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The specificity of applying the approximation approach to solving the linear and nonlinear inverse problems of geophysics, geodesy, and geomorphology is discussed. Within the paradigm proposed by V.N. Strakhov, practically all geophysical problems can be reduced to the systems of linear (and, in some cases, nonlinear) algebraic equations. The method of integral representations is the main one for implementing this approach.The application of various modifications of the method of linear integral representations in the spaces of arbitrary dimension is analyzed. Based on the combined approximations of the topography and geopotential fields, it is possible to determine the optimal parameters of the method for solving a broad range of inverse problems of geophysics and geomorphology and to most fully use the a priori information about the elevations and the elements of the anomalous fields. The method for numerical solving the inverse problem on the distributions of carriers of mass equivalent in terms of the external field in the ordinary three-dimensional space and in the four-dimensional space is described.

Approximation approach in various modifications of the method of linear integral representations