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In-Depth Information
(a)
(b)
(c)
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Fig. 15.
The fi xed probability vectors obtained from the transition probability matrices underlying the digraphs in
Fig. 14. The
y
axis shows proportional space cover by the facies, which is the expected distribution of facies in the
rising/falling sea-level scenarios. The FPV does not
per se
give information about the time needed to achieve this.
The amplitude of the sea-level excursion is defi ned in the transition probabilities. In our model, sea-level rise and fall is
in the range of 1.5-2 m.
temporal transitions has been explored above.
Markov chains and weighted digraphs provided
the opportunity to forecast changes in facies by
manipulating transition likelihoods obtained
from lateral patterns in a living landscape. This
allows translating knowledge of facies transitions
in core or outcrop (= time) for the reconstruc-
tion of ancient landscapes (= space) and vice
versa (Doveton, 1994; Parks
et al
., 2000; Elfeki &
Dekking, 2001, 2005) and the frequency of facies
that can be expected in any time slice. Thus, the
estimation of the lateral dimensions of reservoir
rocks can be improved, for example. The present
study also builds on and expands the concepts
developed in Lehrmann & Rankey (1999), who
showed the value of incorporating knowledge
of lateral facies extension in outcrop to obtain
improved understanding of cyclicity.
The sedimentary systems investigated were
characterized by facies of fairly uniform thickness
for which we assumed comparable sedimenta-
tion rates, thus no rate-adjustments were made for
translations from space into time and vice versa.
Differential sedimentation rates and their realiza-
tion in Markov chains are discussed by Parks
et al.
(2000) who scaled transitions by a constant rela-
tive to sedimentation rate (Schwarzacher, 1969).
Bioherms, for example, may accrete faster vertic-
ally rather than laterally, and faster than sur-
rounding sediments. Such a situation would lead
to a stronger self-transition (loop) in the vertical
than the lateral. Additional to the method of Parks
et al
. (2000), the use of embedded Markov chains
would also be useful since these ignore the self-
transitions that encode within-facies deposition
rate. However, such an analysis would limit itself
to evaluating adjacencies and lose any informa-
tion contained in the loops. Coral frameworks
investigated in this paper were mostly biostromal
(i.e. coral carpets
sensu
Riegl & Piller, 2000), thus
not accreting faster to much greater thickness than
surrounding sediments and no corrections by
loop-multiplication were deemed necessary.
The modern and the Miocene situations
explored in this study have in common that both
were evaluated only in a small piece of the entire
system - whatever was imaged in the Arabian
Gulf and the relatively small Miocene outcrop.
The Ras Hasyan area was described from a
7
1.5 km plane area and the Leitha Limestone
from an outcrop 20 m high and 60 m long. This
difference in scale and the obvious incomplete-
ness with regards to the entire landscape need
not matter since fi rst the relative frequency of
facies is of prime concern and second the living
Arabian Gulf landscape has fractal properties
(Purkis
et al.
, 2005). The correspondence of the
FPVs of Miocene and living Arabian Gulf system
may suggest that, since the Miocene system was
very similar (Riegl & Piller, 2000), it may also
have been fractal. Therefore, the different sizes
of study areas may indeed be of no importance.
