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Complexity in Carbonate Systems
Jon Hill1
Andrew Curtis1
Rachel Wood2
Dan Tetzlaff3
1Univeristy of Edinburgh
2Schlumberger Cambridge Research and University of Cambridge
3Schlumberger Boston Research
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 2
Carbonate Deposition
• There are known differences between siliciclastic and carbonate deposition– In-situ production– Internal vs. external controls
• Carbonates are less predictable – why?• Which processes control this unpredictability?
– Physicochemical vs. Biological
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 3
Carbonate Complexity
• Presence of both internal and external forcings on carbonate production rates
• Internal forcings have feedback mechanisms
• E.g. Andros Island tidal flats (Rankey, 2002) – fractal distribution of facies
Algal MarshOpen Channelsand Ponds
Mangrove
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 4
Complexity
• Previous work has indicated that carbonate deposition is complex– Statistical properties (e.g. Wilkinson, et. al, 1997)– Modelling work (e.g. Burgess and Emery, 2005)
• Implications for stratigraphic interpretation
Here, complexity means complicated and unpredictable
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 5
Open sea water CaCO3
supersaturated
Residence Time = 0
Residence Time ~ 1-100 days
Model Formulation
0 50 100 150 200 250Residence Time in the Lagoon (days)
0
0.2
0.4
0.6
0.8
1
Per
cen
tag
e o
f M
axim
um G
row
th 0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
35
40
45
50
Wat
er D
epth
(m
)
Percentage of Maximum Growth
0 500 1000 1500 2000 2500 30000
0.2
0.4
0.6
0.8
1
Wave Power (W/m )2
Per
cen
tag
e o
f M
axim
um G
row
th
• Forward model, Carbonate GPM – an extension of a siliciclastic model, GPM
• Model includes:– Erosion and transport
– Two carbonate types
– Carbonate production based on:
• Carbonate supersaturation
• Light levels
• Wave energy
• Based on physical and chemical parameters only
Hypothesis: Does carbonate complexity require biological controls?
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 6
0 100 200 300 400 500 600 700 800 900 10000
20
40
60
80
100
120
140
160
180
200
Time (kyr)
Rel
ativ
e S
ea L
evel
(m
)
Model Input
• Input:– Sea level– Starting topography
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 7
Model Output
• Output is a 3D volume of sediment
• Timelines drawn every 5kyr
ReefLagoon
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 8
Residence Time
• Residence time reacts to changes in the topography
Area of high residence time
Residence Time
IslandsDiversion of
flow
Velocity Snapshot
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 9
Cycles
• Cycles picked on points of rapid deepening of water• Around 90 cycles were generated in 1Myr• Each run produced different cycles
– Different Fischer plot– Cannot correlate
-10
-8
-6
-4
-2
0
2
4
6
8
0 10 20 30 40 50 60 70 80 90 100
Cycle Number
Cum
ulat
ive
Dis
tanc
e fro
m M
ean
Cyc
le
Thic
knes
s (m
)
0 100 200 300 400 500 600 700 800 900 10000
20
40
60
80
100
120
140
160
180
200
Time (kyr)
Rel
ativ
e S
ea L
evel
(m
)
Note: linear sea level change
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 10
0 200 400 600 800 1000-1.5
-1
-0.5
0
0.5
1
1.5
Time (kyr)
Wat
er D
epth
(m
)
Water Depth
Rapid initial growth
Different limiting depths
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 11
0 0.02 0.04 0.06 0.08 0.110
-6
10-5
10-4
10-3
10-2
10-1
100
101
Frequency (kyr-1
)
Pow
er
Power Spectrum
No dominant periodicity
Jon Hill, Andrew Curtis, Rachel Wood, Dan TetzlaffSlide 12
Conclusions
• A tiny difference of 1m in initial topography produces very different results
• The model generates autocycles– Different in each run and cannot be correlated
• Average depth converges to different limit• Power spectrum shows no structure
– No simple predictability
• Simple, physicochemical processes produce complex behaviour without biological controls
