Geometric Levelling Data and Some Systematic Faults in Their Treatment

• Autorzy: Cvetkov Vasil

Identyfikatory

DOI

10.29227/IM-2024-01-32

Warianty tytułu

PL

Geometryczne dane niwelacyjne i niektóre błędy systematyczne w ich przetwarzaniu

• Języki publikacji: EN

Abstrakty

EN

The aim of this article is to illuminate some latent systematic faults in the mathematical treatment of precise levelling data. The first one is associated with the use of the average of both measurements of the height differences between the terminal benchmarks in levelling lines. Another weak point in the classical treatment of levelling data is the incomplete minimization of the impact of the spatial network configuration on the produced mean standard errors of the nodal benchmarks from the adjustment. Generating sixty random paired samples of size 1000, derived from three continuous distributions, e.g. Normal (0, 1), Uniform (-1.732, 1.732) and Gamma (1, 1), it was found that the average of two same distributed and ordered observations is very nearby to the theoretical expectation, in comparison to both observations, only in approximately 27-30% of all cases. Contrary, in other 70-74% of cases, either the “first” or the “second” observation is in close proximity to the expectation. The miss of this fact leads to a statistically significant deterioration of the final accuracy of the levelling networks. In the current study, it is also shown that the minimization of the standard errors of the adjusted normal heights of the nodal benchmarks in the Bulgarian Levelling Network 1980 cannot be achieved with the weights w=const.L-1, which are the most popular and used type of weights in the adjustment of geometric levelling networks. Finally, it is illustrated that taking into account the above marks and applying an appropriate adjustment algorithm, the mean of the standard errors of the adjusted heights of the nodal benchmarks in the analysed network is possible to be less than 1mm. The standard error of the adjusted height of the most remoted benchmark “Pushkarov”, which is 598 km far away from the datum point located in Varna, is equal to 1.40mm. The obtained from the adjustment mean standard error for the weight unit is estimated to be 0.164 mm/√km. In comparison, the adjustment mean standard error for the weight unit, but yielded by the classical approach of adjustment of the analysed network, is 1.289 mm/√km or almost 9 times higher. Despite being tedious and time-consuming, it is not on point of discarding the precise geometric levelling as a main geodetic method for solving of a couple of scientific and engineering tasks, where differences in heights have to be determined with the highest accuracy.

Słowa kluczowe

EN

geometric levelling data; systematic faults; bulgarian levelling network; accuracy

PL

geometryczne dane niwelacyjne; błędy systematyczne; bułgarska sieć niwelacyjna; dokładność

• Wydawca: Polskie Towarzystwo Przeróbki Kopalin
• Czasopismo: Inżynieria Mineralna
• Rocznik: 2024
• Tom: Vol. 1, no. 1
• Strony: 293--300
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Cvetkov Vasil

• University of Architecture, Civil Engineering and Geodesy, Geodetic Department, 1 Hristo Smirnenski Blvd., 1164 Sofia, Bulgaria

• https://orcid.org/0000-0001-9628-6768

Bibliografia

• 1. M. Sacher, J. Ihde, G. Liebsch and J. Mäkinen, “EVRF2007 as Realization of the European Vertical Reference System”, Presented at the Symposium of the IAG Sub-commission for Europe (EUREF) in Brussels, June 18–21 2008.
• 2. Ł. Borowski, B. Kubicki and J. Gołąb, “Implementation of the EVRF2007 height reference frame in Poland” Journal of Applied Geodesy, 2023, https://doi.org/10.1515/jag-2023-0020 .
• 3. S. Gospodinov, E. Peneva and P. Penev, “A specific approach to least squares adjustment of the state levelling network”, 22nd International Multidisciplinary Scientific GeoConference SGEM, 2022, https://doi.org/10.5593/sgem2022/2.1/s09.20 .
• 4. National Institute of Geodesy and Photogrammetry, “United precise levelling network of socialistic republics in Eastern Europe, cooperation with Poland, Czechoslovakia, East Germany, Hungary, USSR and Romania”, 1980. (in Bulgarian).
• 5. X. Li, “Modeling the North American vertical datum of 1988 errors in the conterminous United States” Journal of Geodetic Science, vol. 8, no. 1, 2018, pp. 1-13. https://doi.org/10.1515/jogs-2018-0001 .
• 6. L. E. Sjöberg, “Geoid model validation and topographic bias”, Journal of Geodetic Science, vol. 12, no. 1, 2022, pp. 38-41. https://doi.org/10.1515/jogs-2022-0133 .
• 7. Y. Tanaka and Y. Aoki, “A Geodetic Determination of the Gravitational Potential Difference Toward a 100-km-Scale Clock Frequency Comparison in a Plate Subduction Zone”. In: International Association of Geodesy Symposia. Springer, Berlin, Heidelberg, 2022, https://doi.org/10.1007/1345_2022_147 .
• 8. L. Borowski, J. Kudrys, B. Kubicki, M. Slámová and K. Maciuk, “Phase Centre Corrections of GNSS Antennas and Their Consistency with ATX Catalogues.” Remote Sens. 2022, 14, 3226. https://doi.org/10.3390/rs14133226.
• 9. A. Angelov, “Geodetic methods in the study for deformation process of high buildings and engineering facilities”, Monographic, Second Edition, 2022, https://uacg.bg/filebank/att_22864.pdf , (in Bulgarian).
• 10. S. Enman and V. Enman, “Systematic errors in leveling of mountainous areas”, Bull. Geod., 58, 1984, pp. 475-493.
• 11. V. Saaranen, P. Lehmuskoski, M. Takalo and P. Rouhiainen, “The Third Precise Levelling of Finland”, FGI Publications No. 161, Kirkkonummi, 2021, The Third Precise Levelling of Finland (helsinki.fi).
• 12. V. Cvetkov, “Two adjustments of the second levelling of Finland by using nonconventional weights” Journal of Geodetic Science, vol. 13, no. 1, 2023, https://doi.org/10.1515/jogs-2022-0148.
• 13. V. Cvetkov and S. Gospodinov, “Inverse Absolute Height Weighting in the Highest Order Levelling- Networks”, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-4219, https://doi.org/10.5194/egusphere-egu23-4219 , 2023.
• 14. F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä and L. E. Meester, “A Modern Introduction to Probability and Statistics”, London, Springer – Verlag, 2005.
• 15. V. Cvetkov, „Alternative measures of central tendency”, Deutsche Internationale Zeitschrift Für Zeitgenössische Wissenschaft, 38, pp. 4–8, 2022, https://doi.org/10.5281/zenodo.7002877

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki i promocja sportu (2025).