Fundamental Ambiguity in the Definition of Vertical Motion

Vertical motion is generally described as motion normal to some defined horizontal surface or family of surfaces. Such a surface can be constructed geometrically or gravitationally. In the case of a geometrical surface, the ellipsoid is the shape of choice. In the case of a gravitational surface, it needs to be specified which masses are to be included in the definition of the center-of-mass origin, and whether the surface evolves in time along with the configuration of mass (as in a dynamic equipotential) or whether it is static (as in a reference geoid). Vertical motion is therefore not an absolute concept, but rather one of convenience and convention. Even if properly defined, the ability to realize vertical displacement coordinates may be limited by uncertainty in the relationship between observed quantities and the frame definition. Thus discrepancies between two analysis groups’ results on vertical station velocities may not be a result of systematic error, but rather may simply reflect inability to realize the same reference frame.