The plurigaussian model is used in mining engineering, oil reservoir characterization, hydrology and environmental sciences to simulate the layout of geological domains in the subsurface, while reproducing their spatial continuity and dependence relationships. However, this model is well-established only in the stationary case, when the spatial distribution of the domains is homogeneous in space, and suffers from theoretical and practical impediments in the non-stationary case. To overcome these limitations, this paper proposes extending the model to the truncation of intrinsic random fields of order k with Gaussian generalized increments, which allows reproducing spatial trends in the distribution of the geological domains. Methodological tools and algorithms are presented to infer the model parameters and to construct realizations of the geological domains conditioned to existing data. The proposal is illustrated with the simulation of rock type domains in an ore deposit in order to demonstrate its applicability. Despite the limited number of conditioning data, the results show a remarkable agreement between the simulated domains and the lithological model interpreted by geologists, while the conventional stationary plurigaussian model turns out to be unsuccessful.
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This research was funded by the Chilean Commission for Scientific and Technological Research, through projects CONICYT/FONDECYT/REGULAR/No 1130085 and CONICYT PIA Anillo ACT1407. The authors also acknowledge the support from Mr. Claudio Martínez from Codelco-Chile (Andina Division), who provided the data set used in this work.
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Madani, N., Emery, X. Plurigaussian modeling of geological domains based on the truncation of non-stationary Gaussian random fields. Stoch Environ Res Risk Assess 31, 893–913 (2017). https://doi.org/10.1007/s00477-016-1365-9
- Geological domaining
- Subsurface heterogeneity
- Intrinsic random fields of order k
- Generalized covariance function