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Markov Chain analysis was applied to the description of the megascopic lithologic transitions in Pennsylvanian-age eastern Kentucky coals. Coal lithology modeling can be problematic as individual lithotypes can represent near-instantaneous events (vitrain), prolonged degradation (durain), or fire-induced loss of previously deposited lithologies (fusain). Each of the latter lithotypes, potentially representing vastly different amounts of time, could be of the same thickness. Therefore, equal thickness does not necessarily imply equal time. Probability transform matrices that employ uniform lithotype thicknesses were used, allowing transitions between like lithotypes; embedded Markov Chains, thereby only considering transitions between different lithotypes; and continuous-time Markov Chains were employed in the assessment of a section of the No. 5 Block coal (Pennsylvanian Breathitt Group, Martin County, Kentucky). Embedded Markov Chains could successfully simulate the lithologic transitions. A Monte Carlo random process was programmed to simulate thickness variations of lithotypes between the transitions. The proposed hybrid model of Monte Carlo–Markov Chain was able to predict the random pattern that underlies lithotypes transitions and thickness. The hybrid Monte Carlo–Markov Chain technique proved to be effective in the case study in simulating both the lithologic thickness variations and transitions. |
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