Sequential Simulation of a Conditional Boolean Model

• 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
• DOI: 10.1007/s11004-021-09977-3

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.