Markov Models to Link Facies in Space and Time
AAPG Annual Convention & Exhibition, Denver, Colorado, June 7-10, 2009
Comparative sedimentology maintains that knowledge of the Recent can sometimes be helpful to explain the past (and vice-versa). Thus common quantitative denominators must exist between Recent and fossil systems. Here we present a simple way of describing dynamics and 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 the Recent Arabian Gulf (UAE), and results were compared to the Fenk quarry outcrop in Burgenland, Austria, a carbonate ramp of the Miocene (Badenian) Paratethys with equivalent facies. Facies adjacencies (i.e. Moore neighborhood of color-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 t-th state defines likelihoods of t+1st state) and that equivalent facies were comparable in frequency. We expressed the transition probability matrices 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, we investigated changes in facies composition in falling and rising sea level scenarios by adjusting transition likelihoods preferentially into shallower (falling sea level) or deeper (rising sea level) facies. Our model can also be used as a numerical analogue to a Ginsburg-type autocyclic model. The fixed probability vector serves 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.
Riegl, Bernhard and Purkis, Samuel J., "Markov Models to Link Facies in Space and Time" (2009). Oceanography Faculty Proceedings, Presentations, Speeches, Lectures. 71.
0000-0002-6003-9324; F-8807-2011; B-8552-2013