Least‐Squares Adjustments of Seasonal Leveling

Abstract

The vertical motions of 11 control points in the Northern part of Israel (Haifa North‐East) are studied seasonally for a period of one full year (October 1988 to September 1989). The purpose of this paper is to compare the mathematical equivalence between various leveling‐adjustment techniques, namely, the classical minimum variance estimate, free net method, and the least‐squares collocation method, by using, as an example, a number of leveling loops in Northern Israel. A comparison of results showed that there were no significant differences between the free net and the least‐squares collocation methods (LSC). The elevation differences between the bench marks for the free net and condition equations method were the same, but the estimated heights were different. Even though the LSC technique is much more complicated and time consuming, it confirms the stability of points on the bedrock and the vertical movement of points on the high‐tension poles. It is, therefore, convenient to use either the free net method or the LSC method on projects concerning precise leveling.