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 %.