Hydraulic tomography using temporal moments of drawdown recovery data: A laboratory sandbox study

[1] Hydraulic tomography (HT) is a new technology that images the hydraulic heterogeneity of the subsurface. Unlike steady state hydraulic tomography (SSHT), which provides a hydraulic conductivity (K) tomogram, transient hydraulic tomography (THT) provides reliable tomograms of both K and specific storage (Ss). Effective as it may be, THT is a computationally demanding technique. To ease the computational burden, a HT which utilizes zeroth and first temporal moments of transient drawdown recovery data (HT-m) has been developed by Zhu and Yeh (2006). This procedure simplifies the governing equation from a single parabolic equation to two Poisson's equations for the zeroth moment and characteristic time defined as the ratio between the first and zeroth moments. The approach was previously tested using synthetic simulations. The numerical experiments tested the feasibility of HT-m under ideal conditions, where measurements and model are assumed to be free of error. In this paper, we further evaluate the performance of HT-m using cross-hole pumping tests conducted in a heterogeneous, synthetic aquifer constructed in a laboratory sandbox in more realistic situations, where the data used in the inversion are not free of experimental errors. Unlike field tests, the laboratory tests were conducted in a synthetic aquifer created with a prescribed heterogeneity pattern and all forcing functions (initial and boundary conditions and source-sink terms) controlled. Results from the HT-m approach were compared to those from THT previously conducted by Liu et al. (2007). Our results show that the estimation of the K tomogram using the HT-m approach is reasonable, but the estimation of the Ss tomogram is unreliable in comparison to the THT approach.