Markov chain analysis applied to an ancient alluvial plain succession |
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| Authors: | ANDREW D MIALL |
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| Institution: | Institute of Sedimentary and Petroleum Geology, Calgary, Alberta, Canada |
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| Abstract: | Markov chain analysis is a comparatively simple statistical technique for the detection of repetitive processes in space or time. Coal measure cyclothems or fluvial fining-upward cycles are good examples of sedimentary successions laid down under the control of Markovian processes. Analyses of stratigraphic sections commence with a transition count matrix, a two-dimensional array in which all possible vertical lithologic transitions are tabulated. Various probability matrices may be derived from this raw data, and these are then subjected to chi-square tests to determine the presence or absence of the Markov property. This technique is applied to four types of stratigraphic succession which occur in the Devonian rocks of Prince of Wales Island, Arctic Canada. (1) A conglomerate succession of alluvial fan origin. Markov analysis is of little or no assistance in the interpretation of these rocks, in which only two principal lithologies are present. (2) A conglomerate-sandstone succession. Fluvial fining-upward cycles are detectable by visual examination of the sections and are strongly indicated by Markov analysis. (3) A sandstone-carbonate succession, of marginal marine origin, and including both marine and non-marine strata. Cyclicity is weak in these rocks, but analysis suggests that regressions took place much more rapidly than transgressions during their period of deposition. (4) A succession in which the relative proportions of the various lithologies vary markedly with age. The varying nature of the cyclic tendencies is emphasized in this case by dividing the succession into two subintervals, for the purpose of analysis. |
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