ESTIMATION OF ROD SCALE ERRORS IN GEODETIC LEVELING

Comparisons among repeated geodetic levelings have often been used for detecting and estimating residual rod scale errors in leveled heights . Individual rod-pair scale errors are estimated by a two-step procedu re using a model based on either differences in heights, differences i n section height differences, or differences in section tilts. It is s hown that the estimated rod-pair scale errors derived from each model are identical only when the data are correctly weighted, and the mathe matical correlations are accounted for in the model based on heights. Analyses based on simple regressions of changes in height versus heigh t can easily lead to incorrect conclusions. We also show that the stat istically estimated scale errors are not a simple function of height, height difference, or tilt. The models are valid only when terrain slo pe is constant over adjacent pairs of setups (i.e., smoothly varying t errain). In order to discriminate between rod scale errors and vertica l displacements due to crustal motion, the individual rod-pairs should be used in more than one leveling, preferably in areas of contrasting tectonic activity. From an analysis of 37 separately calibrated rod-p airs used in 55 levelings in southern California, we found eight stati stically significant coefficients that could be reasonably attributed to rod scale errors, only one of which was larger than the expected ra ndom error in the applied calibration-based scale correction. However, significant differences with other independent checks indicate that c aution should be exercised before accepting these results as evidence of scale error. Further refinements of the technique are clearly neede d if the results are to be routinely applied in practice.