Discrete mathematical analysis and applications geology and geophysics

Abstract

This article describes a new original approach to the analysis of data which is called the Discrete Mathematical Analysis (DMA). The authors have made an attempt to create a model of a finite limit using fuzzy techniques. The model helped to find the key in terms of classical mathematics to the basic problems of a discrete case – continuity, coherence, closeness, trend etc. DMA is a series of algorithms used to solve the basic tasks of data analysis: clustering, tracing, morphological analysis, trend and so on. All the DMA algorithms are universal and are based on a finite limit. The authors consider this is one of possible approaches to a finite limit and the DMA construction. The article suggests three algorithms of clustering: «Crystal», «Rodin» and «Monolith» and some of their applications in geophysics.