Sequential Simulation of a Conditional Boolean Model

Simulations of object-based models are widely used in various fields of geoscience to represent subsurface heterogeneities. A prototype of such a model is the Boolean model. Based on the stability and decomposition properties, a novel algorithm is proposed to simulate Boolean models, stationary or n...

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Published in:Mathematical geosciences Vol. 54; no. 2; pp. 389 - 411
Main Authors: Troncoso, Alan, Freulon, Xavier, Lantuéjoul, Christian
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Boolean
Boolean algebra
Chemistry and Earth Sciences
Computer Science
Conditioning
Data points
Earth and Environmental Science
Earth Sciences
Environmental Engineering
Environmental Sciences
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical models
Modelling
Physics
Prototypes
Simulation
Statistics
Statistics for Engineering
Statistics Theory
Stochastic geometry
Particle filtering
Poisson process
Geostatistics
Importance sampling
ISSN:1874-8961, 1874-8953
Online Access:Get full text
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Abstract Simulations of object-based models are widely used in various fields of geoscience to represent subsurface heterogeneities. A prototype of such a model is the Boolean model. Based on the stability and decomposition properties, a novel algorithm is proposed to simulate Boolean models, stationary or not, subject to foreground and background point conditions. This algorithm amounts to simulating two independent Boolean models, namely an avoiding Boolean model made of objects that avoid all conditioning data points and a hitting Boolean model, the objects of which hit one or several foreground conditioning data points. The first model is simulated using thinning techniques, and the second model is simulated by particle filtering. Overall, the algorithm produces exact simulations. It is very fast and easy to implement.
AbstractList Simulations of object-based models are widely used in various fields of geoscience to represent subsurface heterogeneities. A prototype of such a model is the Boolean model. Based on the stability and decomposition properties, a novel algorithm is proposed to simulate Boolean models, stationary or not, subject to foreground and background point conditions. This algorithm amounts to simulating two independent Boolean models, namely an avoiding Boolean model made of objects that avoid all conditioning data points and a hitting Boolean model, the objects of which hit one or several foreground conditioning data points. The first model is simulated using thinning techniques, and the second model is simulated by particle filtering. Overall, the algorithm produces exact simulations. It is very fast and easy to implement.
Author Lantuéjoul, Christian
Troncoso, Alan
Freulon, Xavier
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  givenname: Xavier
  surname: Freulon
  fullname: Freulon, Xavier
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  givenname: Christian
  surname: Lantuéjoul
  fullname: Lantuéjoul, Christian
  organization: Centre de Géosciences, MinesParisTech
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CitedBy_id crossref_primary_10_1016_j_geoen_2024_213440
crossref_primary_10_1007_s11053_024_10398_2
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crossref_primary_10_1007_s00477_025_03005_0
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International Association for Mathematical Geosciences 2021.
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Keywords Stochastic geometry
Particle filtering
Poisson process
Geostatistics
Importance sampling
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Snippet Simulations of object-based models are widely used in various fields of geoscience to represent subsurface heterogeneities. A prototype of such a model is the...
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SubjectTerms Algorithms
Boolean
Boolean algebra
Chemistry and Earth Sciences
Computer Science
Conditioning
Data points
Earth and Environmental Science
Earth Sciences
Environmental Engineering
Environmental Sciences
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical models
Modelling
Physics
Prototypes
Simulation
Statistics
Statistics for Engineering
Statistics Theory
Title Sequential Simulation of a Conditional Boolean Model
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