We use transient hydraulic tomography (THT) to characterize a highly heterogeneous unconfined aquifer
at an active industrial site. To the best of our knowledge, this is the most heterogeneous site (with
estimated hydraulic conductivity values ranging over seven orders of magnitude) at which hydraulic
tomography (HT) has been conducted. The use of smart algorithms and advanced computer resources can take
advantage of a relative large number of data (O(10^{3})) and allow for the estimation of a large
number of parameters (O(10^{5}-10^{6})) for high-resolution imaging. Furthermore, by using
the Bayesian-based geostatistical approach to this imaging problem (i.e., characterization or parameter
estimation), we have linearized estimates of the uncertainty in the image. Our estimate of the heterogeneous
hydraulic conductivity field is validated with independent pumping tests that were not used in the inversion;
the predictive capability is very encouraging.

Our research groupâ€™s ability to handle the challenges of complex, large-scale data analysis problems is illustrated through this subsurface characterization work (see Table 1 for size of problem). The main THT field campaign consisted of 26 tests which have been used for data analysis through inversion. With a dense observation network that recorded pressure/hydraulic head changes, we have 834 drawdown response curves and use 4 points each that sufficiently characterize the curves for a total of 3336 data points. An 81 m x 81 m x 19.8 m domain is modeled using the finite-difference groundwater flow model, MODFLOW. A MODFLOW forward model is created for each test, and each consists of over 2.3 million cells. Using the geostatistical approach, we invert for over 200,000 unknown parameters: a distributed hydraulic conductivity field K(x,y,z) as well as a uniform estimate of the specific storage Ss and specific yield Sy. Due to the heterogeneity of the hydraulic conductivity field, this is a very nonlinear problem. Iterative methods with a Levenberg-Marquardt approach are used to deal with the nonlinearity and converge to a best estimate of the heterogeneous hydraulic conductivity field.

**Figure 1** Estimated 3-D hydraulic conductivity fields based on inversion results from
two different viewing perspectives. The pumping well for all tests used in the inversion is at the cross-section
of the two slices (labeled NPM01). The observation locations are indicated by the 5 Continuous Multichannel
Tubing (CMT) well clusters.

The best estimate of K(x,y,z) indicates that the site is very heterogeneous, with K(x,y,z) varying over 7 orders of magnitude (Figure 1). As can be seen in Figure 1, this method is able to identify many small-scale features such as highly permeable and highly impermeable aquifer features over the volume of study. Figure 2 shows the confidence in that estimate, with the posterior standard deviation equal to or less than approximately one log10 unit of K over the study volume. In order to validate our results, an independent pumping test (i.e., not used in the inversion) located at a different pumping location (in one of the CMT zones) was used to test the predictive capability of the estimated parameter field. Results from other independent tests are currently being processed and after analysis they will be included as part of the validation.

**Figure 2** Posterior standard deviation of hydraulic conductivity fields based on
inversion results from two different viewing perspectives. The pumping well for all tests used in the
inversion is at the cross-section of the two slices (labeled NPM01). The observation locations are indicated
by the 5 Continuous Multichannel Tubing (CMT) well clusters.

Figure 3 compares the observed drawdown from the field observations (blue dots) and compares that to the predicted drawdown using the forward model with the estimated parameters from the inversion (red dots). The pink dashed line indicates upper and lower bounds based on plus/minus one standard deviation (1.8 mm) based on the estimated measurement and forward model error. However, it should be noted that this is less than the overall uncertainty since the uncertainty in the parameter field has not been considered. Nevertheless, as can be seen in Figure 3 the results are very good. Due to space limitations, only 12 of the 38 available curves are shown. Overall, only 3 of the 38 curves were significantly off in predicting the drawdown. These corresponded to 3 observation locations directly below the pumping location and could be due to field installation disturbances of the CMTs, coarseness of the parameter field relative to the local scale of the measurements, and/or coarseness of the MODFLOW grid relative to the very small CMT opening where the pumping occurred. These results are quite encouraging!

Number of tests used | Number of drawdown curves | Number of observation (data) points used | Number of cells in each (MODFLOW) forward model | Number of unknown parameters inverted |

26 | 834 | 3336 | 2.3∙ 10^{6} |
2.2∙ 10^{5} |

**Figure 3** Inversion validation with independent pumping test at CMT3-7. Sample
(12 of 38 curves) of results. The field data obtained from FO pressure transducers are in blue and
the simulated drawdown curve using the best estimate of *K(x,y,z)*, *Ss*, and *Sy*
is shown in red with plus/minus one standard error of the observations used in the inversions.

Last updated: 5/22/2014