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

Abstract

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 fi nd 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 im agery 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 defi nes likelihoods of t + 1st state) and that equivalent facies were comparable in frequency. The transition probability matrices are expressed as weighted digraphs and calculated fi xed 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 preferentially 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 fi xed probability vector was used as a proxy for fi nal 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.

Holocene sediment distribution in the Al Wajh platform lagoon (northern Red Sea, Saudi Arabia), a modern analogue for large rift basin carbonate platforms

“…The new findings may also influence the interpretation of ancient carbonates, as discussed for shoal-reef (e.g. Riegl & Purkis, 2009) and platform carbonate (e.g. Strasser & V edrine, 2009;Rankey, 2016;Dyer et al, 2018) successions.…”

A new reef classification model with insights into Phanerozoic evolution of reef ecosystems

“…In the initial stage, organic reefs were commonly classified into two types: structures with relief, called bioherms, and structures interbedded with non-reef sediments, called biostromes (Cumings, 1932). Biostromes were commonly considered to be debris layers, but they can be more complex, commonly with in-place fossils (Riegl & Purkis, 2009).…”