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The secondary indirect topographic effect in physical geodesy


The use of Stokes’ integral by the remove-compute-restore technique is the most common way to determine the geoid today. The method includes direct, primary and secondary indirect topographic effects. This article is mainly devoted to the secondary indirect topographic effect (SITE), which reaches the extreme values of 265 mGal and −0.6 mGal for the uncompensated and Helmert condensation compensated gravity anomalies, respectively. The corresponding effects on the geoid height reach the magnitudes of 328 m and −0.5 m, respectively. Here we emphasize that the SITE is a direct effect, needed in a rigorous gravity anomaly. For surface as well as for classical gravity anomalies, located at the geoid, the SITE can be interpreted as a shift in the normal gravity along the ellipsoidal normal to the point where the normal potential equals the topographically reduced geopotential at the computation point. We show that it may yield a bias of the order of −0.9 m in the Himalayas if not properly considered in the surface anomaly. This bias does not change when using a topographic compensation model, e.g., by Helmert condensation of the topography. The problem is avoided when using the no-topography gravity anomaly with or without compensation.

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Correspondence to Lars E. Sjöberg.

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Sjöberg, L.E. The secondary indirect topographic effect in physical geodesy. Stud Geophys Geod 59, 173–187 (2015).

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  • indirect topographic effect
  • no-topography gravity anomaly
  • secondary indirect topographic effect