1. Stanford Center of Reservoir Forecasting 26th Annual Meeting
Relating stratigraphic architecture to morphodynamic processes
- Implications from a dynamic model of a channelized depositional system
Yinan Wang and Tapan Mukerji

2. SCRF 26th Annual Meeting
Talk Outline

3. SCRF 26th Annual Meeting
Seismic imaging primary means for studying subsurface systems.
Despite high quality, details of heterogeneity are not resolved.
How to predict spatial features of sub-resolution depositional bodies?

4. SCRF 26th Annual Meeting As an alternative, Process-based models
Pros: a highly realistic representation of the subsurface
Cons: computation power and time
As an alternative,
Cell-based/rule-based models：Zoltán Sylvester et al., 2010;
Douglas Jerolmack and Chris Paola, 2007;
Surface-based and objected-based models：Alejandro Leiva,
2009; Antoine Bertoncello, 2010；

5. SCRF 26th Annual Meeting
Talk Outline

6. SCRF 26th Annual Meeting
In a channel system，what processes control the spatial distribution of channel bodies？
Model of channel clustering 1.
Sensitivity of water flow to topography gradient 2.
Avulsion – change of channel courses
Two scales
Model of avulsion
Slingerland and Smith, 2004

7. SCRF 26th Annual Meeting Model Development
Model prototype proposed by Jerlmack and Paola, 2007
Cell Size: taken to be larger than channel width (100m)
Model Domain: 39*39 cells
Boundary Conditions: Reflecting boundaries on the left and right sides
Plan-view channel system in the model

8. SCRF 26th Annual Meeting Model Development Model inputs:
sediment discharge (Qs)
water discharge(Qw)
subsidence rate
avulsion threshold
floodplain deposition rate
initial system slope
initial topographic roughness

9. SCRF 26th Annual Meeting Flow Path Selection
Sensitivity of water flow to topography
Path searching on unvisited floodplain surface
Yellow cells indicate cells occupied by active flow.
Blue line indicates active flow.
Elevation is in gray scale.
Five cells are detected for lowest elevation.

10. SCRF 26th Annual Meeting Flow Path Selection Channel Reoccupation
Yellow cells indicate cells occupied by active flow.
Orange cells indicate cells reoccupied by flow.
Blue line indicates active flow.
Dashed blue line indicates an old channel course.
Elevation is in gray scale.
Path searching on visited floodplain surface

11. Deposition and erosion along the flow path
SCRF 26th Annual Meeting
Deposition and erosion along the flow path
Diffusion Equation:
k - diffusion coefficient; η - elevation 1 2 3

12. SCRF 26th Annual Meeting Avulsion h – channel depth
Superelevation in the model
Superelevation
Jerolmack, 2007
ηbottom – elevation of channel bed
ηtop – elevation of levee crest
vfp – floodplain deposition rate
h – channel depth
Superelevation of levee crests above attendant floodplain are 0.6 to 1.1 times channel flow depth for the Guadalope-Matarranya and Wasatch systems (Morhig et al., 2000).
h – channel depth

13. = + SCRF 26th Annual Meeting Model Avulsion Topography-driven
path searching
Model
Avulsion
Evolution of the entire floodplain
Evolution of channel system
Qs=0.01 m^3/s ;
Qw=20 m^3/s ;
System slope = ;
Subsidence = 0.5 m/yr ;
Avulsion threshold = 1 m ;
Floodplain deposition rate = m/yr ;
Topography Roughness =
N(0,0.1)

14. SCRF 26th Annual Meeting
Talk Outline

15. SCRF 26th Annual Meeting Sensitivity Analysis Monitored model inputs:
Monitored model outputs:
sediment discharge
water discharge
avulsion threshold
floodplain deposition rate
initial topographic roughness
initial system slope
subsidence rate.
compensation index
channel sinuosity
grading interval
avulsion frequency,
local avulsion frequency
regional avulsion frequency

16. SCRF 26th Annual Meeting
Sinuosity decays through time. The inflection point of sinuosity plot indicate the grading interval. Beyond this interval, slope system evolves into equilibrium state.

17. SCRF 26th Annual Meeting
- Standard deviation of sedimentation to subsidence ratio

18. SCRF 26th Annual Meeting Compensation Index k clustering random
Power law exponent tells us about the randomness, evenness, or unevenness of basin filling.
0.5 = Random filling
1.0 = Perfect compensation
0.0 = Perfect “anti” compensation (clustering)
101
clustering
k = 0
100
k = 0.5
random
σss
k = 1
10-1
σss = aT-k
compensation
10-2
10-3
100
101
102
103
Measurement Window (distance or time)

19. SCRF 26th Annual Meeting Plackett-Burman Experimental Design
We investigated the control of parameters by 8 combinations

20. SCRF 26th Annual Meeting Spatial distribution of avulsion occurences
Conceptual illustration of avulsion location

21. SCRF 26th Annual Meeting
Talk Outline

22. SCRF 26th Annual Meeting Summary Future Work
Cell-based models can be simplified an alternative to full physics to reduce computation.
Sensitivity analysis of model parameters and responses.
Slope and Qs
Stratigraphic organization, Grading interval Qw
Channel sinuosity
Superelevation
Regional avulsion frequency
Future Work
Use as a forward model in a stratigraphic inversion scheme.
Feedback and advice welcome!