the state of the art in carbonate numerical stratigraphic forward modelling

CSDMSC-FRG

The State of the Art in Carbonate Numerical Stratigraphic Forward

Modelling

Peter BurgessDept. Earth Sciences,

Royal Holloway University of London, UK

With contributions from Chris Jenkins, Donald Potts, Rick Sarg and Dave Budd

CSDMSC-FRG

Group aim:• To identify and address grand challenges for fundamental

research on ancient and recent carbonate systems

To be achieved by:• Creation of next generation of numerical carbonate process

models under the umbrella of the CSDMS initiative• Creation of supporting carbonate systems databases

Assuming that: • Open-source numerical models and associated quantitative

datasets can be state-of-the-art repositories for our knowledge of how carbonate systems work

• Models can be useful experimental tools applied to develop and enhance carbonate knowledge.

CSDMSC-FRG

Peter Burgess, (Chair) Royal Holloway University of London Andrew Barnett, BG Group David Budd, University of Colorado Govert Buijs, ConocoPhillips Bob Demicco, Binghamton University Carl Drummond, Indiana University-Purdue University Fort Wayne Evan Franseen, University of Kansas Ned Frost, ConocoPhillips Xavier Janson, University of Texas at Austin Chris Jenkins, University of ColoradoGareth Jones, Chevron Energy Technology Company Albert Kettner, CSDMS, INSTAAR, University of Colorado H. Richard Lane, U.S. National Science Foundation Patrick Lehmann, ExxonMobil Exploration Company Mingliang Liu Auburn, University, School of Forestry and Wildlife Sciences William A. Morgan, ConocoPhillips Mohamad Mehdi Nasr Azadani, University of California at Santa Barbara Gene Rankey, University of Kansas Bernhard Riegl, Nova Southeastern University, National Coral Reef InstituteRick Sarg, Colorado School of Mines Fiona Whitaker, University of Bristol Bruce Wilkinson, Syracuse University

N=22

CSDMSC-FRG

• Issues: platforms & prediction, complexity and heterogeneity

– Platform types and facies prediction

– Origins of heterogeneity in carbonates

– Other issues…

• Review of current models

– Depositional models

– Diagenetic models

• New modelling directions

– Cellular automata

– Population modelling

• C-FRG research plans

CSDMSC-FRG

Homoclinal

Distally steepened

Non-rimmed shelf

Ramps

Flat-topped

attached platform

s

Rimmed shelf

Isolatedplatform

Resedimented deep-water grainstone

Oolitic & biolcastic grainstones

Reefs, patch reefs, rudist shoals etc

Tidal flats & sabkha

Facies belts

• Standard paradigm: carbonate factory type, represented by carbonate production profile , controls platform architecture

• Most predictions of facies and sequence strat hinge on this• But is it true?

Tropical(euphotic)

Cool-water(heterozoan)

0

Wat

er D

epth

(m)

100

200

300

400

500

Mud mound

Tropical(oligophotic)

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– Other issues…







• CFG research plans

CSDMSC-FRG

Purkis et al. Wilkinson & Drummond, 2004

Harris & Vlaswinkel, 2008• Planform heterogeneity observed in modern

systems across a wide range of scales• Limited statistical understanding of spatial

distributions at different scales• Understanding of the responsible processes is

even more limited, especially the link with vertical stacking

CSDMSC-FRG

• Vertical stacking in strata also shows significant heterogeneity

• Many carbonates strata exhibit exponential thickness frequency distributions

• Which means lots more thin beds than thick beds

• What does this mean in terms of depositional processes?

Logged section from Grotzinger, 1986, JSP, 56, 813-847

Wilkinson et al, 1996, JSR, 66, p.1065-1068

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– Other issues…








CSDMSC-FRG

• Ocean acidification

• Shoreline change on island nations

• Reefs, shallow and deep, and their change

in response to past and future climate

change

• Tsunami records

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– Other issues…








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SummarySpatial dimensions: 3DProcess dimensions: 1-2DScale: Whole platform and moreLithologies: Multiple, user-defined linked to production curvesTransport is diffusional so ability to make fine-scale heterogeneity is rather limited

USP: Large scale, very flexible and often very fast to run

Refs:Bassant and Harris, 2008Williams, 2010, unpublished PhD thesis

CSDMSC-FRG

SummarySpatial dimensions: 3DProcess dimensions: 1-2D production, 2D transportScale : Platform architecture & platform interiorLithology: very basic, water-depth classification onlyHeterogeneity: some, but limited by poor lithology representation

USP: consideration of autocyclic processes, detailed statistical analysis of results

Refs:Burgess et al 2001,Burgess, 2001,Barnet et al 2002,Burgess and Wright 2003,Burgess and Emery 2004Burgess, 2006

CSDMSC-FRG

SummarySpatial dimensions: 3DProcess dimensions: 1-2D?Scale: Whole platformLithologies: Multiple, realistic Heterogeneity – definitely, but mostly externally forced? And possible issues with numerical artefacts?USP: good wave and current model, plus link to diagenetic processes

Refs:Peterson et al 2006Peterson et al 2008

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– Other issues…








CSDMSC-FRG

Primary facies

Hydraulic conductivity

Porosity

SummarySpatial dimensions: 3DProcess dimensions: 1-2D?Scale: Whole platformLithologies: Multiple, realisticDiagenetic model: hybrid parametric

Refs:Peterson et al 2006Peterson et al 2008

CSDMSC-FRG

Reaction-transport modeling of bed-scale dolomitization to assess pattern formation using Sym.8 simulator

SummarySpatial dimensions: 2DProcess dimensions: 1-2D?Scale: Small-scale bed stackingLithologies: Realistic depiction of bed-scale dolomitization

Refs:Budd, 2010, pers. comm.

Grids centered in30 cm x 10 cm cells

transport & reactions

no flux boundary

no flux boundary

2m x 18 m with 1200 cells.

Isothermal

Flow velocity - from imposed pressure gradient (2nd order PDE) & Darcy equations.

Fluid - Mississippian seawater evaporated to near halite saturation, 4x modern atm CO2

more

less% Dolomite, 0.25 my

Distance (m)

Dol

omite

Vol

ume

Frac

tion

Distance (m)

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– Other issues…








CSDMSC-FRG

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1

2

3

4

5

0

6

Hiatus/no deposition

Primary producer lithotope 1



Byproduct lithotope 1


Erosion

2 0 0 1 15 2 0 3 15 3 2 3 45 2 3 0 45 2 3 4 1

• What happens next to this cell?• 4 same-lithotope neighbours• So persists into next timestep

• Rule-based deterministic models

• Each cell evolves through time according to very simple rules based on contents of neighbouring cells

• Combine with subsidence, sea-level, sediment production etc to make a model of carbonate accumulation ...

Lithofacies mosaic in a CA model

Lithofacies mosaic on a map of Florida Bay

Cellular Automata RulesDistance Min

NeighboursMax

neighboursMin

triggerMax

trigger

2 4 10 6 10

CSDMSC-FRG

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4 4 1 2 4 5 2 2 2 2 2 2 2 2 0 3 3 3 3 3 3 6 3 0 6 6 6 3 0 0 0 0 0 0 0 0 0 4 1 1 4 1 1 1 2 2 2 1 4 40 0 1 1 1 2 2 2 2 2 2 0 0 0 6 3 3 3 3 3 3 3 3 0 6 6 6 3 3 0 0 0 0 0 0 3 3 3 1 1 4 1 1 1 0 0 4 4 0 00 0 0 1 1 4 0 0 2 2 2 0 0 0 0 0 3 3 3 3 3 3 6 3 6 6 6 3 0 0 0 0 0 0 0 3 3 3 3 1 1 1 1 0 0 4 4 0 0 00 0 0 1 1 1 6 6 0 0 1 1 4 0 0 0 0 3 3 3 3 6 3 3 3 3 3 0 0 0 0 0 0 0 3 6 3 3 3 0 0 0 0 0 0 0 0 0 0 00 0 1 1 1 4 6 6 4 4 1 1 1 1 0 0 0 3 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 3 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 00 1 1 1 1 1 1 4 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 01 1 1 1 1 1 1 1 1 4 0 0 1 1 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 6 6 3 3 3 3 4 0 4 0 0 0 0 0 0 0 0 0 1 0 11 1 4 4 4 1 1 1 0 0 0 0 0 4 4 4 4 1 3 0 0 0 0 0 0 0 0 0 3 3 6 3 3 0 0 3 1 1 0 0 0 0 0 0 4 1 1 1 1 14 4 4 0 1 1 1 4 0 0 0 0 4 4 4 4 4 4 1 1 0 0 0 0 0 0 0 3 0 3 6 6 3 0 0 1 3 1 1 0 0 0 0 0 1 1 1 1 1 10 0 1 1 1 1 1 0 0 0 4 1 1 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 0 0 3 4 4 3 1 1 1 4 0 0 0 0 1 1 4 0 0 00 4 4 4 1 0 0 3 3 3 1 1 1 1 4 4 4 4 3 3 3 3 3 6 6 6 6 6 6 6 3 3 3 1 1 3 4 0 0 1 4 0 0 0 1 4 4 4 4 04 1 1 1 0 0 3 0 0 4 1 3 0 0 0 4 4 1 3 3 3 3 6 6 6 6 6 6 6 6 3 3 3 1 1 4 4 0 4 1 1 4 0 0 0 1 4 4 4 44 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 6 6 6 6 6 6 6 6 6 6 3 3 3 1 4 4 4 4 6 0 1 1 0 0 1 4 4 4 41 1 1 1 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 6 6 0 3 0 3 6 6 6 6 3 3 3 4 1 1 0 0 0 1 1 0 1 1 4 4 1 11 1 1 1 1 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 3 3 3 3 3 6 6 6 6 3 3 3 1 1 1 1 4 1 1 1 4 1 4 4 4 1 10 4 1 1 1 4 3 0 3 0 0 3 0 0 0 0 0 5 5 5 3 3 3 3 3 3 3 3 3 5 6 3 3 3 3 0 1 1 1 1 1 1 1 4 4 4 4 4 1 00 4 1 4 1 6 6 6 6 3 3 3 3 3 3 0 3 2 2 2 3 3 3 3 0 3 2 2 2 2 3 3 3 3 3 4 0 0 0 1 1 1 1 4 4 4 4 1 1 00 0 3 0 6 6 6 6 6 6 6 6 6 0 5 0 3 3 2 2 3 3 0 0 0 3 3 2 2 5 3 3 3 3 1 1 4 0 0 0 0 0 0 4 4 4 4 4 1 03 3 3 3 6 6 6 6 6 6 6 6 6 0 5 2 2 5 5 2 3 3 3 0 0 3 5 5 5 5 2 3 3 2 2 1 1 0 0 0 0 0 1 4 4 4 4 4 3 30 3 3 3 6 6 6 6 6 6 6 6 6 0 2 5 5 5 5 2 2 3 3 3 3 3 2 2 5 2 2 2 2 2 2 4 4 4 4 1 1 1 1 1 4 4 4 1 0 00 0 3 3 6 6 3 3 3 3 6 6 6 0 2 2 5 5 5 2 2 2 3 3 3 3 5 5 5 2 2 2 5 2 2 4 4 4 1 1 1 1 1 1 1 1 3 3 0 00 0 0 3 3 3 3 3 3 3 0 0 6 0 2 5 5 5 5 5 0 2 2 3 5 5 5 5 5 5 5 5 2 1 1 4 4 4 4 1 1 1 1 1 0 0 3 3 0 00 0 0 0 0 0 0 0 0 0 3 3 6 2 5 5 5 5 5 0 0 5 5 5 5 5 5 5 5 5 5 5 5 2 1 4 0 0 0 0 4 4 1 1 0 0 3 0 0 00 0 0 0 0 0 0 0 6 3 6 0 0 2 5 5 5 5 0 0 5 5 5 5 5 5 5 2 5 5 5 5 5 0 0 4 4 0 0 0 4 4 4 1 3 3 3 3 0 00 0 0 0 0 0 0 0 3 3 6 0 0 2 5 5 5 5 0 0 5 5 5 5 5 5 2 2 5 5 5 5 5 0 0 4 4 4 4 4 4 4 4 1 3 3 3 3 3 03 0 0 0 0 0 0 0 3 6 6 0 2 5 5 5 5 5 0 0 5 5 5 5 0 0 5 5 5 5 5 5 5 5 1 4 4 4 4 4 4 4 4 4 1 3 3 6 3 33 3 6 6 0 0 0 0 3 6 6 0 2 5 5 5 5 5 0 5 5 5 5 5 5 5 5 5 5 5 5 5 5 2 1 4 4 4 4 4 4 4 4 4 4 1 3 3 3 33 3 3 6 0 0 0 0 3 3 6 2 2 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 5 2 1 1 4 4 4 4 4 4 4 4 4 1 3 3 3 36 3 3 6 0 0 0 0 3 3 6 2 2 2 5 5 5 5 5 5 2 2 2 2 2 2 2 5 5 5 5 5 5 2 2 1 1 4 4 4 4 1 4 4 1 1 4 3 3 63 3 6 0 0 0 0 0 3 3 6 2 2 2 2 0 0 2 5 5 2 0 0 0 2 2 5 5 5 5 5 0 0 5 6 0 0 1 1 1 1 1 1 4 4 1 1 0 3 33 6 0 0 0 0 0 0 3 3 6 6 3 3 0 0 2 2 0 0 0 0 0 0 0 0 0 5 5 5 0 0 0 6 6 0 0 0 0 2 2 1 4 4 4 1 1 0 3 33 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 5 5 2 5 0 5 0 0 0 0 2 2 2 5 2 0 0 1 1 0 0 5 2 2 2 2 1 4 4 4 1 0 0 30 0 0 0 0 0 0 0 0 0 3 3 3 6 6 0 5 5 2 2 0 5 0 0 0 0 5 5 2 2 2 0 1 1 1 1 1 2 2 2 2 2 1 4 4 4 1 0 0 30 0 0 0 0 0 0 0 0 3 3 6 6 6 6 6 0 5 5 2 2 5 0 0 0 2 5 5 2 2 0 0 1 4 4 4 1 2 2 5 2 2 1 4 4 4 4 3 1 00 0 0 0 0 0 0 0 0 0 3 6 6 6 6 6 6 3 3 3 2 5 0 0 2 2 5 2 2 2 0 0 1 4 4 4 2 2 5 0 0 2 1 4 4 4 4 1 3 00 0 0 0 0 0 0 0 0 3 6 6 6 6 6 6 3 3 3 5 5 5 0 2 2 2 2 2 2 0 0 0 1 1 1 1 2 2 2 2 2 2 1 1 4 4 1 1 3 00 0 0 0 0 0 0 0 0 3 6 6 6 6 6 6 6 3 3 3 3 0 0 2 2 2 2 2 0 0 0 0 3 3 1 2 2 2 2 2 2 2 2 1 1 1 1 0 0 33 0 0 0 0 0 0 0 3 3 5 5 6 6 6 6 6 3 3 2 5 0 0 2 5 2 0 6 3 0 0 0 0 3 0 2 2 2 2 2 2 2 2 2 2 1 0 0 0 30 0 0 5 5 0 0 0 3 5 2 2 5 6 6 6 6 3 2 2 5 0 0 3 3 6 3 3 3 0 0 0 0 0 0 3 0 6 6 2 2 2 2 2 2 0 0 5 5 00 0 0 2 2 3 3 3 2 2 5 5 5 2 2 2 2 3 3 5 0 0 0 0 3 3 3 3 0 0 0 0 0 0 0 3 6 6 6 6 2 2 2 2 2 0 0 0 0 00 0 0 2 2 2 2 0 0 2 5 5 5 5 5 5 5 5 2 0 0 0 0 0 3 3 6 0 0 0 0 0 0 0 3 0 6 6 6 6 2 2 5 5 0 0 0 0 0 05 0 0 2 5 5 5 0 0 2 5 5 5 5 5 5 5 5 3 0 0 0 0 3 3 6 0 0 0 0 0 0 0 3 3 0 0 6 6 2 2 2 5 5 2 2 0 0 0 50 0 0 2 5 5 5 5 2 2 2 2 2 3 5 5 5 5 3 3 3 0 3 3 6 0 0 0 0 0 6 3 3 3 0 0 0 5 2 5 5 5 5 5 2 2 2 0 5 55 6 0 2 5 5 5 0 0 0 2 3 3 3 3 3 2 2 0 3 3 3 3 3 6 0 0 0 0 6 6 3 3 6 6 0 2 2 2 5 5 5 5 5 5 2 2 2 6 56 6 6 2 5 5 5 2 0 5 5 3 3 3 3 3 3 0 0 3 6 6 6 3 3 0 0 0 0 6 6 3 3 6 6 0 5 2 2 2 5 5 5 5 5 5 2 2 6 66 6 6 2 5 5 5 2 2 0 0 3 3 3 3 3 3 3 3 3 6 6 6 3 3 3 0 0 0 0 0 0 3 3 6 6 0 2 2 2 0 0 5 5 5 5 5 2 6 60 0 0 2 5 5 2 0 0 5 5 0 0 0 6 6 3 3 3 3 6 6 6 3 3 3 3 0 0 0 0 0 0 0 3 6 6 6 0 0 0 0 5 5 5 5 5 2 0 00 0 2 5 5 5 2 0 0 0 0 0 5 5 6 3 0 3 3 3 3 6 6 3 3 6 3 3 0 0 0 0 0 0 6 3 6 6 6 0 0 2 5 5 5 5 5 2 0 04 4 2 5 5 5 5 0 0 0 0 2 2 2 5 3 3 3 3 3 3 6 3 0 6 6 6 3 3 0 0 0 0 0 0 3 6 6 6 1 1 1 2 5 5 5 5 2 4 41 1 2 5 5 5 5 2 0 2 2 2 2 2 5 3 3 3 3 3 3 6 3 0 6 6 6 3 0 0 0 0 0 0 0 6 3 6 1 1 4 1 2 2 5 5 2 2 1 1

• Animation from “patches” initial condition• Each cell evolves through time according to

very simple rules based on contents of

neighbouring cells• 20 time steps=20 ky • Lateral migration of facies• Increasing lateral heterogeneity/spatial

entropy

1

2

3

4

5

0

6

Hiatus/no depositionPrimary producer lithotope 1Primary producer lithotope 2Primary producer lithotope 3Byproduct lithotope 1Byproduct lithotope 2Erosion

Lithotope/process

• Even this simple model leads to complicated

results

CSDMSC-FRG

CarboCAT •3D cellular automata model desgined to model platform interior heterogeneity, constrained by lithofacies thickness distributions•Multiple facies calculated by cellular automata•Simple sediment transport algorithms•Depth-dependent sediment production rate•Subsidence •Eustatic sea-level oscillations

Cellular Automata RulesDistance Min

NeighboursMax

neighboursMin

triggerMax

trigger

2 4 10 6 10

Initial state map

Final state map

Cross section

Horizontal Distance

Elev

ation

(m)

CSDMSC-FRG

Vertical sections from middle of model grid …

1

2

3

4

5

0

6

Hiatus/no deposition



Primary producer l-tope 3



Erosion

Lithotope/process

Facies

125

m

Facies

60 m

40 m

50 m 0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Lithofacies unit thickness (m)

Cum

ulati

ve N

orm

aliz

ed F

requ

ency

CA facies mosaic

Exponential CDF

max diff

• CarboCAT can generate a good fit with

exponential curve

• Reproduces one important aspect of

carbonate strata

CSDMSC-FRG

Logged section from Grotzinger, 1986, JSP, 56, 813-847

Wilkinson et al, 1996, JSR, 66, p.1065-1068

• Vertical stacking in strata also shows significant heterogeneity

• Many carbonates strata exhibit exponential thickness frequency distributions

• Which means lots more thin beds than thick beds

• What does this mean in terms of depositional processes?

CSDMSC-FRG

Model 1 Model 2

Water Depth (m)

2.5 My elapsed m

odel time

Water Depth (m)

CSDMSC-FRG




– Other issues…








CSDMSC-FRG

• Model spatial and temporal

distribution of carbonate

accumulation based on community

model

• Community model encapsulates

competition, positive feedbacks in

occupied sites, and manipulation of

local environment by organisms

CSDMSC-FRG

Population Approach Lotka-Volterra coupled ordinary differential equations

numericalCARBONATE, Oct 2010

iiJ

jijii

ii

i IMNANK

NRN

dt

dN )()1(

Immigration:• Spat dispersal• Neighbouring cell populations• Suitable settlement substrate

Competition (antagonism):• Space restriction and overgrowth• Nutrient competition including lightby all J against i

Increase (growth):• Growth in number of individuals• Growth in % areal cover

Carrying Capacity:• Physical & trophic habitat suitability•?Full capacity at optimum (restricted by A,M,I of course)

Mortality:• Day-in day-out• Extreme events

CSDMSC-FRG

Dominant Creatures (Favia, Lithothamnion)

Dominant CreatureStock (live % area)

Chagos Bank

Elevation (m)

Temperature (dgC)

WD (log10 m)

Benthic Irradiation(umol phot /m2 /s)

Total Stock (live % area)

071.23E 06.35S 20*0.01dg

Carbonate production(kg/ m2/ yr)

Carbonate thicknessAt yr 12 (m)

CSDMSC-FRG




– Other issues…







• C-FRG research plans

CSDMSC-FRG

•Focus on development of workbench module prototypes based on combined community model and cellular automata approach•Integrate with available sediment transport modules•Development of supporting knowledge base with rate data •New NSF grant proposal (and EU proposal?)•Expand group membership based on working model modules•Testing of model against modern and ancient carbonate systems

CSDMSC-FRG

CSDMSC-FRG

Lithofacies mosaic planform, Florida Bay

CA Lithofacies mosaic

Mid Cretaceous carbonate strata, central Spain – also a lithofacies mosaic?

Cross-section of a lithofacies mosaic from the computer model

12m

Distance

Distance

Dis

tanc

e

CSDMSC-FRG

Transport dictionary Aa ... Ag ... At ... Bd ...Transportable Yes Yes No No

Grain size (mm) 2mm 10mm Null NullBulk density (gcm-3) 2.1 2.2 Null Null

Grain shape?? Messy Spherical Null Null

Production dictionary Aa ... Ag ... At ... Bd ...Name Coral X Grainwithnoname Seagrass Cement

Hardness Skeletal Skeletal Soft NullFeeding habit Filter Mobile carnivore Photosynth NullTrophic Type Pred, sessile Pred, mobile Primary NullTrophic level 5 7 1 Null

Ingestion size Large Large Small NullTemp range 21-27 16-27 15-27 Null

Salinity range NullMineralogy Aragonite Calcite Aragonite Aragonite

Roughness dictionary Aa ... Ag ... At ... Bd ...Roughness Rough Smooth Rough Smooth

Form Upstanding FlatBafflement Some Lots None

Form drag 2.1

What carbonate properties should SedGrid store and how?

The hypothetical cell: [Aa 0.05; Ag 0.90; At 0.05]The hypothetical cemented cell: [Aa 0.05; Ag 0.80; At 0.05; Bd 0.10]

CSDMSC-FRG

• Ooid factory controlled by tidal currents

• Net circular hydrodynamic pattern around the shoal – spin cycle

• Combined production and transport is the key

Reeder & Rankey, 2008

CSDMSC-FRG

SIMSAFADIM - Bitzer, K., Salas, R., 2002. SIMSAFADIM: three-dimensional simulation of stratigraphic architecture and facies distribution modeling of carbonate sediments. Computers and Geosciences, 28, 1177-1192.

CARB3D - Paterson, RJ, Whitaker, FF, Smart, PL, Jones, DG & Oldham, D. 'Controls on early diagenetic overprinting in icehouse carbonates: insights from modeling hydrological zone residence times using CARB3D+', Journal of Sedimentary Research, 78 (4), (pp. 258-281), 2008. ISSN: 1527-1404 10.2110/jsr.2008.029

STRATA - STRATA: Freeware for analyzing classic stratigraphic problems. P.B. Flemings and J.P. Grotzinger http://hydro.geosc.psu.edu/Papers/Gsa_strata/gsa.html

SEDSIM - Griffiths, C. SEDSIM Stratigraphic Forward Modeling. http://sepmstrata.org/PDF-Files/Simulations/SedsimBackgroundGriffiths03.pdf. CSIRO Petroleum 2003.

SEDPAK - Strobel, S., Cannon, R., Kendall, G.St. C. C.St., Biswas, G. and Bezdek, J. 1989. Interactive (SEDPAK) simulation of clastic and carbonate sediments in shelf to basin settings. Computers & Geosciences, 15(8), 1279-1290.

CARBOCAT - Burgess (unpubl) 2009. CarboCAT. “http://csdms.colorado.edu/wiki/Model:CarboCAT”.REEFHAB - Kleypas, J. A. 1997. Modeled estimates of global reef habitat and carbonate production since the Last Glacial Maximum.

Paleoceanography, 12(4), 533-545.CYCLOPATH - Burgess, P.M. and Wright, V.P, 2003. Numerical forward modelling of carbonate platform dynamics: An evaluation of

complexity and completeness, Journal of Sedimentary research, v.73, p.637-652.SEALEX - Koelling, M., Webster, J.M., Camoin, G., Iryu, Y., Bard, E., Seard, C. (in press): SEALEX - Internal reef chronology and virtual drill

logs from a spreadsheet-based reef growth model. Global and Planetary Change. “doi: 10.1016/j.gloplacha.2008.07.011”FUZZYREEF - Parcell, W.C., 2003, Evaluating the development of Upper Jurassic reefs in the Smackover Formation, Eastern Gulf Coast,

U.S.A. through fuzzy logic computer modeling. Journal of Sedimentary Research, 73, 498-515.

the state of the art in carbonate numerical stratigraphic forward modelling

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