CONSTRUCTION OF ANALYTICAL APPROXIMATIONS OF GEOPOTENTIAL FIELDS WITH THE CONSIDERATION OF THEIR FRACTAL STRUCTURE

Abstract

Principal trends in the development of mathematical geophysics at the modern stage include the comprehensive development of the approximation approach. Researchers widely use approximations of external elements of gravitational and magnetic fields by equivalent source assemblages (source-like approximations) and numerical field simulations. We propose a new method for the approximation of geopotential fields by grid distribution of sources. This method takes into account the fractal structure of the fields and is based on the quadrotree technique used for the compression of digital graphic images.