Using spherical harmonic series to approximate the Earth`s gravitational field in a local area

One of the most important tasks of modern physical geodesy is to determine a high-frequency part of the Earth’s gravity field (EGF), which inevitably depends on the individual characteristics of a particular computational area. The author investigates the practical aspects of a relatively new theory for modeling the said part of the EGF in a local area, using a series of special spherical functions ensuring local orthogonality. With the global gravitational model EGM2008 as input information, we aim to construct a local analytical one for the high-frequency component of the EGF in the Republic of Burundi territory. To overcome the main technical difficulty, the problem of solving rank-deficient systems of linear algebraic equations (SLAE), special regularization techniques are employed. The developed algorithm generalizes the classical global spherical harmonic analysis (GSHA) and is treated as one of the preferred alternative methods of regional modeling. It enables representing fields with high spatial resolution using a much smaller number of parameters rather than the classical GSHA. Compared with other possible methods of regional analysis, the advantage of the LSGA is ultimate provision of a solution, not only analytical, but also meeting the Laplace differential equation, which, as we know, is fundamentally important in many problems of geophysics in general and physical geodesy in particular