Geophysical Journal | 2014 volume 36 3

On solving reverse problems of geophysics applying the methods of the theory of dynamic systems

© I.E. Stepanova, D.N. Rayevsky

Methods of solving the reverse problems of geophysics on discovery of the forms of anomaly- forming bodies by the study of solving nonlinear differential equation, which is transformed into infinite chain of linear differential equations - the so-called chain of Toda hierarchies. Infinite system of linear differential equations is in its turn closely tied with geometric parameters of the area sought for - its moments. Moments of the area in three-dimensional space determine reflection of some canonical area upon some unknown source of anomalous field, which can be found by minimization of some regularizing functional. Examples of solving reverse problems of ore type - when the source of gravity field is limited in space and has a stellar property in relation to some of its interior point are presented.

Key words: regularization, dynamic system, Toda chains, conform reflection, moments of the area.

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