摘要：This paper proposes and demonstrates improvements for theMonte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is atype of Bayesian Monte Carlo method aimed at input data uncertaintypropagation in implicit 3-D geological modeling. In the Monte Carlo process,a series of statistically plausible models is built from the input datasetof which uncertainty is to be propagated to a final probabilistic geologicalmodel or uncertainty index model.Significant differences in terms of topology are observed in the plausiblemodel suite that is generated as an intermediary step in MCUP. Thesedifferences are interpreted as analogous to population heterogeneity. Thesource of this heterogeneity is traced to be the non-linear relationshipbetween plausible datasets' variability and plausible model's variability.Non-linearity is shown to mainly arise from the effect of the geometricalrule set on model building which transforms lithological continuousinterfaces into discontinuous piecewise ones. Plausible model heterogeneityinduces topological heterogeneity and challenges the underlying assumptionof homogeneity which global uncertainty estimates rely on. To address thisissue, a method for topological analysis applied to the plausible modelsuite in MCUP is introduced. Boolean topological signatures recordinglithological unit adjacency are used as n-dimensional points to beconsidered individually or clustered using the density-based spatialclustering of applications with noise (DBSCAN) algorithm. The proposedmethod is tested on two challenging synthetic examples with varying levelsof confidence in the structural input data.Results indicate that topological signatures constitute a powerfuldiscriminant to address plausible model heterogeneity. Basic topologicalsignatures appear to be a reliable indicator of the structural behavior ofthe plausible models and provide useful geological insights. Moreover,ignoring heterogeneity was found to be detrimental to the accuracy andrelevance of the probabilistic geological models and uncertainty indexmodels.Highlights. Monte Carlo uncertainty propagation (MCUP) methods often producetopologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtainedthrough topological signature clustering. Downloadandlinks Article (PDF, 9443 KB) How to cite Back to top top How to cite. Pakyuz-Charrier, E., Jessell, M., Giraud, J., Lindsay, M., and Ogarko, V.: Topological analysis in Monte Carlo simulation for uncertainty propagation, Solid Earth, 10, 1663–1684, https://doi.org/10.5194/se-10-1663-2019, 2019. 1 Introduction Back to toptop Input data uncertainty propagation is an essential part of risk-aware 3-Dgeological modeling (Schweizer et al., 2017; Wang et al., 2017; Nearing etal., 2016; Aguilar et al., 2018; Mery et al., 2017; Dang et al., 2017; Lark etal., 2013; Carter et al., 2006). Accurate quantification of geometricaluncertainty is indeed key to determine the degree of confidence one can putinto a model. How reliable a 3-D geological model is and how this reliabilityvaries in space are indispensable data to seek improvement of said model.Monte Carlo uncertainty propagation (MCUP) algorithms have recently beenproposed to tackle this issue (de la Varga and Wellmann,2016; Pakyuz-Charrier et al., 2018a). MCUP methods (Fig. 1) aim topropagate the measurement uncertainty of structural input data (interfacepoints, foliations, fold axes) through implicit 3-D geological modelingengines to produce probabilistic geological models and uncertainty indexmodels. To do so, each structural input datum is replaced by a probabilitydistribution (thought to best represent its measurement uncertainty) called adisturbance distribution (Pakyuz-Charrier et al., 2018a).Disturbance distributions are then sampled using Markov-chain Monte Carlo(Cherpeau et al., 2010) or random methods to generate alternativestatistically plausible datasets. Plausible datasets can then be used tobuild a suite of plausible 3-D geological models which may be merged intoprobabilistic geological models or uncertainty index models. A probabilisticgeological model quantifies the observed lithological frequencies in eachcell in the form of a categorical distribution. An uncertainty index modelexpresses the dispersion of these categorical distributions. Recent works(Thiele et al., 2016a, b; Pellerin et al., 2015) havedemonstrated that the plausible 3-D geological model suite may display greatgeometrical variability to the point of making some plausible modelstopologically distinct from one another. Plausible model heterogeneity isdamaging to the relevance of MCUP because the probabilistic geologicalmodels and uncertainty index models implicitly assume plausible modelhomogeneity.Figure 1MCUP simplified procedure, modified from Pakyuz-Charrier et al. (2018).
