vertical deflection
A measure of how far the direction of the local gravity field has been shifted at a certain point on the Earth by local anomalies such as nearby mountains.
vertical deflection: gravity's local detour from true vertical
Vertical deflection is the angle between the true vertical (the direction of the local gravity vector) and the astronomical vertical (the direction to the celestial pole as observed from that point). At most locations on Earth, these directions do not align perfectly. Nearby topographic masses, subsurface density variations, and the Earth's irregular shape all pull gravity sideways, bending the plumb line away from the geodetic reference frame by small but measurable amounts.
The deflection typically ranges from a few arcseconds to tens of arcseconds depending on local geology. A mountain range can deflect gravity by 10 to 50 arcseconds or more; deep sedimentary basins can produce opposite effects. These deflections are usually broken into two components: the north-south component and the east-west component, both measured relative to the geodetic meridian.
Why Surveyors Must Account for It
Traditional survey instruments like theodolites and levels rely on gravity to establish vertical and horizontal references. If you ignore vertical deflection when working over significant topographic relief or across geologically anomalous regions, your heights and azimuths will contain systematic errors. A structure staked out without accounting for deflection in mountainous terrain may be off by several centimetres per kilometre of horizontal distance. Modern GPS-based surveys eliminate much of this problem, but classical levelling networks and astrogeodetic surveys still require deflection corrections.
Vertical deflection values are computed from high-resolution gravity measurements (gravimeter surveys) combined with digital elevation models. Agencies like national geodetic surveys publish deflection grids for their territory, allowing practitioners to interpolate values at specific locations. The deflection is subtracted from observed zenith angles to obtain corrected values that align with the geodetic system.
The phenomenon is intimately tied to the distinction between the geoid (the equipotential surface that gravity follows) and the reference ellipsoid (the mathematical surface used for coordinate systems). Vertical deflection is, in essence, the local slope of the geoid relative to the ellipsoid, made visible in how a plumb bob swings.