Scholarly record
LINE DISCREPANCIES AS WEIGHTS IN THE ADJUSTMENT OF PRECISE LEVELLING NETWORKS
Abstract
Precise levelling networks play an important role in the research of many scientific processes, e.g. the recent crustal movements, the change of ocean and sea levels, geoid or quasi-geoid, etc. Their appropriate adjustment goes through the choice of suitable weights, which have physical common sense and minimize the standard errors of the adjusted heights. The conventional weights are supposed to be inversely proportional to the length of levelling lines, due to the assumption that the accumulation of errors in the geometric levelling is proportional to the square root of the distance between benchmarks. On the other hand, it is a well-known fact that the more accurate random observations are, the less is their spread around the quantity expectation. Thus, the absolute values of the discrepancies in the lines in levelling networks seem reasonable and natural candidates of weights. In order to check the -supremacy- of the conventional weights in the geometric levelling, we adjusted the Third Levelling network of Finland in two variants. In the first variant, we used the traditional weights inversely proportional to the length of the levelling lines. In the second variant, we used weights inversely proportional to the absolute values of the discrepancies in the lines. The t-Test Paired Samples for means applied with the means of the sample of the standard errors yielded by both variants revealed that the second variant produced statistically significant better results at significance level greater than 99 %.
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References9
Afrasteh Y., Slobbe D.C., Sacher M. et al., (2023), Realizing the European Vertical Reference System using model-based hydrodynamic leveling data. J Geod 97, 86. DOI: 10.1007/s00190-023-01778-2
Cvetkov V., Two adjustments of the second levelling of Finland by using nonconventional weights, Journal of Geodetic Science, vol. 13, no. 1, 2023, DOI: 10.1515/jogs-2022-0148
Gospodinov S., Peneva E., P. Penev, A specific approach to least squares adjustment of the state levelling network, 22nd International Multidisciplinary Scientific GeoConference SGEM 2022, Albena, Bulgaria, 2020, DOI: 10.5593/sgem2022/2.1/s09.20
Kanev D., Mladenovski M., The recent vertical movements of the Earth�s crust in Bulgaria, Publications of Bulgarian Cartographic Association, Vol. IX, pp. 17-26, 1969, in Bulgarian
Kunchev I., On standards and specifications for vertical control surveys, Annual of the University of Architecture, Civil Engineering and Geodesy � Sofia, Vol. 54, Issue 2, pp. 253 � 262, 2021, ISSN 1310-814X, ISSN 2534-9759 (on-line), in Bulgarian
Montgomery D., G. Runger, (2014), Applied Statistics and Probability for Engineers (6th ed.), Wiley, ISBN-13 9781118539712
Peneva E., I. Georgiev, 2010, Evaluation of the Quasigeoid Models EGG97 and EGG07 with GPS/levelling Data for the Territory of Bulgaria, In IAG Book series �Gravity, Geoid and Earth Observation�, International Association of Geodesy Symposia 135, Mertikas (ed.), Springer-Verlag Berlin Heidelberg, p. 303-307, ISBN 978-3-642-10633-0, DOI: 10.1007/978-3-642-10634-7_39.
Saaranen V., Lehmuskoski P., Takalo M., P. Rouhiainen, The Third Precise Levelling of Finland. FGI Publications No. 161, Kirkkonummi, 2021, ISBN 978-951-48-0266-9 (print), ISSN 2342-7353 (online)
Specifications for precise levelling I and II order, GUGK, 1980, Sofia, in Bulgarian
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