Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multi-method and multiscale validation of hydraulic conductivity tomograms

SummaryHydraulic tomography potentially is a viable technology that facilitates subsurface imaging of hydraulic heterogeneity. To date, a comprehensive validation of hydraulic tomography has not been done either at the laboratory or field scales. The main objective of this paper is to examine the accuracy of hydraulic conductivity (K) tomograms obtained from the steady-state hydraulic tomography algorithm of [Yeh, T.-C. J., Liu, S., 2000. Hydraulic tomography: development of a new aquifer test method. Water Resources Research 36, 2095–2105]. We first obtain a reference K tomogram through the inversion of synthetic cross-hole test data generated through numerical simulations. The purpose of reference K tomogram generation is to examine the ability of the algorithm to image the heterogeneity pattern under optimal conditions without experimental errors and with full control of forcing functions (initial and boundary conditions as well as source/sink terms). Parallel to the generation of synthetic data, we conduct hydraulic tests at multiple scales in a laboratory aquifer with deterministic heterogeneity to generate data that are used to validate K tomograms from hydraulic tomography. Measurements include multiple K estimates from core, slug, single-hole and cross-hole tests as well as several unidirectional, flow-through experiments conducted on the sandbox under steady-state conditions. Validation of K tomograms involved a multi-method and multiscale approach proposed herein which include: (1) visual comparisons of K tomograms to the true sand distributions and the reference K tomogram; (2) testing the ability of the K tomogram to predict the hydraulic head distribution of an independent cross-hole test not used in the computation of the K tomogram; (3) comparison of the conditional mean and variance of local K from the K tomograms to the sample mean and variance of results from other measurements; (4) comparison of local K values from K tomograms to those from the reference K tomogram; and (5) comparison of local K values from K tomograms to those obtained from cores and single-hole tests. The multi-method and multiscale validation approach proposed herein further illustrates the robustness of steady-state hydraulic tomography in subsurface heterogeneity delineation.