HR: 0830h
AN: H11G-0920    [PDF]
TI: First-order variance of solute travel time in non-stationary media
AU: * Cirpka, O A
EM: Olaf.Cirpka@IWS.Uni-Stuttgart.DE
AF: Universit\"at Stuttgart Institut f\"ur Wasserbau, Pfaffenwaldring 61, Stuttgart, 70550 Germany
AU: Nowak, W
EM: Wolfgang.Nowak@IWS.Uni-Stuttgart.DE
AF: Universit\"at Stuttgart Institut f\"ur Wasserbau, Pfaffenwaldring 61, Stuttgart, 70550 Germany
AB: We study solute-flux statistics in heterogeneous porous media exhibiting non-stationary covariance functions of the log-conductivity field. In particular, we investigate the cases of 1) variance scaling, in which the variance undergoes a spatial trend, 2) the blending of multiple covariance functions, including the case of zonal stationarity, 3) non-stationarity because of uncertainty in parameters describing the spatial trend of the mean log-conductivity, and 4)non-stationarity as a result of conditioning. All of these cases can be traced back to stationary covariance functions undergoing particular modifications. We calculate the first-order variance of travel time by quadratic multiplication of the discretized covariance matrix of log-conductivity fluctuations with the sensitivity matrix of the travel-time at the points of interest. The sensitivities are calculated by the adjoint-state method. The matrix-matrix multiplications are performed by Fast Fourier Transformation techniques requiring to embed the stationary counterparts of the non-stationary fields into periodic domains. The method is very efficient with respect to both computational effort and memory requirements. We apply the approach to a two-dimensional field of 1000 $\times$ 500 elements in which the correlation length and the variance have a spatial trend, and the parameters of the trend-model for the mean are uncertain. We include the case of conditioning on head and total-flux measurements.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2003 Fall Meeting