24. Mai 2007, 16:00 Uhr

Simulation of random fields using non-Gausssiandependence

24.05.07, 16:00 – 17:30 Uhr
Jing Li
Institut für Wasserbau
Lehrstuhl für Hydrologie und Geohydrologie
As flow and transport simulations are often used for environmental riskassessment (for example the contaminant plume underground) and the flowbehavior is considerably influenced by the spatial structure ofheterogeneous hydraulic conductivity fields, it is of vital importancetoclarify the role of spatial dependence structures for the estimation offlowand transport. In the traditional spatial simulations, a multivariatelognormal distribution is often assumed for the conductivity fields,whichcontradicts the usually non-Gaussian distribution of conductivities inreality. Moreover the sole descriptor for spatial dependence which isusedby the multi-Gaussian assumption fails to characterize the oftenoccurreddeviation from the central tendency. Therefore there is a need for newnon-Gausssian simulation methods and hence for new types of randomfunctions.Recently, copulas have been evoking considerable interest in financialmathematics because they provide an innovatory way of modeling thedependence structure between variables. Our research is carried out todevelop new families of random functions with distinct non-Gaussianproperties for spatial simulations of hydraulic conductivities.In the presentation, at first, a brief introduction for the concept ofcopulas and dependence will be given. Second, the methodology of usingcopulas to investigate spatial variabilities will be presented. Third,several random fields of hydraulic conductivity with arbitrary marginaldistributions and a given copula will be demonstrated and compared.Finally,the approach of Euler characteristics to study the connectivity of thefields will be discussed.
Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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