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Sequential Simulation with Complex Training Images using Search Tree Partitioning
Alexandre BoucherDept. of Environmental Earth System Science
Stanford University
SCRF 21st ANNUAL MEETINGMay 8, 2008
Two SNESIM Drawbacks
Size of the search tree• Function of TI, template size and # of categories
• Controls the simulation speed
Unrealistic training image• Requirements of training image do not conform to analogs
• Uses a single complex training image
• Affects pattern reproduction in an unknown manner
• Difficult to know if probability fields are consistent with TI
Current Practice : Probability Field
Encourages some classes at certain locations by providing pre-defined high local probability of occurrence
Current Practice : Regions Simulation
• Awkward from modeler perspective
• Possible incompatibility between training images
• Does not refer to a unique geological concept
Divide simulation grid into regions and simulate each region with a different training image
Search Tree PartitioningPartitioning TI into partition classes such that their associated patterns are
• homogenous
• can be efficiently stored in a search tree
Building imbricated search tree
1. Process the TI with spatial filters that respond to critical patterns
2. Transform these filter scores into partition classes
– Dual training image : Categories and the partition classes
3. Generate a vector of imbricated search trees
Simulation
1. Simulate the partition classes
2. Simulate the categories
– The partition classes act as a look-up table to retrieve the search tree.
– Adequate imbrication of the search trees ensure patterns reproduction
FracturesFractures with varying orientation
Simulation with a global search tree
Two options : 1 – Deconvolution of the patterns into regions2 – Generate partition classes that reflect the patterns
The trends are not reproduced
Generation of Partition ClassesSobel filters to detect the lineation direction
East-West gradient North-South gradient Average angle
Average angles clustered into5 partition classes
A search tree is build for each partition class
Patterns Recorded by the Paritition Classes
Build one search tree per partition : 5 small imbricated trees
Partition #1 Partition #2 Partition #5
Unconditional simulation associated with each search tree:
#1 #2 #3 #4 #5
Simulation with Search Tree Partitioning
1. Simulation of the angles using direct sequential simulation with a trend
2. Clustering the simulated angles into partition classes
3. Simulation of the fractures
Multiple-Facies Simulation
7 facies simulation
Three geologically meaningful partition classes
TI courtesy of Chevron
Grid upscaled: block size 5x5x5
Simulating the Partition Classes
1. Thickness for each layer is simulated using a 1-D direct sequential simulation
2. Simulation
Conditioning with Search Tree Partitioning
Building imbricated search tree1. Forward transform TI into ancillary data
2. Cluster simulated ancillary data into partition classes
– Dual training image : Categories and partition classes
3. Generate vector of imbricated search trees; one tree per partition class
Simulation1. Partition the actual ancillary data into partition classes
2. Simulate the categories
– Partition classes act as a look-up table to retrieve the search tree
– Adequate imbrication of search trees on the grid ensure patterns reproduction
Partition classes derived from ancillary data and used for
constraining/soft conditioning
Reference facies Layer 7 Reference facies Layer 8
ShaleConglomerateWater SandGas Sand
Constraining to Seismic Attributes
L. Stright
P-Im
peda
nce
S-Im
peda
nce
Vp/
Vs
Coarse Scale Seismic AttributesReference Layer 7 Test Case Layer 8
k-means
Classification from vector quantization
L. Stright
Reference facies Layer 8
ShaleConglomerateWater SandGas Sand
Partition Class Layer 8
Realization #2Realization #1
Simulations with search tree partitioning
Coarse Data Constrained Simulations
L. Stright
Downscaling Directional Continuity
No connection
E-W connection only
N-S connection only
N-S and E-W connection only
Extract directional connectivity in block of size 10x10
Upscaled connectivity index
E-W ConnectivityN-S Connectivity
Existence of a continuous path across the coarse pixel
Accuracy Assessment
Constraining directional connectivity index
Simulation #1 Simulation #2
0.340.610.570.770.62STP
0.230.210.150.680.39Tau-model
0.080.220.200.480.29No constraint
Global No EW NS EW and NSAccuracy assesment:
Accuracy of connection:
0.70.590.53
STPTau-modelNo constrain
Lessons Learnt
Defining partition classes• number of partition classes matters• must relate to the patterns (smart clustering)• can be simulated
Simulating partition classes• clustered from continuous simulation• simulated directly• choose the most suitable simulation algorithm
Advantages
Adds local information without distorting TI-derived ccdf
Improves on region approach by
- requiring only one training image
- implicitly modeling transitions between regions
Facilitates hierarchical framework
Provides soft conditioning to coarse scale measurements
Dichotomy : simulation - modeling
Modelers
• Focus at finding an analog
• Fewer compromises for algorithmic requirements
Geostatisticians
• Access to a larger set of training images
• Better visualization of the sought-after patterns
Efficient use of their respective strengths
Thank You
Questions?
Regions Approach
The transitions betweens regions are never modeled
A N-S fractures training images is rotated to the mean fractures angles for eacg partition classes