S- and R-approximations of the Earth's surface topography

Abstract

The linear integral representation method has been developed from the Backus and Gilbert [G. Backus and F. Gilbert, Numerical application of formalism for geophysical inverse problems, Geophys. J. R. Astron. Soc. 13 (1967), pp. 247–276; G. Backus and F. Gilbert, The resolving power of gross Earth data, Geophys. J. R. Astron. Soc. 16 (1968), pp. 169–205] method for solving problems, in which the number of data is sufficiently large; at the same time the spatial distribution of some physical properties is represented by a large number of the parameters, or even is an unknown function of spatial coordinates. The linear integral representation method enables us to obtain the solution using discrete and approximately given data. The two versions of the linear integral representation method are applied to the determination of a function describing the Earth's surface topography. Results of numerical experiments and examples of a real topography are presented. The methods proposed are applicable to the solution of various geophysical, geomorphological and geodetic problems.