Uncertainty assessment of nonstationary data

地质统计学使用统计技术来评估地质矿床的资源或储量。最近，这些技术在了解稀疏采样的矿床、油藏、二氧化碳封存地点、污染区域和许多其他随地质矿床而来的空间分布现象的不确定性方面越来越受欢迎。这项工作涉及技术的发展，以更好地模拟具有复杂非平稳地质特征的矿床。最近的研究探索了在采矿或石油研究的背景下考虑非平稳特征的建模方法；典型特征包括河道、脉体、曲线地层、背斜、卷前沉积等。建议的工作是将这些非平稳技术扩展到包括环境数据，特别是时空数据。研究计划有三个方面：(1)推广非平稳空间建模技术，以包括非平稳时空数据的情况；(2)开发技术和工具来推断非平稳技术所需的复杂输入统计；(3)将基于对象的模型条件化为硬数据和软数据，以生成条件非平稳模型。

Geostatistics uses statistical techniques to assess the resources or reserves for a geological deposit. Lately, these techniques have become increasingly popular for understanding the uncertainty in sparsely sampled mineral deposits, petroleum reservoirs, CO2 sequestration sites, contaminated areas and many other spatially distributed phenomenon that follow geological deposits. This work relates to the development of techniques to better model deposits that exhibit complex nonstationary geological features. Recent research has explored modeling methodologies that consider nonstationary features in the context of mining or petroleum studies; typical features include channels, veins, curvilinear strata, anticlines, roll front deposits, etc. The proposed work is to expand these nonstationary techniques to include environmental data, specifically spatial-temporal data. There are three aspects of research planned (1) generalize nonstationary spatial modeling techniques to include cases of nonstationary spatial-temporal data and (2) develop techniques and tools to infer the complex input statistics required for nonstationary techniques and (3) condition object based models to hard and soft data to generate conditioned nonstationary models. The long term objective of this program is to develop and mature methodologies to deal with modeling spatial or spatial-temporal phenomenon that are nonstationary. Determining when nonstationarity in the mean (trend), covariance (locally varying anisotropy) and higher orders (cumulants, objects and multiple point statistics) is also an important focus of the proposed work. A variety of techniques are explored with in this work including cumulants, non-Euclidean distances and object based modeling.