Separation Between Geoid and Quasi-Geoid: Analysis of the Differences Between Normal-Orthometric and Rigorous Orthometric Heights

The orthometric and normal heights are the two altitude systems most used in the practical realization of the local and national vertical geodesic data. The main difference between these two concepts is that the actual mean gravity along the plumb line between the geoid and the topographic surface theoretically defines the orthometric heights, as well as the normal mean gravity along the plumb line between the reference ellipsoid and teluroid is used in the definition of normal heights. In the Brazilian geodetic system, only a correction of non-parallelism is applied, resulting in the normal-orthometric heights. The objective of this work is to calculate the separation between geoid and quasi-geoid obtained through the systems of normal-orthometric and rigorous orthometric heights. By means of numerical tests, it was observed that the separation is greater when using the brazilian system with values between -0.5 and 0.5 meters. On the other hand, by using the new rigorous heights, the average gravity along the long plumb line is evaluated, taking into account the variations of topographic densities and masses above the geoid, the values are smaller, being inthe range of -0.05 to 0.2 meters. It can be said that the ri