Conditional Simulation of Hydrofacies Architecture: A Transition Probability Approach

Abstract

In many hydrogeological investigations of groundwater flow and contaminant transport, considerable uncertainty arises from unknown physical heterogeneity of the aquifer system materials. Indicator geostatistics may offer tools for stochastic simulation of heterogeneity, however, existing methods were not designed with hydrogeological problems in mind. Typically, hydrogeological data are vastly undersampled in lateral directions. Subsequently, geostatistical analyses must rely, in part, on geologic interpretation to yield geologically plausible results. Compared to traditional variogram-based approaches, the transition probability/Markov approach introduced herein more rigorously considers spatial cross-correlations (juxtapositional tendencies), yet is more conducive to integration of geologic interpretation. Three-dimensional (3-D) Markov chains are introduced as a conceptually simple yet theoretically powerful model of spatial variability, supported in theory and pract ice by numerous prior 1-D geologic applications to vertical sedimentary successions. The geostatistical conditional simulation algorithms of sequential indicator simulation and simulated quenching (zero-temperature annealing) are modified to include consideration for all spatial cross-correlations. "Nonstationarities" related to anisotropy directions, proportions of depositional units and commingling depositional systems also can be considered. Example applications are given for alluvial fan and fluvial depositional systems in California in portions of the Livermore Valley, Kings River alluvial fan and Salinas Valley