# Encyclopedia of Geodesy

Living Edition
| Editors: Erik Grafarend

# Disturbing Potential from Deflections of the Vertical: From Globally Reflected Surface Gradient Equation to Locally Oriented Multiscale Modeling Multiscale modeling

• Willi Freeden
• Christian Gerhards
• Helga Nutz
• Michael Schreiner
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-02370-0_126-1

## Definition

Deflection of the Vertical

Difference between the direction of the normal vector associated with the reference potential and the normal vector associated with the (actual) gravity potential.

Disturbing Potential

Difference between the normal potential and the true (measured) potential.

## Introduction

The force of gravity, i.e., the resultant of gravitational and centrifugal force, provides a directional structure to the space above the Earth’s surface. It is tangential to the vertical plumb lines and perpendicular to all (level) equipotential surfaces. Any water surface at rest is part of a level surface. Level (equipotential) surfaces are ideal reference surfaces, for example, for heights. The geoid is defined as that level surface of the gravity field which best fits the mean sea level. Gravity vectors can be measured by absolute or relative gravimeters. The highest accuracy relative gravity measurements are conducted at the Earth’s surface. Gravity data are converted into...

## Keywords

Gravity Anomaly Mantle Plume Beltrami Operator Surface Gradient Reference Ellipsoid
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Willi Freeden
• 1
• Christian Gerhards
• 2
• Helga Nutz
• 1
• Michael Schreiner
• 3
1. 1.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
2. 2.Computational Science CenterUniversity of ViennaViennaAustria
3. 3.Institute for Computational Engineering ICEUniversity of BuchsBuchsSwitzerland