Vertical deflection

The vertical deflection (deflection of the plumb line, astro-geodetic deflection) at a point on the Earth is a measure of how far the direction of the local gravity field has been shifted by local anomalies such as nearby mountains. (Here "gravity" means apparent gravity—true gravity "reduced" by the earth's spin). They are widely used in geodesy, for surveying networks and for geophysical purposes.

The vertical deflection (abbrev. VD or ξ,η) is the angle between the true zenith (plumb line) and the line perpendicular to the surface of the reference ellipsoid chosen to approximate the earth's sea-level surface. VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10″ (flat areas) or 20–50″ (alpine terrain).

The deflection of the vertical has a north-south component ξ and an east-west component η. The value of ξ is the astronomic latitude minus the geodetic latitude (taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network coordinates. The value of η is the astronomic longitude minus the geodetic longitude (taking east longitudes to be position and west longitudes to be negative). When a new mapping datum replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will change too.

The NGS website gives vertical deflection anywhere in the United States here and here.

The deflections reflect the undulation of the geoid and gravity anomalies, for they depend on the gravity field and its inhomogeneities.

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Wikipedia