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Discussion papers
https://doi.org/10.5194/se-2019-78
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-2019-78
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Method article 10 May 2019

Method article | 10 May 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Solid Earth (SE).

Topological Analysis in Monte Carlo Simulation for Uncertainty Estimation

Evren Pakyuz-Charrier1,3, Mark Jessell1, Jérémie Giraud1, Mark Lindsay1, and Vitaliy Ogarko2 Evren Pakyuz-Charrier et al.
  • 1Centre for Exploration Targeting, The University of Western Australia, 35 Stirling Hwy, Crawley WA 6009 Australia
  • 2International Centre for Radio Astronomy Research, The University of Western Australia, 35 Stirling Hwy, Crawley WA 6009 Australia
  • 3Intrepid Geophysics, 3 Male Street, Brighton VIC 3186 Australia

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for Uncertainty Estimation (MCUE) method. MCUE is a type of Bayesian Monte Carlo aimed at input data uncertainty propagation in implicit 3D geological modeling. In the Monte Carlo process, a series of statistically plausible models are built from the input data set which uncertainty is to be propagated to a final probabilistic geological model (PGM) or uncertainty index model (UIM).

Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUE. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets’ variability and plausible model’s variability. Non-linearity is shown to arise from the effect of the geometrical ruleset on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces geological incompatibility and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUE is introduced. Boolean topological signatures recording lithological units’ adjacency are used as n-dimensional points to be considered individually or clustered using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data.

Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the PGMs and UIMs.

Evren Pakyuz-Charrier et al.
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Evren Pakyuz-Charrier et al.
Data sets

CarloTopo synthetic GeoModeller model and relevant MCUE outputs E. Pakyuz-Charrier https://doi.org/10.5281/zenodo.1202314

Evren Pakyuz-Charrier et al.
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Short summary
This paper improves the Monte Carlo simulation for Uncertainty Estimation (MCUE) method applied to 3D geological modelling. Significant heterogeneity is observed in the model suite. The study demonstrates that such heterogeneity arises from piecewise non-linearity inherent to 3D geological models and contraindicates use of global uncertainty estimation methods. Topological clustering driven uncertainty estimation is proposed as a demonstrated alternative to address plausible model heterogeneity.
This paper improves the Monte Carlo simulation for Uncertainty Estimation (MCUE) method applied...
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