Topological analysis in Monte Carlo simulation for uncertainty propagation

Topological analysis in Monte Carlo simulation for uncertainty propagation
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不确定性传播蒙特卡罗模拟中的拓扑分析

DOI：
10.5194/se-10-1663-2019
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发表时间：
2019
期刊：
Solid Earth
影响因子：
3.4
通讯作者：
V. Ogarko
V. Ogarko
中科院分区：
地球科学2区
文献类型：
--
作者：
Evren Pakyuz;M. Jessell;J. Giraud;M. Lindsay;V. Ogarko

文献摘要

被引文献

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抽象的。本文提出并论证了改进 蒙特卡罗模拟不确定性传播（MCUP）方法。 MCUP 是一个 针对输入数据不确定性的贝叶斯蒙特卡罗方法类型 隐式 3-D 地质建模中的传播。在蒙特卡罗过程中， 根据输入数据集构建一系列统计上合理的模型 其中不确定性将被传播到最终的概率地质 模型或不确定性指数模型。在合理的拓扑方面观察到显着差异 作为 MCUP 中的中间步骤生成的模型套件。这些 差异被解释为类似于群体异质性。的 这种异质性的根源可追溯到非线性关系 合理的数据集的可变性和合理的模型的可变性之间。 非线性主要是由几何效应引起的 模型构建的规则集将岩性连续性转变为 接口变成不连续的分段接口。合理的模型异质性 引起拓扑异质性并挑战基本假设 全球不确定性估计所依赖的同质性。为了解决这个问题 问题，一种应用于合理模型的拓扑分析方法 介绍了 MCUP 中的套件。布尔拓扑签名记录 岩性单元邻接被用作n维点 使用基于密度的空间单独考虑或聚类 具有噪声的应用程序聚类 (DBSCAN) 算法。拟议的 该方法在两个具有不同水平的具有挑战性的合成示例上进行了测试 对结构输入数据的置信度。结果表明拓扑特征构成了强大的 判别式来解决合理的模型异质性。基本拓扑 签名似乎是结构行为的可靠指标 合理的模型并提供有用的地质见解。而且， 发现忽略异质性不利于准确性和 概率地质模型和不确定性指数的相关性 模型。 亮点。 蒙特卡罗不确定性传播 (MCUP) 方法通常会产生 拓扑上不同的合理模型。可以使用拓扑特征来区分合理的模型。可以获得拓扑相似的概率地质模型 通过拓扑签名聚类。
Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. 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 mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity 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 MCUP is introduced. Boolean topological signatures recording lithological unit 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 probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.