This monograph considers all aspects related to the solution of the inverse gravimetric problems, from the measurements to the visualization of the solution, mapping the initial data; selection of the best model of the unknown distribution of masses; aquisition of a characteristic (having the most concentrated masses) solution; gravi-equivalent mass scattering; and selection of a single body out of all obtained body-solutions, which corresponds best to the available geological-geophysical data.
The modern methods for minimization of the respective objective functions are considered, emphasizing the specificity of the inverse problems of the potential fields and using the author's experience in solving these problems. The models when the respective objective functions have only one minimum are considered as well as the conditions for a uniqueness of the inverse gravimetric problem solution.
The ``concentration-scattering'' method for the solution of the inverse gravimetric problem is modified and adapted for the determination of the Earth's figure and its outer gravitational field by solving of the inverse astro-gravi-geodetic problem; simultaneous determination of the Earth's figure and of Earth's masses causing gravitational field almost equal to that measured on the Earth's surface.
This book is designed for geophysicists, mathematicians, physicists, geodesists and geologists dealing with the theory and practice of the interpretation of gravitational measurements and determination of the Earth's figure.