Modelling the local gravity field by rectangular harmonics with numerical validations

For the representation of the Earth’s global gravity field, Spherical Harmonics (SH) are widely used in geodetic community. On the other hand, for the representation of a local or regional gravity field, Spherical Cap Harmonics (SCH) and Rectangular Harmonics (RH) are alternative techniques with important advantages over SH. Although SCH are extensively presented in literature, RH are found in very few applications, especially of the gravity field. This work derives different functional forms of the disturbing potential, outside of the Earth’s masses, using RH. Also, the necessary transformation from geocentric into local rectangular coordinates is presented. The Rectangular Harmonic Coefficients (RHC) of the different mathematical models of the disturbing potential can be estimated through a least squares’ adjustment process. In order to select the best mathematical model, numerical experiments, based on data generated from a geopotential model, are conducted and the results are validated. Then, for the best model of the disturbing potential, its functionals (gravity anomaly and disturbance, height anomaly, geoid undulation and deflection of vertical) are given in terms of RHC. We conclude that RH representations are both suitable and convenient for the modelling of the local or regional gravity field.