Geophysical Journal | 2001 volume 23 5

On setting up of regularizing operators of the definition of star-shaped domains similar to the preset ones

© Chernaya O.A.

Arange of questions concerning the solubility of the inverse problem of the logarithmic potential for a body similar to the preset one is considered. Among the paramount problems that of projecting of elements of the Gilbert's space of data on a set of the values of the operator of the direct correspondence of the problem in the condition when the data are highly erroneous and their immediate use may violate the constraints that provide the existence of a regularizing operator. The adaptive procedures of smoothing are built by methods of regularizing with considering the subsequent use of the data. The global regularizing operators of the definition of star - shaped domains similar to a circle or a layer of a constant thickness are built as successions of local regularizing operators for the corresponding successions of linear integral equations of the first kind whose right-hand parts use the smoothed initial data. In turn, the local regularizing operators for linear integral equations are built as parametrized minimizing successions of functionals that are a weighted sum of the functional of the type of discrepancy with one of the proposed stabilizators ensuring unambiguous solubility of the given equation.

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