Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Mathematical problems in geophysical investigations of solid Earth

The classic theory of geophysical fields interpretation связана is linked with the solition of uncorrect problems and with theory of regularization, which is developed by A.N.Tichonov, V.K.Ivanov, M.M.Lavrentiev and their scientific schools.The use of that theory allowed us to develope significant results in construction of volume distribution of physical features in a frame of block-homogeneous models and linear approximation of field distribution. The further evolution of geophysical methods for monitoring research of unstationary heterogenic media with needness goes towards more complicated problems of mathematical physics,for which not only inverse but straight problems become uncorrect. In the Institute of geophysics had been developed (Hachay,1997) a conception of common threestaged interpretation of alternating electromagnetic and seismic fields in dynamical variant. In that conception as regulariztion approach is used the idea of data filtration in the area of operator definition for inverse one dimensional problem and the idea of approximation of anomaly fields by field class with define features. It had been elaborated algorythms,which realize all interpretation stages, which allow to research the effectivity of that approach for analyse of practical data in a frame of identical operator equations,which differ by curnel functions.The problem of complex interpretation of geophysical data is linked with the data base and systems of observation for that geophysical fields,which are included in that complex. We had elaborated a planshet method of electromagnetic and seismic research in frequency - geometrical variant,which is widely used for mapping and monitoring high complicated geological media in surface and underground (mines) variants in a frame of two ranged ierarchic model with estimation of an influence of the third range. That is illustrated by a series of modelling results, natural results and results of verification. Thr research is supported by grants of RFBR №№ 02-05-64229, 02-05-96433.

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