Comparing a Fixed-Path Markov Chain Geostatistical Algorithm with Sequential Indicator Simulation in Categorical Variable Simulation from Regular Samples

Abstract

The Markov chain random field (MCRF) theory provided the theoretical support for a new, nonlinear Markov chain geostatistic. This study compares a MCRF-based netting-and-mesh-filling (NMF) algorithm with indicator kriging simulation algorithms and demonstrates their differences in simulating categorical variables from regular samples. The MCRF-NMF algorithm and indicator kriging simulation algorithms—SIS-SIK (sequential indicator simulation with simple indicator kriging) and SIS-OIK (SIS with ordinary indicator kriging)—are all applied to the same datasets. Results show that: (1) MCRF-NMF generates higher simulation accuracy in realizations and lower spatial uncertainties than SIS-OIK does; for a medium dataset, the former achieves a relative increase of 13.2% in simulation accuracy of simulated realizations; (2) MCRF-NMF obeys interclass relationships in simulated maps but SIS-SIK and SIS-OIK do not; and (3) MCRF-NMF generates polygons in simulated realizations, but SIS-SIK and SIS-OIK typically generate dispersed patterns. An imperfection with MCRF-NMF is that simulated polygons in realizations exhibit rough boundaries. However, optimal results based on maximum occurrence probabilities provide an attractive prediction map. Although MCRF-NMF has some limitations as a fixed-path algorithm, its advantage for improving simulation accuracy of simulated realizations makes it valuable.