# harmonic coefficients

## Approximation of gravity anomalies by method of ASHA on Arctic area

We consider the method of constructing the local gravity field using technique called spherical cap harmonic analysis (SCHA). This approach involves using of  associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions. They are mutually orthogonal over the spherical cap in each set. However, in general these functions are not orthogonal. Thus, for using both of these sets of functions it is traditionally used least squares method. However, for higher orders it is quite difficult to compute eigenvalues and norms of these functions.

## The main relations for determining the harmonic coefficients of the distribution of the Earth's gravitational potential according to the GOCE satellite data

The last achievements of the physical geodesy is the project of European Space Agency – the GOCE satellite (Gravity of field and steady – state of Ocean Circulation Explorer) which uses the satellite gradientometry method. The gravitational field of the Earth is represented traditionally as a series of spherical harmonic functions, i.e. to model the gravitational field of the finite number of parameters, the so–called coefficients Cnm, Snm. In this paper we analyze the basic relationships for the determination of these coefficients.

## On the construction of the models of Earth's gravity field from GOCE data

As well-known, one of the oldest geodetic problems has today a new development. There is the method of satellite gradientometry allowing essentially improvement of the Earth's gravity field. So, the development of geodesy together with the expansion of various types of measurements is characterized by traditional increase of their level of accuracy and solving the basic problems of geodesy – definition of shape and gravity field of the Earth on the new level.

## Construction of the normal equations matrix for modeling of local gravitational field

We consider the method of constructing the local gravity field using nonorthogonal basic functions, which are solution of the Laplace equation in spherical cap or spherical segment. This approach involves using of associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions. They are mutually orthogonal over the spherical cap in each set. Thus, for using both of these sets of functions it is traditionally used least squares method. However, for higher orders it is quite difficult to compute eigenvalues of these functions.