Comparative Results of Repeated Distance Measurements

Abstract

A simple statistical approach is applied to the repeated EDM of 1,383 lines, the average time interval of which is about 8 years, to obtain knowledge about the accuracy of EDM and possible accumulation of strain. The ratio d of a measured distance change to the distance is computed for each of these lines. This relative change in distance, d, shows a trend of decrease in magnitude with increasing line length. Then, the data of d are classified into three distance ranges, D ≤ 10krn, 10km < D ≤ 20km and D > 20km. The histograms of d illustrated for each of the distance ranges suggest that d has a normal distribution with non-zero mean. The χ ² test applied to the data of d provides support to this view. The standard deviation of d for a shorter distance range is larger than that for a longer distance range. The expression of random error in EDM divided by distance D; (a + bD)/D, is applied to describe the dependence of the standard deviation of d on D. The constant a is found to be about 10mm or more. This gives error in the phase difference determination of EDM. The quantity b is obtained as 1mm/km or less. This should provide information about distant-dependent random error and possible accumulation of strain. But it can be fully understood only in terms of error in atmospheric correction. The rate of horizontal crustal deformation must be much smaller in general than that so far estimated, even though the average interval between repeated measurements is short.