On the Errors of spherical Harmonic Developments of Gravity at the Surface of the Earth.
Abstract
The spherical harmonic expansion of the external gravity field of the earth is divergent at the surface of the earth. From the practical point of view a truncated series can be used if the errors are small. The errors are of two types: the truncation error and the downward continuation error. This report investigates the latter, which is caused by the disturbing topography above the point where the series is developed. This error is studied for potentials, gravity anomalies and for the vertical gradient of gravity. It is shown that the usual relation between the spherical harmonics of T and del(Delta (g) del(r) is also valid for their errors, while the relation between T sub n and Delta (g sub n) does not hold for the downward continuation errors. The relative errors of Delta (g) are found to be more serious than those for T.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1977
- Accession Number
- ADA052713
Entities
People
- Lars Sjoeberg
Organizations
- Ohio State University