On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation

Abstract

Topography is a problem in geoid determination by the Stokes formula, a high degree Earth Gravitational Model (EGM), or for a combination thereof. Herein, we consider this problem in analytical/harmonic downward continuation of the external potential at point P to a geocentric spherical sea level approximation in geoid determination as well as to a sphere through the footpoint at the topography of the normal through P. Decomposing the topographic bias into a Bouguer shell component and a terrain component, we derive these components. It is shown that there is no terrain bias outside a spherical dome of base radius equal to the height H P of P above the sphere, and the height of the dome is about 0.4 × H P. In the case of dealing with an EGM, utilizing Molodensky truncation coefficients is one way to cope with the bias.

Keywords

• analytical continuation
• downward continuation
• harmonic continuation
• (quasi)geoid determination
• topographic bias