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

16-19 September 2007 • Suzdal, Russia

From observations to non-linear models in geoinformatics

A. D. Gvishiani

Geophysical Center, Russian Academy of Sciences, Moscow, Russia

Abstract

Development of artificial intelligence approach to geophysical data handling is one of the most important achievements during the 50 years passed after successful completion of IGY. The presentation is devoted to a new approach to analysis of discrete geophysical data. This approach – Discrete Mathematical Analysis (DMA) – is an attempt of modeling 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 present study DMA is realized in two series of algorithms. The first series of algorithms ("Monolith", "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, and FLARS, search of fuzzy monotonies and extrema, morphological analysis) represent a functional approach to finite time series. The tasks fulfilled by the second series are similar to classical analysis of smooth functions. Thus, DMA is a set of algorithms of universal character bound by the common formal framework (discrete limit). DMA contains new fundamental solutions of classical tasks of data analysis: clusterization and search for linear structures in stationary multidimensional arrays; construction of smooth skeletons, search for signals and morphological analysis in time series. At present DMA has numerous successful geological and geophysical applications. In the cases of study of magnetic and gravimetric anomalies this approach gives a possibility of revealing the vague features in the Earth's crust structure. As a result of relief data analysis this approach gives a possibility of revealing areas of increased tectonic activity. In the case of analysis of volcano monitoring data this approach allows us to distinguish in the time series between the anomalies concerned with different factors (storm rains, increase in hydrothermal activity, etc.). The DMA is one of approaches used now to deal with the problems in non-linear geophysics.

Citation: A. D. Gvishiani (2007), From observations to non-linear models in geoinformatics, 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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