Comparison of Pseudorandom Number Generators and Their Application for Uncertainty Estimation Using Monte Carlo Simulation

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.

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Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Solid Earth ◽

10.5194/se-9-385-2018 ◽

2018 ◽

Vol 9 (2) ◽

pp. 385-402 ◽

Cited By ~ 20

Author(s):

Evren Pakyuz-Charrier ◽

Mark Lindsay ◽

Vitaliy Ogarko ◽

Jeremie Giraud ◽

Mark Jessell

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Input Data ◽

Structural Data ◽

Uncertainty Estimation ◽

Data Sets ◽

Geological Modeling ◽

Input Uncertainty ◽

Wide Range ◽

Geological Models

Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the mining industry, and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator's parameterization) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3-D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed. The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of incorrect disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e., scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminish the occurrence of artifacts.

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Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modelling

Hydrology and Earth System Sciences ◽

10.5194/hess-7-680-2003 ◽

2003 ◽

Vol 7 (5) ◽

pp. 680-692 ◽

Cited By ~ 55

Author(s):

S.-T. Khu ◽

M. G. F. Werner

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Hybrid Genetic Algorithm ◽

Model Performance ◽

Simulation Models ◽

Uncertainty Estimation ◽

Hydrological Modelling ◽

Reliable Estimate ◽

Artificial Neural ◽

Estimation Of Uncertainties

Abstract. Monte-Carlo (MC) simulation based techniques are often applied for the estimation of uncertainties in hydrological models due to uncertain parameters. One such technique is the Generalised Likelihood Uncertainty Estimation technique (GLUE). A major disadvantage of MC is the large number of runs required to establish a reliable estimate of model uncertainties. To reduce the number of runs required, a hybrid genetic algorithm and artificial neural network, known as GAANN, is applied. In this method, GA is used to identify the area of importance and ANN is used to obtain an initial estimate of the model performance by mapping the response surface. Parameter sets which give non-behavioural model runs are discarded before running the hydrological model, effectively reducing the number of actual model runs performed. The proposed method is applied to the case of a simple two-parameter model where the exact parameters are known as well as to a widely used catchment model where the parameters are to be estimated. The results of both applications indicated that the proposed method is more efficient and effective, thereby requiring fewer model simulations than GLUE. The proposed method increased the feasibility of applying uncertainty analysis to computationally intensive simulation models. Keywords: parameters, calibration, GLUE, Monte-Carlo simulation, Genetic Algorithms, Artificial Neural Networks, hydrological modelling, Singapore

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