Abstract
This study emphasizes that the harmonic downward continuation of an external representation of the Earth’s gravity potential to sea level through the topographic masses implies a topographic bias. It is shown that the bias is only dependent on the topographic density along the geocentric radius at the computation point. The bias corresponds to the combined topographic geoid effect, i.e., the sum of the direct and indirect topographic effects. For a laterally variable topographic density function, the combined geoid effect is proportional to terms of powers two and three of the topographic height, while all higher order terms vanish. The result is useful in geoid determination by analytical continuation, e.g., from an Earth gravity model, Stokes’s formula or a combination thereof.
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Sjöberg, L.E. The topographic bias by analytical continuation in physical geodesy. J Geod 81, 345–350 (2007). https://doi.org/10.1007/s00190-006-0112-2
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DOI: https://doi.org/10.1007/s00190-006-0112-2