Materials of the International Conference
50th Anniversary of the International Geophysical Year
and Electronic Geophysical Year

16-19 September 2007 • Suzdal, Russia

Discrete mathematical analysis (DMA) in nonlinear approach to geophysical data studies

A. D. Gvishiani1, S. M. Agayan1, J. Zlotnicki2, and M. Diament3

1Geophysical Center, Russian Academy of Sciences, Moscow, Russia

2UMR 6524, CNRS-OPGC, Clermont-Ferrand, France

3D\'{e}partement des Observatoires Volcanologiques, I.P.G.P., France

Abstract

The presentation is devoted to a new approach to analysis of discrete geophysical data. This approach - Discrete Mathematical Analysis (DMA) – is an attempt of modelling of discrete analogues of such fundamental mathematical notions as limit and continuity. The goal of DMA is to model a human ability to analyze discrete complex data: indeed, expert can easily cope with such an analysis in case of small amount of data. The task of DMA is to realize this ability in the cases of large data volumes. Mathematical background of DMA is fuzzy logic and fuzzy mathematics. In the presented study DMA is realized in two series of algorithms. The first series of algorithms ("Ģīnolith", "Crystal", "Roden", and "Tracing") are related to stationary multidimensional arrays, dealing with highlighting condensations, including clusters and linear structures. The second series (algorithms "Equilibrium", "Forecasting", DRAS, FLARS, FCARS, search of fuzzy monotonies and extrema, morphological analysis) represent a functional approach to finite time series. Thus, DMA is a set of algorithms of universal character bound by the common formal framework (discrete limit). DMA contains new fundamental solutions of classic tasks of data analysis: clusterization and search of linear structures in stationary multidimensional arrays; construction of smooth skeletons, search of signals and morphological analysis in time series.

Citation: A. D. Gvishiani, S. M. Agayan, J. Zlotnicki, and M. Diament (2007), Discrete mathematical analysis (DMA) in nonlinear approach to geophysical data studies, in: Materials of the International Conference '50th Anniversary of the International Geophysical Year and Electronic Geophysical Year', GC RAS, Moscow, doi:10.2205/2007-IGY50conf.

© 2007 Geophysical Center RAS and authors


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