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. Therefore, we substantiate the use of technique adjusted spherical harmonic analysis (ASHA) for constructing local field of gravity anomalies. The technique ASHA provides of projection of initial data of gravity anomalies from segment of sphere to hemisphere and continued using of spherical functions of integer degree and integer order. Obviously, on hemisphere we will also obtain two sets of orthogonal functions. For the first system of functions difference n-m will be even. In turn, for the second system of functions difference n-m will be odd. With using technique ASHA we constructed field of gravity anomalies up to 100 order on Arctic area using accelerated algorithm of computation of normal equations matrix and harmonic coefficients. This algorithm provides designing of initial data on a uniform grid. In such uniform grid distance between parallels can be arbitrary. In turn, the distance between meridians must keep constant value. In this case, during the construction of the normal equations matrix we can use discrete orthogonal relation between basis functions in longitude. Also we built field of gravity anomalies on Arctic area using model EGM 2008 up to 360 order. To estimate accuracy we compared obtained model of gravity anomalies and constructing field of gravity anomalies from model EGM 2008. We found the main characteristics of initial field of gravity anomalies on Arctic area and the model values and their differences.

- Dzhuman B.B. Pro pobudovu modeli lokalnoho hravitatsiinoho polia [On the constraction of local gravitational field model]. Heodynamika, 2013, No.1(14), рр.29–33.
- Lukianchenko Yu.O.Pobudovanormalnykhrivniandliaopratsiuvanniadanykhmisii GOCE[Constraction of normal equations mission for processing data GOCE]. Heodynamika. 2013, No.1(14), рр. 34–37.
- Marchenko A.N., Dzhuman B.B. Pobudova matrytsi normal’nykh rivnyan’ dlya modelyuvannya lokal'noho hravitatsiynoho polya [Construction of the normal equations matrix for modeling of local gravitational field]. Geodesy, Cartography and Aerial Photography. 2014, 79, рр. 29–34.
- De Santis A. Conventional spherical harmonic analysis for regional modeling of the geomagnetic feld. Geophys. Res. Lett. 1992, Issue 19, рр. 1065–1067.
- De Santis A., Torta J. Spherical cap harmonic analysis : a comment on its proper use for local gravity field representation // J. of Geod., 1997, 71, рр. 526–532.
- Haines G.V. Computer programs for spherical cap harmonic analysis of potential and general felds. Comput. Geosci., 1988,14,рр.413–447.
- Haines G.V. Spherical cap harmonic analysis. J. Geophys. Res.,1985,90, рр. 2583–2591.
- Hofmann-Wellenhof B., Moritz H. Physical Geodesy, Wien New York, Springer Science + Busines Media, 2005, рр. 403.
- Hwang C., Chen S. Fully normalized spherical cap harmonics: application to the analysis of sea-level data from TOPEX/POSEIDON and ERS-1. Geophys. J. Int., 1997,129, рр. 450–460.
- Hwang J.,Han H., Han S., Kim K., Kim J., Kang M., Kim C. Gravity and geoid model in South Korea and its vicinity by spherical cap harmonic analysis. J. of Geodynamics, 2012, 53, рр. 27–33.
- Jiancheng L., Spherical cap harmonic expansion for local gravity field representation / L.Jiancheng, C.Dingbo, N. Jiancheng // Manuscr. Geod., 1995, 20, рр. 265–277.
- NGA, Arctic Gravity Project, The National Imagery and Mapping Agency, 2008, http://earth-info.nga.mil/GandG/wgs84/agp/
- Thebault E., Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R-SCHA) / E.Thebault, M.Mandea, J. Schott // J. of Geophys. Research, 2006, 111, 13 p.