Why hydraulic tomography works?

Head measurements at a single observation well during a cross-hole pumping test carry a great amount of information about aquifer heterogeneity other than the average property of the aquifer as implied in Theis analysis of aquifer test. In this commentary, we use simple examples and a probabilistic reasoning approach based on Darcy’s law to unravel this information, buried in the results of quantitative stochastic analyses of flow in heterogeneous aquifers (Bakr et al. 1978; Dagan 1985, 1989) and vadose zones (Yeh et al. 1985a, 1985b, 1985c; Yeh and Zhang 1996). We subsequently use this information to elucidate the principles of hydraulic tomography (HT), sequential pumping tests, or multi-well interference tests (see Yeh and Liu 2000; Illman et al. 2009; Brauchler et al. 2011; Cardiff and Barrash 2011). Consider a pumping test in a one-dimensional heterogeneous confined aquifer (i.e., a horizontal soil column) which contains a pumping and an observation port. Ends of the aquifer are held at the same prescribed constant head, flow is at steady state, and the pumping rate, Q , is known. We now ask what the pumping rate and the drawdown at the observation port tell us about the spatial variation of the aquifer hydraulic conductivity (K ).