Hierarchical MPS-Based Three-Dimensional Geological Structure Reconstruction with Two-Dimensional Image(s)

Multiple-point statistics(MPS)is a useful approach to reconstruct three-dimensional models in the macroscopic or microscopic field.Extracting spatial features for three-dimensional reconstruction from two-dimensional training images(TIs),and characterizing non-stationary features with directional ductility are two key issues in MPS simulation.This study presents a step-wise MPS-based three-dimensional structures reconstruction algorithm with the sequential process and hierarchical strategy based on two-dimensional images.An extension method is proposed to construct three-dimensional TIs.With a sequential simulation process,an initial guess at the coarsest scale is simulated,in which hierarchical strategy is used according to the characteristics of TIs.To obtain a more refined realization,an expectation-maximization like iterative process with global optimization is implemented.A concrete example of chondrite micro-structure simulation,in which one scanning electron microscopy(SEM)image of the Heyetang meteorite is used as TI,shows that the presented algorithm can simulate complex non-stationary structures.