50th Anniversary of the International Geophysical Year and Electronic Geophysical Year 16-19 September 2007 • Suzdal, Russia ## The use of analytical approximations to solve problems of geophysics, geodesy and geoinformatics
## Abstract At present one of major problems of gravimetry, magnetometry, geodesy and geoinformatics is the problem of replacing cartographic presentations of data under investigation with the data analytical approximations related to a finite though large amount of parameters. The most simple approximations that at the same time are acceptable in gravimetry, magnetometry, geodesy and geoinformatics are linear analytical approximations. Such approximations may be constructed in different ways but their finding is always reduced to detecting stable approximated solutions of linear algebraic equations sets (LAES). In the general case, vector of data N components and vector of approximation parameters x has M components. The most significant is the case of M = N. In gravimetry and magnetometry, two major methods of finding linear analytical approximations of external field elements are used in cases when the Earth is considered as lower half space: a) the method of linear integral presentations; b) the method of point sources. V. N. Strakhov elaborated a new general theory to find stable approximations of solutions for LAES of any type (that is LAES may be normally defined (N = M), overdefined (N > M), underdefined (N < M) and proposed a number of new methods to find vectors x. The new theory is based on the new definition of vectors x, namely it is a vector for which approximate but reasonably accurate relations are fulfilled.Citation: V. N. Strakhov, A. V. Strakhov, I. E. Stepanova, and E. A. Zhalkovskiy (2007), The use of analytical approximations to solve problems of geophysics, geodesy and geoinformatics, in: Materials of the International Conference
'50th Anniversary of the International Geophysical Year and Electronic Geophysical Year',
GC RAS, Moscow, doi:10.2205/2007-IGY50conf.
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