Analysis of the gravity field. Direct and inverse problems (Q2160160)

The book consists of three parts. First part ``Forward Modeling of the Gravity Field'' contains three chapters: Chapter 1 ``Gravitation''; Chapter 2 ``The Gravitational Signal of Homogeneous Bodies, Bounded in Horisontal Plane''; Chapter 3 ``Fourier Methods''. Second part ``The Preprocessing of Gravity Data: From Observations to a Gravity map on Local Horizontal Plane'' contains three chapters: Chapter 4 ``The Gravity Fields of the Earth''; Chapter 5 ``Gravity Surveying and Preprocessing''; Chapter 6 ``Gravity Processing''. Third part ``Inverse Theory and Applications'' contains three chapters: Chapter 7 ``Elementary Inverse Theory''; Chapter 8 ``On the Mathematical Characterization of the Inverse Gravity Problems''; Chapter 9 ``General Inversion Approaches''. The Chapter 1 introduces the basic concepts of gravitation forces, the concepts of gravitation potential and the ordinary elements of vector calculus used to describe the properties of the gravitation field. The second Chapter is devoted to the calculation of gravitational fields created by bodies of regular geometric shape. The third Chapter outlines the main properties of the Fourier transform necessary for analytical and numerical methods of studying gravitational fields. In the fourth Chapter, the definition of the Earth's gravitational field is given. Investigated Normal Gravity Fields and described Gravity Models. Considered gravitational anomalies. In the first section of the Chapter 5 authors clarify some type of observations that can be performed on the gravity field. Then they review the measuring principles of existing most common gravimeters, especially with purpose of specifying their typical use and their performance in terms of accuracy. After this they come to the observation the gravity meter and its use in the relative gravimetry mode. The sixth Chapter is one of the central chapters of the book. It consists of 8 sections. 6.2. The Terrain Correction, 6.3. Bouguer and Nettleton, 6.4. The Residual Terrain Correction, 6.5. Gridding Gravity Disturbances on a Plane at Constant Height: Determistic Approaches, 6.6. Gridding Gravity Disturbances on the \(S_0\) Plane, by a Stochastic Approaches, 6.7. From Grids of Gravity to Grids of Different Functionals. The seventh chapter is devoted to the definition, under sufficiently severe conditions, of bodies that perturb the gravity field. Methods for determining the mass of the perturbing body, the Barycenter of the body and its depth, mean depth of the ibterface between two layers are presented. The eighth chapter discusses the existence of non-unique solutions in inverse problems arising in the study of gravitational fields, and the instability of mathematical models describing these fields. An analysis is made of regularization methods that are adequate to inverse problems of gravity. The ninth chapter discusses the problems of applying the Tikhonov regularization method to solving ill-posed gravimetry problems in a formulation close to practice. The book contains extensive material on the theory of gravitational fields, both necessary for an initial acquaintance with the subject and useful for specialists dealing with problems of gravity exploration.