Directional hydrostratigraphic units simulation using MCP algorithm
Understanding the geological uncertainty of hydrostratigraphic models is important for risk assessment in hydrogeology. An important feature of sedimentary deposits is the directional ordering of hydrostratigraphic units (HSU). Geostatistical simulation methods propose efficient algorithm for assessing HSU uncertainty. Among different geostatistical methods to simulate categorical data, Bayesian maximum entropy method (BME) and its simplified version Markov-type categorical prediction (MCP) present interesting features. In particular, the zero-forcing property of BME and MCP can provide a valuable constrain on directional properties. We illustrate the ability of MCP to simulate vertically ordered units. A regional hydrostratigraphic system with 11 HSU and different abundances is used. The transitional deterministic model of this system presents lateral variations and vertical ordering. The set of 66 (11 × 12/2) bivariate probability functions is directly calculated on the deterministic model with fast Fourier transform. Despite the trends present in the deterministic model, MCP is unbiased for the HSU proportions in the non-conditional case. In the conditional cases, MCP proved robust to datasets over-representing some HSU. The inter-realizations variability is shown to closely follow the amount and quality of data provided. Our results with different conditioning datasets show that MCP replicates adequately the directional units arrangement. Thus, MCP appears to be a practical method for generating stochastic models in a 3D hydrostratigraphic context.
KeywordsBayesian maximum entropy (BME) Markov-type categorical prediction (MCP) Bivariate probabilities Hydrostratigraphic units (HSU) Units ordering Categorical simulation Model uncertainty
Constructive comments from two anonymous reviewers were helpful improving the manuscript. In particular, one reviewer suggested to us the idea of comparing MCP to Gaussian simulator as in Sect. 2.4. The authors thank A. Bolduc, Y. Michaud and H. Russell for their support from the Groundwater Geoscience Program, Geological Survey of Canada, Natural Resources Canada. Research was partly financed by NSERC (RGPIN-2015-06653).
- Bajc A, Mulligan R, Rainsford D, Webb J (2015) Results of 2011–13 overburden drilling programs in the southern part of the County of Simcoe, south-central Ontario; Ontario Geological Survey, Miscellaneous Release-Data 324. Techical reportGoogle Scholar
- Christakos G (1992) Random field models in earth sciences. Academic Press, San Diego. https://doi.org/10.1016/B978-0-12-174230-0.50005-6 Google Scholar
- D’Or D (2003) Spatial prediction of soil properties, the Bayesian Maximum Entropy approach. Ph.D. thesis, Université catholique de LouvainGoogle Scholar
- Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86. http://www.jstor.org/stable/2236703
- Ortiz JM (2003) Characterization of high order correlation for enhanced indicator simulation. Ph.D. thesis, University of Alberta, Edmonton, Alberta, CanadaGoogle Scholar