HR: 09:30h
 AN: H41H-07    [Abstracts]
 TI: Temporal Moments in Hydrogeophysics
 AU: Pollock, D
 EM: davina.pollock@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: Electrical Resistivity Tomography (ERT) has been tested as monitoring tool for salt-tracer experiments by various authors. So far, the analysis of such experiments has been done by a two-step procedure [Kemna et al., 2002; Vanderborght et al., 2005; Singha and Gorelick, 2005]. In the first step, classical geophysical inversion methods have been used to infer the distribution of electrical conductivity, which is transferred to an estimated concentration distribution of the tracer. Subsequently, the inferred concentration images were analyzed to estimate hydraulic quantities such as the velocity distribution. This approach has two disadvantages:

  1. The concentration distribution is reconstructed with a high spatial resolution, but the estimate is uncertain, and the estimation uncertainty is spatially correlated. These correlated uncertainties should be accounted for in the estimation of hydraulic conductivity from concentration values. The latter, unfortunately, is not practical because the reconstructed data sets are very large.
  2. The geophysical inversion is not enforced to be in agreement with basic hydromechanical constraints. E.g., Singha and Gorelick [2005] observed an apparent loss of solute mass when using ERT as monitoring tool.
We propose considering the temporal moments of potential-difference time series. These temporal moments depend on temporal moments of concentration, which have already been used in the inference of hydraulic- conductivity distributions (Cirpka and Kitanidis, 2000). In our contribution, we present the complete set of equations leading from hydraulic conductivity via hydraulic heads, velocities, temporal moments of concentrations to temporal moments of potential differences for given flow and transport boundary conditions and electrode configurations. We also present how the sensitivity of temporal moments of potential differences on the hydraulic conductivity field can be computed without the need of storing intermediate sensitivities. With these methods, we have developed the kernel of a fully coupled hydrogeophysical inversion approach, in which the direct target of inversion is the hydraulic-conductivity field. By construction, the estimated concentration distribution is prevented to show unphysical behavior.
DE: 1832 Groundwater transport
 DE: 1835 Hydrogeophysics
 DE: 1872 Time series analysis (3270, 4277, 4475)
 DE: 1894 Instruments and techniques: modeling
 SC: Hydrology [H]
 MN: 2007 Fall Meeting