Approximation methods for solving direct and inverse problems in earth exploration (Q2787997)

The book is devoted to approximate methods of solving direct and inverse problems of gravimetry. It consists of 8 chapters and an appendix. The first chapter gives a brief overview of research on approximate methods for solving the direct and inverse gravimetric problems. Besides, this chapter contains the material used in the main part of the book. The second chapter consists of six sections. In the first section, the smoothness of potential fields is investigated. The other sections are devoted to the construction of various algorithms for the reconstruction of potential fields. In the third chapter the expansion of potential fields into series of spherical functions are investigated. The fourth chapter is devoted to approximate methods of representation of the potential fields into a series of spherical functions. In the fifth chapter main attention is paid to the construction and generalization of iterative methods. The sixth chapter is devoted to solving of inverse problems of potential theory. The method of reducing inverse problems to the nonlinear singular integral equations is presented. Various iterative methods for solving of the obtained nonlinear singular integral equations are proposed and validated. In the seventh chapter, approximate methods of analytic continuation of potential fields are considered. The main mathematical apparatus used in this chapter are the multidimensional analogs of Cauchy type and the Stratton-Chu integrals. In the last chapter algorithms of numerical approximation of transformations of potential fields are presented. In the appendix the developed programs are described and solution of model examples is given.