## 1. Introduction

[2] Hydraulic tomography, a sequential aquifer test, has recently been proposed to characterize aquifer heterogeneity [*Gottlieb and Dietrich*, 1995; *Butler and Liu*, 1993; *Butler et al.*, 1999; *Yeh and Liu*, 2000]. Specifically, fully screened wells are divided into many vertical intervals using packers. Water is pumped from an aquifer at one of the intervals to create a steady state flow condition. Hydraulic head responses at other intervals are then monitored, yielding one set of head/discharge data. Then the pumping location is moved to another interval, and the resulting steady state head responses at other locations are collected accordingly, resulting in a second data set. By performing this procedure sequentially, a large number of head/discharge data sets can be obtained. With a proper inverse methodology, these data sets can be used to produce a detailed image of heterogeneity in the aquifer.

[3] Several researchers [*Scarascia and Ponzini*, 1972; *Sagar et al.*, 1975; *Giudici et al.*, 1995; *Snodgrass and Kitanidis*, 1998] have investigated the use of data corresponding to different flow situations to improve the uniqueness of the inverse solution or to reduce uncertainties in the identification of flow model parameters. Until recently, very few researchers have investigated the idea of hydraulic tomography. *Gottlieb and Dietrich* [1995] proposed a hydraulic tomography method and employed a least squares based inverse approach to illustrate its potential to identify the permeability distribution in a hypothetical two-dimensional saturated soil. *Butler et al.* [1999] applied the hydraulic tomography concept to networks of multilevel sampling wells. They developed new techniques for measuring drawdown at multilevel sampling ports that had previously been unobtainable. They suggested that such sampling techniques could facilitate the implementation of hydraulic tomography in the field. Until recently, even fewer researchers have attempted to develop a realistic three-dimensional (3-D) inverse model for hydraulic tomography because computational burdens hinder applications of classical inverse algorithms to 3-D hydraulic tomography. *Yeh and Liu* [2000] have developed a sequential geostatistical inverse approach that eases the burdens and allows one to efficiently interpret the abundant data sets produced by hydraulic tomography. In their study, not only did they demonstrate the robustness of their inverse approach, but they also investigated the network design issue for hydraulic tomography, and addressed uncertainty in the hydraulic conductivity estimate.

[4] Hydraulic tomography has been tested using numerical experiments [*Gottlieb and Dietrich*, 1995; *Yeh and Liu*, 2000] but not laboratory or field experiments. In numerical experiments, effects of conceptual model errors are absent because synthetic tomography data are generated from the same model used in the inversion. Model inputs are also assumed to be error-free. Conversely, in field experiments, the effects of conceptual model errors are unknown. Model inputs, such as boundary conditions, pumping rates, mean, variance, and correlation scales, are always subject to uncertainty. Further, the pressure head/discharge data inevitably contain unknown measurement errors. Field experiments are thus the most appropriate test for hydraulic tomography.

[5] Nevertheless, field experiments are so costly that well-controlled sandbox experiments are a reasonable alternative. In this paper, we tested the effectiveness of our sequential inverse approach [*Yeh and Liu*, 2000] with two sandbox experiments. The first experiment represented a stratified aquifer system, while the other represented a more complex and realistic heterogeneous aquifer. In addition, numerical experiments were conducted to diagnose anomalies in the inverse results from the sandbox experiments, and to explore conditions under which the hydraulic tomography can be effective.