New geostatistical techniques: Non-Gaussian, well conditioned simulation approaches

环境变量在空间和/或时间上往往是高度可变的。它们的特征需要地质统计学方法。目前的大多数方法都依赖于或隐式地依赖于多高斯假设。然而，潜在的确定性过程往往导致非高斯结构。传统上数量有限的直接观测越来越多地得到遥感和地球物理数据等间接测量的补充。间接数据通常与目标变量呈非线性关系，对应于时空积分。这些数据往往包括地质统计框架内的大量数据，处理这些数据需要适当的模型和相应的数值技术。本研究的目的是发展新的地质统计条件模拟方法，既能处理不同的数据来源，又能反映非高斯依赖性。排名统计和基于公式的方法构成了建议技术的基础。与基于秩的方法相关的问题定义了观测的代表性，以及条件场的数值有效模拟，是提出的研究的重点。这些方法将与昆士兰大学（澳大利亚）的研究人员共同开发。研究了该方法在地表水文和地下地球物理领域中的应用。所需资金应仅用于支付合作伙伴的旅费。

Environmental variables are often highly variable in space and/or in time. Their characterization requires geostatistical methods. Most of the present methods rely ex- or implicitly on a multi-Gaussian assumption. However the underlying deterministic processes often lead to non-Gaussian structures. The traditional limited number of direct observations is more and more complemented by indirect measurements such as remote sensing and geophysical data. The indirect data are usually non-linearly related to the target variable and correspond to space time integrals. The treatment of these data, often comprising a huge amount of data in a geostatistical framework, requires appropriate models and corresponding numerical techniques. The purpose of this research is to develop new geostatistical conditional simulation methods, which can cope with different sources of data and which can also reflect non-Gaussian dependence. Rank statistics and copula-based methods form the basis of the suggested techniques. Problems associated with the rank based methods defining the representativity of the observations, and the numerically efficient simulation of conditional fields, are in the focus of the proposed research. The methods will be developed together with researchers of the University of Queensland (Australia). Application to examples in the domain of surface hydrology and subsurface geophysics are to be investigated. The required funds should only cover the travel costs of the collaborating partners.