# The Computation of the External Gravity Field and The Geodetic Boundary-Value Problem

- Hyman Orlin

Published Online: 18 MAR 2013

DOI: 10.1029/GM009p0127

Copyright 1966 by the American Geophysical Union.

Book Title

## Gravity Anomalies: Unsurveyed Areas

Additional Information

#### How to Cite

Moritz, H. (1966) The Computation of the External Gravity Field and The Geodetic Boundary-Value Problem, in Gravity Anomalies: Unsurveyed Areas (ed H. Orlin), American Geophysical Union, Washington, D.C.. doi: 10.1029/GM009p0127

#### Publication History

- Published Online: 18 MAR 2013
- Published Print: 1 JAN 1966

#### Book Series:

#### ISBN Information

Print ISBN: 9780875900094

Online ISBN: 9781118664018

- Summary
- Chapter
- References

### Keywords:

- Earth' physical surface;
- External gravity field;
- Fictitious surface layer;
- Free-air reduction;
- Geodetic boundary

### Summary

In the usual way of computing the external gravity field, the Earth is considered as a level surface, although, strictly speaking, the free-air gravity anomalies refer to the nonlevel physical surface of the Earth. The main purpose of the present paper is to give formulas and, as an appendix, some estimates for the effect of topographic height on these computations. An application of Green's identities yields direct but complicated formulas for the effect of the disturbing potential *T* and the gravity anomaly Δ*g* outside the Earth. A simpler solution for *T* is obtained through the use of a fictitious surface layer, a coating, on the Earth's physical surface. A third method, which seems to be optimal for practical computations, is a free-air reduction to sea level. The accurate performance of this reduction is a problem of downward continuation of Δ*g*, which may be handled by interative solution of a simple integral equation. After this reduction, however, the conventional spherical formulas can be applied. In addition, the paper presents connections between the determination of the external gravity field from surface data, which is related to the conventional boundary-value problems of potential theory, and the determination of the Earth's physical surface itself, which is a specifically geodetic boundary-value problem.