“…• Three-dimensional (3-D) transition probability models of spatial variability are readily developed from 1-D Markov chains along principal stratigraphic directions (Carle and Fogg, 1997). • Continuous-lag Markov chains have been found suitable for 3-D modeling of vertical and lateral spatial transitioning among geo-or hydro-facies (Carle 1996;Carle and Fogg, 1996;Carle and Fogg, 1997;Carle et al, 1998;Fogg et al, 1998;Zhang and Fogg, 2003;Proce et al, 2004;Ye and Khaleel, 2008;Engdahl et al, 2010a;Bianchi et al, 2011;Pozdniakov et al, 2012;Purkis et al, 2012;Bakshevskaia and Pozdniakov, 2016;Krage et al, 2016;Sartore et al, 2016;Zhu et al, 2016a;Meirovitz et al, 2017;Guo et al, 2019b).…”