Planar, spherical and ellipsoidal approximations of Poisson's integral in near zone

Abstract

Abstract:Planar, spherical, and ellipsoidal approximations of Poisson's integral for downward continuation (DWC) of gravity anomalies are discussed in this study. The planar approximation of Poisson integral is assessed versus the spherical and ellipsoidal approximations by examining the outcomes of DWC and finally the geoidal heights. We present the analytical solution of Poisson's kernel in the point-mean discretization model that speed up computation time 500 times faster than spherical Poisson kernel while preserving a good numerical accuracy. The new formulas are very simple and stable even for regions with very low height. It is shown that the maximum differences between spherical and planar DWC as well as planar and ellipsoidal DWC are about 6 mm and 18 mm respectively in the geoidal heights for a rough mountainous area such as Iran.

Geoid versus quasigeoid: a case of physics versus geometry

“…The numerical error can be mitigated through regularization (e.g., Novák et al, 2001;Kingdon and Vaníček, 2011). Even without regularization, the error in geoid determination resulting from the ill conditioning of the downward continuation of gravity values only reaches a few centimeters in regions with elevations over 3 km (e.g., Huang, 2002;Goli, 2011), and less at lower elevations.…”

Various parameterizations of “latitude” equation – Cartesian to geodetic coordinates transformation

“…However, as suggested by Novak et al (2001) and demonstrated by Kingdon and Vanicek (2011), the ill-conditioning can be mitigated through regularization, and even without regularization Huang (2002) claimed that the geoid error only reaches a few centimetres in regions with elevations over 3 kilometres. Goli and Najafi (2011) showed that planar approximation of the Poisson equation can considerably speed up the laborious computational process at the prize of about 1 cm additional uncertainty in the geoid height.…”