Markov chains as a conceptual probabilistic model according to Vistelius

Abstract

This geo-historical case study analyses Vistelius’ ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences. Vistelius (1915–1995) is regarded as one of the founders of mathematical geology. He was the first to define mathematical geology as “a scientific discipline concerned with the construction, analysis and use of conceptual mathematical models of geological events to solve concrete problems” (Vistelius in Principles of mathematical geology, Nauka, Leningrad, 1980; Principles of mathematical geology, Kluwer Academic Publishers, Dordrecht, 1992). Mathematical models in this context should be primarily probabilistic because of the large number of influencing natural factors. They must be conceptual to avoid fundamental errors in application. Vistelius devoted his seminal book to geological random sequences and their description and analysis using Markov models as stochastic tools. He applied this approach to grain sequences in granitic intrusive rocks and to sedimentary rock layers. Among other things, Vistelius has used Markov chain analysis in mineral resource exploration to distinguish between “ideal” granites, which are not subsequently mineralized, and mainly hydrothermally mineralized, sometimes ore-bearing granites which contain at least two generations of main minerals. The application of this special conceptual stochastic model is demonstrated on Lusatian granite (Saxony, Germany).