## 1. Introduction

[2] Characterization of subsurface heterogeneity in aquifer parameters is a topic of great interest to hydrogeologists. There are a number of approaches to capture the spatial variability of parameters such as hydraulic conductivity (*K*) and specific storage (*S*_{s}). One approach which is receiving recent attention is hydraulic tomography (HT). Various inverse methods for HT have been developed which utilize pumping test data simultaneously or sequentially [e.g., *Gottlieb and Dietrich*, 1995; *Yeh and Liu*, 2000; *Bohling et al.*, 2002; *Brauchler et al.*, 2003; *Zhu and Yeh*, 2005, 2006; *Li et al.*, 2005; *Fienen et al.*, 2008]. In particular, *Yeh and Liu* [2000] developed an algorithm for steady state hydraulic tomography (SSHT) through the use of the sequential successive linear estimator (SSLE). *Zhu and Yeh* [2005] then extended the SSHT to transient hydraulic tomography (THT).

[3] THT is an effective technique in imaging *K* and *S*_{s}, but is computationally costly. To overcome the computational challenge for THT analysis, *Zhu and Yeh* [2006], inspired by the moment generating function approach by *Harvey and Gorelick* [1995], developed an approach that utilizes the zeroth and first temporal moments of drawdown recovery data, instead of drawdown recovery data itself. The method requires the full drawdown recovery curve to calculate the temporal moments [*Zhu and Yeh*, 2006].

[4] The governing equations for the temporal moments are Poisson's equations. These equations demand less computational resources as opposed to the parabolic equation that governs drawdown recovery evolution. Likewise, the adjoint equations for evaluating sensitivities of the moments for parameter estimation also take the same forms. Therefore a HT which uses the temporal moments of drawdown recovery data (HT-m) expedites the interpretation of THT surveys.

[5] While various algorithms for HT have been developed and some of them have been tested numerically, several sandbox studies have been conducted to evaluate the performance of both SSHT [*Liu et al.*, 2002; *Illman et al.*, 2007, 2008] and THT [*Liu et al.*, 2007]. In the field, THT has also been applied in unconsolidated media [*Straface et al.*, 2007], while a HT based on the steady shape analysis [*Bohling et al.*, 2002] was reported for unconsolidated materials by *Bohling et al.* [2007]. Most recently, *Li et al.* [2008] utilized their HT approach to image floodplain deposits.

[6] To date, the evaluation of the HT-m has not been accomplished either in the laboratory or the field setting. A field validation is our ultimate goal, but prior to that, laboratory validations are necessary in which the heterogeneity pattern is prescribed, and all forcing functions and errors can be controlled as opposed to field conditions in which all of these factors are unknown. The objectives of this paper are to invert cross-hole pumping test data obtained in a laboratory aquifer using the HT-m algorithm and to investigate the performance of HT-m in comparison to the THT approach of *Zhu and Yeh* [2005].