HR: 1340h
AN: H13D-1351    [Abstracts]
TI: Efficient Method for Geostatistical Inverse Modeling on Unstructured Grids
AU: * Li, W
EM: Wei.Li@EAWAG.CH
AF: Swiss Federal Institute of Aquatic Science and Technology (EAWAG), Überlandstr. 133, Dübendorf, 8600 Switzerland
AU: Cirpka, O A
EM: Olaf.Cirpka@EAWAG.CH
AF: Swiss Federal Institute of Aquatic Science and Technology (EAWAG), Überlandstr. 133, Dübendorf, 8600 Switzerland
AB: A certain class of geostatistical inverse methods is based on cokriging-like techniques, in which the cross-covariance functions between the measured heads and the log-conductivity distribution span the solution space. Unfortunately, the explicit computation of the full cross-covariance matrix is computationally prohibitive for large-scale problems. Spectral methods [Nowak et al., 2003], based on periodic embedding and fast Fourier transformation, are restricted to cases in which the domain is discretized by regular grids. These methods can not be applied to unstructured grids which may be better suited to discretize irregularly shaped domains and allow grid refinement in sensitive parts of the domain. To cope with this problem, we apply the Karhunen-Loève expansion [Loève, 1977]. Here, the random spatial variable is parameterized by weighted base functions, which are the eigenfunctions of the covariance function times the square-root of the corresponding eigenvalues. Typically, the series of eigenvalues are sorted in a decreasing order and truncated. To minimizes the costs of the eigen-decomposition, we embed the domain into a larger periodic one. For the latter, the eigenfunctions are known a priori as trigonometric functions. The corresponding eigenvalues are given by fast Fourier transformation. The reproduction of the covariance function by continuous trigonometric functions is independent of the discretization scheme of the domain. Thus, irregularly shaped domains may be discretized by unstructured grids. We apply the method to the artificial test case of an unconfined aquifer, where the irregularly shaped domain is discretized by triangular elements.
DE: 1829 Groundwater hydrology
DE: 1869 Stochastic hydrology
DE: 1873 Uncertainty assessment (3275)
DE: 3205 Fourier analysis (3255)
DE: 3260 Inverse theory
SC: Hydrology [H]
MN: Fall Meeting 2005