Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field

Stratigraphic (or lithological) uncertainty refers to the uncertainty of boundaries between different soil layers and lithological units, which has received increasing attention in geotechnical engineering. In this paper, an effective stochastic geological modeling framework is proposed based on Markov random field theory, which is conditional on site investigation data, such as observations of soil types from ground surface, borehole logs, and strata orientation from geophysical tests. The proposed modeling method is capable of accounting for the inherent heterogeneous and anisotropic characteristics of geological structure. In this method, two modeling approaches are introduced to simulate subsurface geological structures to accommodate different confidence levels on geological structure type (i.e., layered vs. others). The sensitivity analysis for two modeling approaches is conducted to reveal the influence of mesh density and the model parameter on the simulation results. Illustrative examples using borehole data are presented to elucidate the ability to quantify the geological structure uncertainty. Furthermore, the applicability of two modeling approaches and the behavior of the proposed model under different model parameters are discussed in detail. Finally, Bayesian inferential framework is introduced to allow for the estimation of the posterior distribution of model parameter, when additional or subsequent borehole information becomes available. Practical guidance of using the proposed stochastic geological modeling technique for engineering practice is given.