Multiple-point geostatistical simulation based on conditional conduction probability

Multiple-point geostatistical (MPS) simulation can enhance extraction and synthesis of various information in earth and environmental sciences. In particular, it is able to characterize the complex spatial structures of heterogeneous phenomena more accurately. In this paper, we propose a new MPS simulation method based on conditional conduction probability, namely the CCPSIM algorithm, to mitigate the uncertainty of MPS realizations. In CCPSIM, the simulated nodes will be treated differently from the original samples. The probability distributions of the simulated nodes will be used as prior conditions to calculate the probability distributions of the following nodes, and the prior conditions will be conducted during the whole simulation process. 2D and 3D synthetic tests are used to verify the applicability and advantages of CCPSIM. The results confirm that CCPSIM is able to reproduce spatial patterns of heterogeneous structures presented in categorical training images, and it reduces the uncertainty of the MPS realizations caused by the undistinguished using of the original known samples and the simulated uncertain values.