Geophysical Journal | 2008 volume 30 3

Criteria of optimality and properties of solving inverse problems

© Kobrunov A.I.

The problems which appear during inversion of gravity data in case of different formulations of this task are being analysed. The central one is the problem of hidden identity, which is the feature to inherit specific analytical properties in solving on substantial classes of uniqueness as well as in inadequate in relation to initial prerequisites effects on the result of solving introduced criteria of optimality in relation to parameters of the medium. These effects are specific for other geophysical methods as well, which have the expansion up to the problems with non-zero area of equivalency. Some prerequisites are selected for appearance of effects of hidden equivalency, the reasons of their appearance are being revealed and analysed. They are mainly the obvious membership of the obtained solution to the problem of inversion, the projection on the chosen model class of the special kind of diversity. Properties of these diversities and their interrelations produced by the constructions of optimality criteria are being studied and the ways of their constructive application are being considered as well.

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