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

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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.