Analysis and simulation of namurian sediments in central Scotland using a Markov-process model

Abstract

Many difficulties inherent in analyzing cyclical successions in terms of an idealized cycle and, to a lesser extent, in terms of the modal cycle and composite sequence can be overcome by structuring data in terms of probabilities of upward transitions from one lithology to another. This enables a finite Markov-process model to be used. Transition probability matrices have been constructed from two versions of the same borehole section through paralic Namurian (Pendleian Stage, E 1 ) sediments east of Stirling. The first version does not allow, but the second allows, adjacent items to be of the same lithology. The matrix derived from the first version indicates the following preferred upward succession of lithologies: coal, mudstone, siltstone, sandstone, seatclay, silty and sandy rooty beds, coal. A version of the Chi-square test strongly rejects the hypothesis that the lithologies were deposited in random order. The second matrix is used as computer input forTestmark, Stochex, andMarchain programs, the last of which stimulates a realistic vertical succession. The transition probability data fit readily into the broad framework of deltaic cycles.