Markov based transition probability geostatistics in groundwater applications: assumptions and limitations

Abstract

Markov based transition probability geostatistics (MTPG) for categorical variables, as implemented by the methodological framework introduced by Carle and Fogg (Math Geol 29(7):891–918, 1997) and extended thereafter, have been extensively applied for the three-dimensional (3D) statistical representation of hydrofacies in real-world aquifers, and the conditional simulation of 3D lithologies for groundwater flow and transport simulations. While conceptually simple and easy to implement, conditional simulation using the MTPG approach is not limitation free. However, to the best of our knowledge, there is no study that raises such concerns in the light of theoretical arguments and numerical findings. That said, the purpose of this study is twofold: (1) present a brief and coherent overview of the basic theory, fundamental assumptions, and limitations of the MTPG methodological framework, and (2) assess its capabilities on the basis of a simple two-dimensional test-case, using large ensembles of stochastic realizations. Contrary to real-world 3D aquifers, where the actual geology is unknown, and the quality of the simulations can be assessed solely on the basis of semi-quantitative arguments using properly selected sets of stochastic realizations, test-cases allow for direct quantitative assessments based on the application of statistical measures to large ensembles of synthetic realizations. Our analysis and obtained results show that stochastic modeling of actual geologies using the MTPG approach of Carle and Fogg (1997), is characterized by simplifying assumptions and theoretical limitations, with the simulated random fields exhibiting statistical structures that strongly depend on the problem under consideration and the modeling assumptions made, leading to increased epistemic uncertainties in the obtained results.

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