Geology Reference
In-Depth Information
Markov models for linking environments and facies in space and
time (recent Arabian Gulf, Miocene Paratethys)
BERNHARD M. RIEGL and SAMUEL J. PURKIS
National Coral Reef Institute, Nova Southeastern University Oceanographic Center,
8000 N. Ocean Drive, Dania, FL 33004, USA (E-mail: rieglb@nova.edu)
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
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
t
th state defi nes likelihoods of
t
+ 1st state) and
that equivalent facies were comparable in frequency. The transition probability matri-
ces 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 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
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.
Keywords
Arabian Gulf, Leitha Limestone, Paratethys, Markov chain, compara-
tive sedimentology, Walther's Law, landscape pattern, remote sensing, carbonate
sedimentation.
INTRODUCTION
reconstruction of the lateral facies mosaic in any
time-slice, be it in the past or the present (Doveton,
1994; Parks
et al
., 2000). All this suggests that a
quantitative expression of temporal information
from core or outcrop into spatial information on
a map of a landscape, and vice versa, would be
interesting and in the tradition of comparative
sedimentology (Ginsburg, 1974, 1975).
Invoking the present for reconstruction of the
past obviously requires some understanding of its
The actualistic principle and comparative
sedimentology see the present as a key to the past
(Ginsburg, 1974). Additionally, a liberal interpreta-
tion of Walther's Law (Middleton, 1973) might
suggest that in some special cases the past may
even hold a key to the present or future, since
knowledge of the conformable strata in out-
crop, if time-transgressive, might allow some
