## The theory and formulas used by the calculation service of the ICGEM are described in the Scientific Technical Report STR09/02

*(critics and comments are welcome)*

####
The Report can be downloaded here.

The revised edition of the Report can be downloaded here.

#### Introduction

The intention of this report is to present the definitions of
different functionals of the Earth's gravity field and possibilities
for their approximative calculation from a mathematical
representation of the outer potential. In history this topic has
usually been treated in connection with the boundary value problems
of geodesy, i.e. starting from measurements at the Earth's surface
and their use to derive a mathematical representation of the
geopotential.

Nowadays global gravity field models, mainly derived from satellite
measurements, become more and more detailed and accurate and,
additionally, the global topography can be determined by modern
satellite methods independently from the gravity field. On the one
hand the accuracy of these gravity field models has to be evaluated
and on the other hand they should be combined with classical (e.g.
gravity anomalies) or recent (e.g. GPS-levelling-derived or
altimetry-derived geoid heights) data. Furthermore, an important
task of geodesy is to make the gravity field functionals available
to other geosciences. For all these purposes it is necessary to
calculate the corresponding functionals as accurately as possible
or, at least, with a well-defined accuracy from a given global
gravity field model and, if required, with simultaneous
consideration of the topography model.

We will start from the potential, formulate the definition of some
functionals and derive the formulas for the calculation. In doing so
we assume that the Earth's gravity potential is known outside the
masses, the normal potential outside the ellipsoid and that
mathematical representations are available for both. Here we neglect
time variations and deal with the stationary part of the potential
only.

Approximate calculation formulas with different accuracies are
formulated and specified for the case that the mathematical
representation of the potential is in terms of spherical harmonics.
The accuracies of the formulas are demonstrated by practical
calculations using the gravity field model EIGEN-6C2
(Förste et al. 2012).

More or less, what is compiled here is well-known in physical
geodesy but distributed over a lot of articles and books which are
not cited here. In the first instance this text is targeted at
non-geodesists and it should be “stand-alone readable”.