouguer gravity anomaly is compatible with Helmert’s definition of orthometric heights. According to Helmert, the mean actual gravity along the plumbline between the geoid and the topographic surface in the definition of orthometric height is computed approximately from the measured surface gravity by applying the Poincaré-Prey gravity reduction. This study provides theoretical proof and numerical evidence that this assumption is valid. We demonstrate that differences between

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27

Tukka, A. A., H. Tata, and O. T. Idowu. "A Computational Tool for Local Gravimetric Geoid Determination Using Least Squares Collocation." Journal of Spatial Information Sciences 2, no. 1 (2025): 251–74. https://doi.org/10.5281/zenodo.14961951.

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<em>This study presents a computational tool (TUIDOTA), for determining local gravimetric geoids using Least Squares Collocation (LSC) techniques, essential for geodetic applications. The geoid provides a reference surface for determining the height of the earth's surface. The study focuses on evaluating the potential of the tool within Akure South Local Government Area in Ondo State of Nigeria, representing mountainous terrains. High-quality terrestrial gravity data, geopotential, and digital elevation models were used. The developed tool facilitates the selection between SLSC and NSLSC, maki

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Barzaghi, Riccardo, Carlo Iapige De Gaetani, and Barbara Betti. "The worldwide physical height datum project." Rendiconti Lincei. Scienze Fisiche e Naturali 31, S1 (2020): 27–34. http://dx.doi.org/10.1007/s12210-020-00948-0.

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Abstract The definition of a common global vertical coordinate system is nowadays one of the key points in Geodesy. With the advent of GNSS, a coherent global height has been made available to users. The ellipsoidal height can be obtained with respect to a given geocentric ellipsoid in a fast and precise way using GNSS techniques. On the other hand, the traditional orthometric height is not coherent at global scale. Spirit levelling allows the estimation of height increments so that orthometric heights of surveyed points can be obtained starting from a benchmark of known orthometric heights. A

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FEDORCHUK, A. "Analysis of modern models of counterfeiting surfaces for determination of heights by GNSS-leveling method." Modern achievements of geodesic science and industry 2, no. 44 (2022): 31–41. http://dx.doi.org/10.33841/1819-1339-2-44-31-41.

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This paper discusses various sources of information related to the issue of determining heights by GNSS-leveling. Implementation of the GNSS leveling method requires the presence of geoid or quasi-geoid heights, which today can be obtained from the corresponding models. In recent decades, scientists from around the world have developed many global, regional and local models of geoid and quasigeoid. This has contributed to the emergence of numerous publications on GNSS leveling. The purpose of the work is to perform the analysis of modern models of reference surfaces on the basis of materials o

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Kerkovits, Krisztián, and Mátyás Gede. "Parametrization of the Hungarian Stereographic Map Sheets." Advances in Cartography and GIScience of the ICA 4 (August 7, 2023): 1–5. http://dx.doi.org/10.5194/ica-adv-4-13-2023.

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Abstract. A topographic map series of Northern Transylvania was drawn in the 1940s. Georeferencing them needs information about their coordinate systems. These maps used two reference systems known as the Budapest and the Marosvásárhely Stereographic projections. The datum transformation parameters of the former had already been determined in previous studies, but they had to be adjusted slightly to use a common Ferro–Greenwich difference for both systems. Parameters of the Marosvásárhely system were only available as a Molodenskiy transformation determined with insufficient accuracy. In this

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31

Sideris, Michael G. "Rigorous gravimetric terrain modelling using Molodensky’s operator." manuscripta geodaetica 15, no. 2 (1990): 97–106. http://dx.doi.org/10.1007/bf03655394.

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32

Kureniov, Y. P., and T. N. Malik. "About the article «Theory of Molodenskiy and geoid» by L.V. Ogorodova." Geodesy and Cartography 887, no. 5 (2014): 61–62. http://dx.doi.org/10.22389/0016-7126-2014-887-5-61-62.

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Sansó, F. "New estimates for the solution of Molodensky’s problem." manuscripta geodaetica 14, no. 2 (1989): 68–76. http://dx.doi.org/10.1007/bf03655207.

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Sideris, M. G., and K. P. Schwarz. "Solving Molodensky’s series by fast Fourier transform techniques." Bulletin Géodésique 60, no. 1 (1986): 51–63. http://dx.doi.org/10.1007/bf02519354.

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Ferreira, Vagner Gonçalves, and Silvio Rogério Correia De Freitas. "Análise do termo de primeira ordem das séries de Molodenskii para o problema de valor de contorno da geodésia." Boletim de Ciências Geodésicas 16, no. 4 (2010): 557–74. http://dx.doi.org/10.1590/s1982-21702010000400005.

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Neste trabalho, avaliou-se o termo de primeira ordem das séries de Molodenskii usando as seguintes abordagens: a solução dada pela série de Molodenskii; a solução pelo gradiente vertical; e a solução pela correção de terreno como aproximação do termo <img border=0 width=32 height=32 src="../../../../img/revistas/bcg/v16n4/a05simb03.jpg">. As duas últimas soluções foram obtidas por Moritz. As duas primeiras soluções mostraram-se coerentes entre si nas condições aqui analisadas. A comparação foi feita em termos de anomalia de altitude de primeira ordem <img border=0 width=32 height=32 s

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Yu.M., Neyman, and Sugaipova L.S. "Theory of Molodensky’s coefficients in Hotine‒Koch integral transform." Geodesy and Aerophotosurveying 64, no. 4 (2020): 371–79. http://dx.doi.org/10.30533/0536-101x-2020-64-4-371-379.

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Известная теория коэффициентов Молоденского, используемая при решении задачи определения аномалий высоты по аномалиям силы тяжести с помощью преобразования Стокса, адаптирована для решения задачи вычисления высот геоида по возмущениям силы тяжести с использованием интегрального преобразования Хотина‒Коха. Показано, что в частотной области выражение для усечённого ядра Хотина‒Коха отличается от полного ядра сомножителем, который предлагается назвать частотной характеристикой оператора усечения ядра Хотина‒Коха на внутреннюю зону радиуса ψ0.

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Vaľko, M., M. Mojzeš, J. Janák, and J. Papčo. "Comparison of two different solutions to Molodensky’s G1 term." Studia Geophysica et Geodaetica 52, no. 1 (2008): 71–86. http://dx.doi.org/10.1007/s11200-008-0006-2.

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Sjöberg, L. E. "The geoid or quasigeoid – which reference surface should be preferred for a national height system?" Journal of Geodetic Science 3, no. 2 (2013): 103–9. http://dx.doi.org/10.2478/jogs-2013-0013.

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Abstract Most European states use M. S. Molodensky’s concept of normal heights for their height systems with a quasigeoid model as the reference surface, while the rest of the world rely on orthometric heights with the geoid as the zero-level. Considering the advances in data caption and theory for geoid and quasigeoid determinations, the question is which system is the best choice for the future. It is reasonable to assume that the latter concept, in contrast to the former, will always suffer from some uncertainty in the topographic density distribution, while Molodensky’s approach to quasige

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Guo, Dongmei, Xiaodong Chen, Zhixin Xue, et al. "High-Accuracy Quasi-Geoid Determination Using Molodensky’s Series Solutions and Integrated Gravity/GNSS/Leveling Data." Remote Sensing 15, no. 22 (2023): 5414. http://dx.doi.org/10.3390/rs15225414.

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This study presents a methodology for constructing a quasi-geoid model with millimeter-level accuracy over the Shangyu area in China, following the guidelines of the International Association of Geodesy Joint Working Group 2.2.2, known as “The 1 cm geoid experiment”. Our approach combines two steps to ensure exceptional accuracy. First, we employ Molodensky’s theory to model the gravity field, accounting for non-level surfaces and considering complex terrain effects. Through an exhaustive analysis of these influential factors, we implement a comprehensive suite of applicable formulae within Mo

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Tenzer, Robert, and Ismael Foroughi. "On the Applicability of Molodensky’s Concept of Heights in Planetary Sciences." Geosciences 8, no. 7 (2018): 239. http://dx.doi.org/10.3390/geosciences8070239.

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41

Wang, Y. M. "Numerical aspects of the solution of Molodensky’s problem by analytical continuation." manuscripta geodaetica 12, no. 4 (1987): 290–95. http://dx.doi.org/10.1007/bf03655133.

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42

Mihalache, Raluca Maria, and Andreea Manescu. "Interpolation Grid for Local Area of Iasi City." Present Environment and Sustainable Development 8, no. 1 (2014): 157–64. http://dx.doi.org/10.2478/pesd-2014-0014.

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Abstract Definitive transition to GNSS technology of achieving geodetic networks for cadastre implementation in cities and municipalities, enforce establishing a unique way of linking between current measurements and existing geodetic data, with a sufficient accuracy proper to urban cadastre standards. Regarding city of Iasi, is presented a different method of transformation which consist in an interpolation grid for heights system. The Romanian national height system is „Black Sea-1975” normal heights system. Founded in 1945 by Molodenski, this system uses the quasigeoid as reference surface,

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YU, Jin-Hai, Zhuo-Wen ZHU, and Fu-Qing PENG. "A Wavelet Arithmetic Of Theg1-Term In The Molodensky's Boundary Value Problem." Chinese Journal of Geophysics 44, no. 1 (2001): 111–18. http://dx.doi.org/10.1002/cjg2.121.

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44

Tenzer, Robert, Pavel Novák, Ilya Prutkin, Artu Ellmann, and Peter Vajda. "Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients." Studia Geophysica et Geodaetica 53, no. 2 (2009): 157–67. http://dx.doi.org/10.1007/s11200-009-0010-1.

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Popadyev, V. V. "On the advantage of normal heights." Geodesy and Cartography 939, no. 9 (2018): 2–9. http://dx.doi.org/10.22389/0016-7126-2018-939-9-2-9.

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The author analyzes the arguments in the report by Robert Kingdon, Petr Vanicek and Marcelo Santos “The shape of the quasigeoid” (IX Hotin-Marussi Symposium on Theoretical Geodesy, Italy, Rome, June 18 June 22, 2018), which presents the criticisms for the basic concepts of Molodensky’s theory, the normal height and height anomaly of the point on the earth’s surface, plotted on the reference ellipsoid surface and forming the surface of a quasigeoid. The main advantages of the system of normal heights, closely related to the theory of determining the external gravitational field and the Earth’s

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Yurkina, M. I. "Molodensky’s theory of the Earth’s figure determination using topographic reductions and integration over the Earth’s surface." manuscripta geodaetica 14, no. 1 (1989): 7–12. http://dx.doi.org/10.1007/bf03655194.

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Janák, Juraj, Petr Vańiček, Ismael Foroughi, Robert Kingdon, Michael B. Sheng, and Marcelo C. Santos. "Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach." Contributions to Geophysics and Geodesy 47, no. 3 (2017): 201–29. http://dx.doi.org/10.1515/congeo-2017-0011.

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AbstractThe aim of this paper is to show a present state-of-the-art precise gravimetric geoid determination using the UNB Stokes-Helmert’s technique in a simple schematic way. A detailed description of a practical application of this technique in the Auvergne test area is also provided. In this paper, we discuss the most problematic parts of the solution: correct application of topographic and atmospheric effects including the lateral topographical density variations, downward continuation of gravity anomalies from the Earth surface to the geoid, and the optimal incorporation of the global gra

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Tenzer, Robert, Pavel Novák, Peter Vajda, Artu Ellmann, and Ahmed Abdalla. "Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients." Studia Geophysica et Geodaetica 55, no. 1 (2011): 55–71. http://dx.doi.org/10.1007/s11200-011-0004-7.

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Bucha, Blažej, Christian Hirt, and Michael Kuhn. "Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky’s truncation coefficients." Journal of Geodesy 93, no. 1 (2018): 65–83. http://dx.doi.org/10.1007/s00190-018-1139-x.

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Tenzer, Robert, and Vladislav Gladkikh. "Application of Möbius coordinate transformation in evaluating Newton's integral." Contributions to Geophysics and Geodesy 41, no. 2 (2011): 95–115. http://dx.doi.org/10.2478/v10126-011-0004-1.

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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

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