Local earth gravity/potential modeling using ASCH

In Geodesy, the heights of points are normally orthometric heights measured above the geoid (an equipotential surface created by the earth masses and rotation which approximately coincides with the mean sea level) or the normal heights. It is necessary to transform the GNSS/GPS measured ellipsoidal heights (h) to classical physical heights (orthometric H/Normal H). The total gravity potential of the earth (W) is the summation of two components; gravitational potential (V) by earth masses and the centrifugal potential (Ω). The centrifugal potential is directly calculated, while the gravitational potential (V) needs to be modeled globally or locally using given measurements. The global models of the earth gravitational potential/gravity models (or so-called geoid models) are mostly given using spherical harmonics (SH). A modified approach of SH was defined to fit the use of SH for regional gravity/potential modeling called spherical cap harmonics (SCH). Due to the numerical difficulties of SCH, a simplified approach of SCH is selected to be used for a combined modeling of the earth potential using a variety of observations. This approach is called the Adjusted Spherical Cap harmonics.