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Identifying Unsaturated Hydraulic Parameters Using an Integrated Data Fusion Approach on Cross-Borehole Geophysical Data

^a Univ. of Copenhagen, Dep. of Geography and Geology, Øster Voldgade 10, DK-1350 Copenhagen K, Denmark
^b Lancaster Univ., Dep. of Environmental Science, Lancaster, LA1 4YQ, UK
^c Univ. of Copenhagen, Niels Bohr Institute, Juliane Maries Vej 28, DK-2100 Copenhagen Ø, Denmark

View larger version (29K): [in this window] [in a new window]   FIG. 1. Schematic drawing of the field site setup at Arrenæs, Denmark. The light gray area indicates the infiltration area.

View larger version (22K): [in this window] [in a new window]   FIG. 2. (a) Background moisture content profiles estimated using cross-borehole ground penetrating radar (GPR) and electrical resistivity tomography (ERT); (b) sediment samples from a nearby well (d10, d50 and d90 are the 10th, 50th and 90th percentiles of the grain size distribution; data provided by Copenhagen Energy), and (c) the five-layered model used in the hydrologic forward simulation. The boundaries of the different materials were deduced from (a) and (b).

View larger version (35K): [in this window] [in a new window]   FIG. 3. The methodology used for the integrated data fusion (GPR, ground penetrating radar; ERT, electrical resistivity tomography; r and s, residual and saturated moisture content; and n, empirical parameters; Ks, saturated hydraulic conductivity).

View larger version (24K): [in this window] [in a new window]   FIG. 4. The misfit values of the one-layered models. For illustration purposes, only the 500 realizations with the lowest misfit values are included in the figure. The parameter ranges of the five realizations with the lowest misfit values are indicated with red; r is residual moisture content, and n are empirical parameters, Ks is saturated hydraulic conductivity.

View larger version (32K): [in this window] [in a new window]   FIG. 5. The simulated zero-offset profile (ZOP) travel times resulting from the one-layered model for three selected days: (a) Day 0, (b) Day 1, and (c) Day 8. The five realizations with the lowest misfit values are highlighted with red. The measured travel time profile is highlighted with green.

View larger version (23K): [in this window] [in a new window]   FIG. 6. The misfit values of the one-layered models using only data collected from Day 8. For illustration purposes, only the 500 realizations with the lowest misfit values are included in the figure. The parameter ranges of the five realizations with the lowest misfit values are indicated with red; an arrow points out the realization with a higher saturated hydraulic conductivity value; r is residual moisture content, and n are empirical parameters, Ks is saturated hydraulic conductivity.

View larger version (51K): [in this window] [in a new window]   FIG. 7. The simulated zero-offset profile (ZOP) travel times resulting from the one-layered model for two selected days: (a) Day 1 and (b) Day 8. Only data collected from Day 8 were used to calculate the misfit values. The five realizations with the lowest misfit values are highlighted with red. The measured travel time profile is highlighted with green. An arrow points out the realization with a higher saturated hydraulic conductivity value.

View larger version (54K): [in this window] [in a new window]   FIG. 8. Travel time profiles from the five-layered model for two selected days: (a) Day 1 and (b) Day 8. The five realizations with the lowest misfit values are highlighted with red. The measured travel time profile is highlighted with green.

View larger version (36K): [in this window] [in a new window]   FIG. 9. A synthetic evaluation of the five-layered model analysis using the two data types combined. For illustration purposes, only the 500 realizations with the lowest misfit values are included in the figure. The parameter ranges of the five realizations with the lowest misfit values are indicated with red and the "true" parameter value is shown with a red diamond.

View larger version (40K): [in this window] [in a new window]   FIG. 10. A synthetic evaluation of the five-layered model analysis using only ground penetrating radar (GPR) data for (a) Day 8 and (b) Days 1 to 8. For illustration purposes, only the 500 realizations with the lowest misfit values are included in the figure. The parameter ranges of the five realizations with the lowest misfit values are indicated with red and the "true" parameter value is shown with a red diamond; r is residual moisture content, and n are empirical parameters, Ks is saturated hydraulic conductivity.

View larger version (31K): [in this window] [in a new window]   FIG. 11. The misfit values of the five-layered model using only electrical resistivity tomography (ERT) data, using only ground penetrating radar (GPR) data, and combining ERT and GPR data in the analysis. For illustration purposes, only the 500 realizations with the lowest misfit are included in the figure. Only the misfit plot of the top three layers of the saturated hydraulic conductivity, Ks, and the empirical parameter n are shown.

View larger version (26K): [in this window] [in a new window]   FIG. 12. Travel time profiles as they developed with time. The five best realizations of the combined analysis (red) are shown along with the measured profiles (green).

View larger version (38K): [in this window] [in a new window]   FIG. 13. Moisture content profiles of the five best realizations of the combined analysis as they developed with time. The background moisture content profile (Day 0) is illustrated with black in the subsequent seven measurement times, while the range of all the realizations of moisture content curves is indicated with gray.

View larger version (15K): [in this window] [in a new window]   FIG. 14. Relative solute concentration profiles of the five best realizations of the combined analysis as they developed with time. The range of all the realizations of solute curves is indicated with gray.