FROM STOKES’ INTEGRAL TO APPROXIMATION BY MEANS OF SRBF
The problem of determining quasigeoid from gravimetry has a well-known solution by means of Stokes’ integral. To solve the same problem using regional gravity data, different modifications of Stokes’ kernel can be used. One of them was proposed by O.M. Ostach. In [1] the frequency characteristic of the 0truncation operator of Stokes’ kernel onto inner zone of ψ0 radius is introduced. There it was established thatexpansion of the truncated (by Ostach) Stokes’ kernel into Legendre polynomials differs from the expansion of Stokes’ kernel by this frequency characteristic. In this article the fundamental equation of physical geodesy in local area is proposed to solve by means of spherical radial basis functions (SRBf) instead of integrating. New scaling functions and wavelets are introduced. These functions use the frequency characteristic of the truncation operator of Stokes’ kernel that intercepts contribution of far zone. The two-step numerical experiment has been carried out in order to test these new scaling functions. At first, gravity anomalies and height anomalies were calculated from EGM2008 on a regular grid in 4°×6° and 2°×4° areas, respectively. At the first step gravity anomalies were approximated by linear combination of scaling functions with identically equal to 1 frequency characteristic. At the second step height anomalies were modelled by means of the new scaling functions but with the same poles and coefficients of linear combination. Comparison of modelled quantities against calculated ones has shown a high precision of recovering of height anomalies from regional gravity data.