spherical trapezium

Aim. The main task of the geodesy is to determine the shape and size of the Earth and its changes over time. An integral part of determining the shape and size of the Earth is the construction of a geoid surface model, both global and regional. Today larger and more precise arrays of input data (geopotential functionals) appear to construct such a model, methods for their processing are rapidly becoming generated. One of such methods is an extention in a series of spherical functions on a spherical trapezium.

Aim. There are many methods for modeling a regional gravitational field in which the Legendre spherical functions of integer degree of the real order are used. They relate, however, mainly to the region which form represents a segment of the sphere. In addition, for their use, the input data must be transformed into a sphere segment with its center at the north pole.