1. Modeling sub-seismic depositional lobes using spatial statistics
Annual Meeting 2014
Stanford Center for Reservoir Forecasting
Modeling sub-seismic depositional lobes using spatial statistics
Yinan Wang and Tapan Mukerji

2. Motivation Modeling sub-resolution lobes with surface-based method
How to find information and create rules
Comparable
Modeling
SCRF 2014

3. Tank Experiments TDB-10-1 TDB -10-1: Tulane Delta Basin, Jan 20101 m
Sediment composition:
70% 110 μm quartz sand
30% 440 μm coal sand
Constant boundary conditions
Sediment supply: L/sec
Water discharge: L/sec
Base-level rise rate: 5mm/hr
Measurement:
Topography sampled every 2 minutes along 3 strike transects.
Total run time: 2500 minutes
TDB-10-1
Wang et al., 2011
SCRF 2014

4. Interpretation Overhead photos Observable lobe elements
Classification tree
Range of Interpretation Resolution
Lobe Complex
SCRF 2014

5. Spatial Point Process
Record of complex center
SCRF 2014

6. Spatial Point Pattern Analysis
Spatial point pattern analysis is based on Ripley’s K function.
Point-to-point distances are used.
Edge Effect Correction
Spatial point pattern analysis is performed based on Ripley’s K function. The analysis uses all point-to-point distances to describe two-dimensional distribution patterns. In spatial point pattern analysis a circle of radius d is centered in each point, and the number of neighbors within the circle is counted. The
dotted lines give a confidence envelope for complete spatial randomness
Randomness envelop
SCRF 2014

7. Spatial Point Pattern Analysis
Besag’s L function：
Large Scale
Medium Scale
Small Scale
SCRF 2014

8. Comparability searching
Searching through TDB-10-1 archive to detect the lobe stacking pattern that is comparable with DB-03 (Delta Basin at St. Anthony Falls Lab).
TDB-10-1
DB-03
SCRF 2014

9. Surface-based modeling
Parent and offspring events
Surface-based modeling with rule algorithms
The Matern cluster process in which each parent has a Poisson() number of offspring, independently and uniformly distributed in a disc of radius r centred around the parent.
SCRF 2014

10. Two-Step Simulation: Parent Events
Parent events (DB-03):
Spatial location of each lobe complex that appears in the history.
Time sequence of each event
These parents then become cluster centers for a random number of "offspring" events.
SCRF 2014

11. Two-Step Simulation: Offspring events
Clustering patterns of lobe elements – medium and small scale lobes (TDB-10-1) N N
L - Size of clusters
N - Number of offspring events L L
SCRF 2014

12. Model Results Modeling the medium scale lobes
Modeling the small scale lobes
Thickness
Thickness
SCRF 2014

13. Conclusion and Future Work
Spatial point pattern analysis:
identifying the distribution of lobes at any scale of experimental strata
helping integrate the stratigraphic organization of a complex system
Future Work
Relationship between complexity and uncertainty
Rule Selection for rule-based modeling
Complexity in Surface Models
Thickness
Facies Indicator
SCRF 2014