Abstract. This paper describes the first major attempt to compare seven different inverse approaches for identifying aquifer transmissivity. The ultimate 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 variability and uncertainty in hydrogeologic properties are significant. Seven geostatistical methods (fast Fourier transform (FF), fractal simulation (FS), linearized cokriging (LC), linearized semianalytical (LS), maximum likelihood (ML), pilot point (PP), and sequential self-calibration (SS)) were compared on four synthetic data sets. Each data set had specific features meeting (or not) classical assumptions about stationarity, amenability to a geostatistical description, etc. The comparison of the outcome of the methods is based on the prediction of travel times and travel paths taken by conservative solutes migrating in the aquifer for a distance of 5 km. Four of the methods, LS, ML, PP, and SS, were identified as being approximately equivalent for the specific problems considered. The magnitude of the variance of the transmissivity fields, which went as high as 10 times the generally accepted range for linearized approaches, was not a problem for the linearized methods when applied to stationary fields; that is, their inverse solutions and travel time predictions were as accurate as those of the nonlinear methods. Nonstationarity of the "true" transmissivity field, or the presence 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 1og•0 (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 information from pumping tests did not result in major changes in the outcome. While the methods differ in their underlying theory, and the codes developed to implement the theories were limited to varying degrees, the most important factor for achieving a successful solution was the time and experience devoted by the user of the method. •2Stanford University, Stanford, California.•3Duke Engineering and Services, Inc., Austin, Texas.•4University of Arizona, Tucson.•Slnstitut Franqais du Pftrole, Rueil-Malmaison, France.•6University of California, Berkeley.Copyright 1998 by the American Geophysical Union. Paper number 98WR00003.0043-1397/98/98WR-00003509.00 tion, or performance assessment of planned waste disposal projects, it is no longer enough to determine the "best estimate" of the distribution in space of the aquifer parameters. A measure of the uncertainty associated with this estimation is also needed. Geostatistical techniques are ideally suited to filling this role. Basically, geostatistics fits a "structural model" to the data, reflecting their spatial variability. Then, both "best estim...

Paper 2 of this three‐part series uses synthetic data to investigate the properties of the adjoint state maximum likelihood cross‐validation (ASMLCV) method presented in paper 1 (Samper and Neuman, this issue (a)). More than 40 synthetic experiments are performed to compare various conjugate gradient algorithms; investigate the manner in which computer time varies with ASMLCV parameters; study the effect of sample size and choice of kriging points on ASMLCV estimates ; evaluate the ability of various model structure identification criteria to help select the most appropriate semivariogram model among given alternatives; study the conditions required for parameter identifiability, uniqueness, and stability; quantify the statistics of cross‐validation errors; test hypotheses concerning the distribution and autocorrelation of these errors; and illustrate the computation of approximate quality indicators for ASMLCV parameter estimates.

Paper 3 of this three‐part series presents applications of our adjoint state maximum likelihood cross‐validation (ASMLCV) method to real data from aquifers. The Madrid basin in Spain serves as the source of information about 11 hydrochemical variables (pH, electrical conductivity, silica content, and the concentration of major ions) and two isotopes (oxygen 18 and carbon 14). Due to a lack of sufficient vertical resolution, our analysis is restricted to the horizontal plane. With the exception of oxygen 18 and silica, the variables appear to be free of a horizontal drift. No discernible directional effects are seen. All variables exhibit a large nugget effect which is indicative of background noise. We conclude that more detailed and careful sampling in three dimensions is required if groundwater quality information is to become less prone to such noise and thereby more useful in the context of quantitative hydrogeological analyses. Despite the existing noise, we are able to confirm geostatistically some (though not all) of the hypotheses advanced by others about hydrochemical evolution and isotope changes in the basin. The ability of ASMLCV to filter out spatial variations from part of the measurement noise is illustrated on carbon 14 data. The same data are also used to investigate the utility of model structure identification criteria in selecting the best among a set of alternative semivariogram models.

This report documents the research performed during the period M a y 1995-May 1996 for a project of the US. Nuclear Regulatory Commission (sponsored contract NRC-04-090-051) by the University of Arizona. The project manager for this research is Thomas J. Nicholson, OtEce of Nuclear Regulatory Research. The objectives of this research were to examine hypotheses and test alternative conceptual models concerning unsaturated flow and transport through fractured rock, and to design and execute confirmatory field and laboratory experiments to test these hypotheses and conceptual models at the Apache Leap Research Site near Superior, Arizona. Each chapter in this report summarizes research related to a specific set of objectives and can be read and interpreted as a separate entity. Topics include: crosshole pneumatic and gaseous tracer field and modeling experiments designed to help validate the applicability of contiuum geostatistical and stochastic concepts, theories, models, and scaling relations relevant to unsaturated flow and transport in fractured porous tuffs; use of geochemistry and aquifer testing to evaluate fracture flow and perching mechanisms; investigations of *Up% fractionation to evaluate leaching selectivity; and transport and modeling of both conservative and nonconservative tracers.