Combined method of <Emphasis Type="Italic">F</Emphasis>-, <Emphasis Type="Italic">S</Emphasis>-, and <Emphasis Type="Italic">R</Emphasis>-approximations in solving the problems of geophysics and geomorphology

The interrelation between different modifications of the method of linear integral representation is studied. Combined approximations of the topography and geopotential fields enable more refined tuning of the method in solving inverse problems of geophysics and geomorphology and provide a more complete allowance for the a priori information about the surface elevation data and elements of anomalous fields. A technique for finding the numerical solution for the inverse problem for determining the mass distributions equivalent in terms of the external field is presented. The results of the mathematical experiment are discussed.     

On increasing the efficiency of the modified method of <Emphasis Type="Italic">S</Emphasis>-approximations

An advanced method for solving the system of linear algebraic equations (SLAE) based on the application of Chebyshev polynomials is described. The modified S-approximations of the elements of gravity field are found by the efficient approaches applied to the solution of SLAE that describes the geophysically informative problem. The results of the mathematical experiment are presented.     

On the interpretation of large gravimagnetic data by the modified method of <Emphasis Type="Italic">S</Emphasis>-approximations

The modified method of S-approximations applied for processing large and superlarge gravity and magnetic prospecting data is considered. The modified S-approximations of the elements of gravitational field are obtained due to the efficient block methods for solving the system of linear algebraic equations (SLAEs) to which the geophysically meaningful problem is reduced. The results of the mathematical experiment are presented.     

Improving the Methods for Processing Large Data in Geophysics and Geomorphology Based on the Modified S- and F-approximations

Izvestiya, Physics of the Solid Earth - Abstract—We consider an improved version of the block contrasting method for processing large and super large gravimetric and geomorphological data....     

Separation of Potential Fields Generated by Different Sources Based on Modified S-Approximations

Izvestiya, Physics of the Solid Earth - Abstract—The paper addresses issues related to constructing the analytical approximations of geopotential fields based on a modified method of...     

Analytical Models of the Physical Fields of the Earth in Regional Version with Ellipticity

Izvestiya, Physics of the Solid Earth - Abstract—The regional version of the method of linear integral representations is used to interpret the data on the anomalous physical fields of the...     

Parametric Structural Approach to Constructing Digital Models of the Relief and Gravitational Field of the Earth Using Analytical S-Approximations

Izvestiya, Atmospheric and Oceanic Physics - This paper discusses the peculiarities of applying the parametric structural approach to constructing analytical approximations of the relief of the...     

Combined Method of <Emphasis Type="Italic">F</Emphasis>-, <Emphasis Type="Italic">S</Emphasis>-, and <Emphasis Type="Italic">R</Emphasis>-Approximations of Increased Dimensionality in Solving the Problems of Geophysics and Geomorphology

The interrelation between different variants of the method of linear integral representations in the spaces of an arbitrary dimension is considered. The combined approximations of the topography and geopotential fields allows the selection of the optimal parameters of the method in solving a wide range of inverse problems in geophysics and geomorphology, as well as a most thorough use of the a priori information about the elevations and elements of anomalous fields. A method for numerically solving an inverse problem on finding the equivalent, in terms of the external field, mass distributions in the ordinary three-dimensional (3D) space and in the four-dimensional (4D) space is described.