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A MYTH CONCERNING THE GEOMETRIC LEVELLING: CLOSING ERRORS AND LOOP CIRCUMFERENCES
Abstract
The geometric levelling of the highest order has been the main method for many scientific and engineering tasks for more than 150 years. One of them is the monitoring of the recent vertical movements of the Earth-s crust. In order to understand the low of accumulation of the discrepancies in levelling lines, many investigators have planned and performed various experiments and analysis through the years. As a result, the systematic effects of many sources of measurement errors have been studied, and partly or fully solved. However, the basic assumption about the relationship between the closing errors in levelling loops and the circumferences of the loops has hardly ever been the topic of wide discussions. It seems that this relationship is undoubted. The main objective of this article is to demonstrate that this popular belief about the accumulation of closing errors in the precise levelling is not valid regarding the data of the Third levelling of Bulgaria, the Second and the Third levelling of Finland. Using correlation and regression analysis we found that there is no statistically significant connection between closing errors and loop circumferences in the analyzed levelling networks. The correlation coefficients are below 0.35 considering each network, which means that the determination coefficients are up to 0.10. That is to say, the circumferences of the levelling loops cannot explain more than 10% of the variance of the closing errors. In addition, the p-values of the regression parameter b in the equation |??|=??+??.??0.5 are 0.104, 0.725 and 0.976, in the case of the Third levelling of Bulgaria, the Second and the Third levelling of Finland, respectively. Based on the above facts, we can conclude that some basic assumptions and methods regarding the processing of geometric levelling data should be an object of further modern consideration and revision.
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References8
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