Page 176 - Carbonate Sedimentology and Sequence Stratigraphy

APPENDIX B: INTRODUCTION TO MODELING PROGRAMS STRATA AND CARBONATE 3D 167

Oceanic Sedimentation Epeiric Sedimentation
Sedimentation Rate Sedimentation Rate
0 .0001 .0002 0 .0001 .0002
0
C =0.1 C =0.3
1
2
C =0.3 C =0.1
1
2
50 w = 10 w = 10
0
0
100
Water Depth 150 w = 100 w = 100
0
0

200

250

300

Fig. B.3.— Carbonate production rate vs. depth for epeiric settings (left) and oceanic settings (right). After Flemings and Grotzinger
(1996), modified.

accelerated to velocities of over 50 km/h during the de- tropical production function by combining a zone of con-
scent on the continental slope (Allen, 1985, p.238). Mod- stant maximum production with a zone of exponential pro-
eling such situations with a diffusion equation requires duction decrease below. The formula is
an abrupt switch to very high diffusion coefficients at a
depth where the models assume low values. dS/dt = c 1 · exp[−c 2 (w − w 0 )]
3. Another problem area for the diffusion approach are
the margins of carbonate platforms. They have sharply where dS/dt is the production of sediment per unit time,
convex curvatures and thus should be the site of inten- c 1 is the maximum production rate (occurring in the upper-
sive erosion. Instead, we observe rapid upward growth most part of the water column) , c 2 is the constant of the
of reefs or sand shoals in this setting. The reason is exponential decrease, w 0 is the depth to which the maxi-
that organic construction and intensive abiotic precip- mum production rate extends and w is the water depth at
the point under consideration. The formula above holds for
itation of carbonate cement override the effects of ero-
the range w > w 0 ;for w < w 0 , sediment production dS/dt =
sion. In addition, organic binding and marine cementa-
c 1 .
tion harden the sediment thus slowing down erosion.
In epeiric settings, light is again the dominant control.
However, in contrast to oceanic settings, restriction, clas-
Carbonate production functions
tic influx and other nearshore effects are assumed to pre-
vent maximum production close to shore. Consequently,
In carbonate environments, the dispersal of material can
the production maximum lies offshore at some modest wa-
also be modeled by the diffusion equation. In contrast
ter depth. Production rate, dS/dt, is given by
to siliciclastics, however, the material for sedimentation,
is not provided by an eroding hinterland but produced dS/dt = c 1 · (w/w 0 ) · exp[1 − w/w 0 ]
within a designated area by a carbonate production func-
tion. STRATA considers essentially tropical systems (T fac- where c 1 and w 0 are the rate and depth of maximum pro-
tory in our terminology) and offers two production func- duction respectively, and w is again the water depth under
tions depending on the setting – oceanic and epeiric (Fig. consideration.
B.3. Oceanic and epeiric production functions may be com-
In oceanic carbonate settings, the basic control on produc- bined by specifying their respective domains in the model.
tion is light (see Figs 2.3, 2.4). STRATA approximates the