Structuring Observational Data for Markov and Semi-Markov Models in Geology.
NORTHWESTERN UNIV EVANSTON ILL DEPT OF GEOLOGICAL SCIENCES
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Observational data may be structured in various ways for estimating transition probabilities in Markov models. These normally involve taking observations at fixed intervals in time or space. For some studies it is more meaningful to make observations at irregular intervals that correspond to natural division points in the phenomenon studied. In this latter case semi-Markov models are appropriate. Although Markov properties are present in many geological phenomena, stratigraphic data are particularly useful for illustrating three aspects of data collection that are emphasized here 1 the equal interval approach, in which questions of optimum spacing arise 2 irregular spacing related to actual rock boundaries such as top and bottom contacts of lithologic units that make up the section and 3 hierarchical spacing in which the individual beds that make up the lithologic units are the objects of interest. These three ways of collecting data are used on the same stratigraphic section to bring out these differences in approach. The problem of optimum spacing in method 1 is examined and the more severe problem of adequate operational definitions of bed thickness measurement from subsurface borehole records. Author
- Geology, Geochemistry and Mineralogy