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

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

Tank Experiments TDB-10-1 TDB -10-1: Tulane Delta Basin, Jan 2010 1 m Sediment composition: 70% 110 μm quartz sand 30% 440 μm coal sand Constant boundary conditions Sediment supply: 0.011 L/sec Water discharge: 0.451 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

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

Spatial Point Process Record of complex center SCRF 2014

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

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

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

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

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

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

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

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