A COMPARISON OF 7 GEOSTATISTICALLY BASED INVERSE APPROACHES TO ESTIMATE TRANSMISSIVITIES FOR MODELING ADVECTIVE TRANSPORT BY GROUNDWATER-FLOW

This paper describes the first major attempt to compare seven differen t inverse approaches for identifying aquifer transmissivity. The ultim ate objective was to determine which of several geostatistical inverse techniques is better suited for making probabilistic forecasts of the potential transport of solutes in an aquifer where spatial variabilit y and uncertainty in hydrogeologic properties are significant. Seven g eostatistical methods (fast Fourier transform (FF), fractal simulation (FS), linearized cokriging (LC), linearized semianalytical (LS), maxi mum likelihood (ML), pilot point (PP), and sequential self-calibration (SS)) were compared on four synthetic data sets. Each data set had sp ecific features meeting (or not) classical assumptions about stationar ity, amenability to a geostatistical description, etc. The comparison of the outcome of the methods is based on the prediction of travel tim es and travel paths taken by conservative solutes migrating in the aqu ifer for a distance of 5 km. Four of the methods, LS, ML, PP, and SS, were identified as being approximately equivalent for the specific pro blems considered. The magnitude of the variance of the transmissivity fields, which went as high as 10 times the generally accepted range fo r linearized approaches, was not a problem for the linearized methods when applied to stationary fields; that is, their inverse solutions an d travel time predictions were as accurate as those of the nonlinear m ethods. Nonstationarity of the ''true'' transmissivity field, or the p resence of ''anomalies'' such as high-permeability fracture zones was, however, more of a problem for the linearized methods. The importance of the proper selection of the semivariogram of the log(10) (T) field (or the ability of the method to optimize this variogram iteratively) was found to have a significant impact on the accuracy and precision of the travel time predictions. Use of additional transient informatio n from pumping tests did not result in major changes in the outcome. W hile the methods differ in their underlying theory, and the codes deve loped to implement the theories were limited to varying degrees, the m ost important factor for achieving a successful solution was the time and experience devoted by the user of the method.