Markov Models for Linking Environments and Facies in Space and Time (Recent Arabian Gulf, Miocene Paratethys)

If, as comparative sedimentology maintains, knowledge of the Holocene can sometimes be helpful to explain the past (and vice versa), common quantitative denominators might exist between recent and fossil systems. It may also be possible to describe dynamics and find linkages between space and time with a unique set of quantitative tools. To explore such conceptual links, spatial facies patterns mapped using satellite imagery were compared with temporal patterns in analogous ancient outcropping facies using Markov chains and graphs. Landsat and Ikonos satellite imagery was used to map benthic facies in a nearshore carbonate ramp (Ras Hasyan) and offshore platform system (Murrawah, Al Gharbi) in recent deposits of the Arabian Gulf (United Arab Emirates), and results were compared with the Fenk Quarry outcrop in Burgenland, Austria, a carbonate ramp of the Miocene (Badenian) Paratethys. Facies adjacencies (i.e. Moore neighbourhood of colour-coded image pixels of satellite image or outcrop map) were expressed by transition probability matrices, which showed that horizontal (spatial) facies sequences and vertical (temporal) outcrop sequences had the Markov property (knowledge of tth state defines likelihoods of f + 1st state) and that equivalent facies were comparable in frequency. The transition probability matri-ces are expressed as weighted digraphs and calculated fixed probability vectors which encapsulate information on both the spatial and temporal components (size of and time spent in each facies). Models of temporal functioning were obtained by modifying matrices (digraphs) of spatial adjacency to matrices (digraphs) of temporal adjacency by using the same vertices (facies) but adjusting transitions without changing paths. With this combined spatio-temporal model, changes in facies composition in falling and rising sea-level scenarios are investigated by adjusting transition likelihoods pref-erentially into shallower (falling sea level) or deeper (rising sea level) facies. The model can also be used as a numerical analogue to a Ginsburg-type autocyclic model. The fixed probability vector was used as a proxy for final facies distribution. Using Markov chains it is possible to use vertical outcrop data to evaluate the relative contribution of each facies in any time-slice which can aid, for example, in estimation of reservoir sizes and to gain insight into temporal functioning as derived from spatial pattern.