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

SCRF 26th Annual Meeting Talk Outline

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?

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；

SCRF 26th Annual Meeting Talk Outline

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

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

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

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.

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

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

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

= + 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 = 0.0007 ; Subsidence = 0.5 m/yr ; Avulsion threshold = 1 m ; Floodplain deposition rate = 0.0625 m/yr ; Topography Roughness = N(0,0.1)

SCRF 26th Annual Meeting Talk Outline

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

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.

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

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)

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

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

SCRF 26th Annual Meeting Talk Outline

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!