Analysis of hydraulic tomography using temporal moments of drawdown recovery data

Transient hydraulic tomography (THT) is a potentially cost-effective and high-resolution technique for mapping spatial distributions of the hydraulic conductivity and specific storage in aquifers. Interpretation of abundant well hydrographs of a THT survey, however, is a computational challenge. We take on this challenge by developing an estimation approach that utilizes the zeroth and first temporal moments of well hydrographs, instead of drawdown itself. 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 evolution. Likewise, the adjoint equations for evaluating sensitivities of the moments for parameter estimation also take the same forms. Therefore a temporal moment approach is expected to expedite the interpretation of THT surveys. On the basis of this premise we extend our sequential successive linear estimator to use the zeroth moment and characteristic time of the drawdown-recovery data generated by THT surveys. We subsequently investigate computational efficiency and accuracy of the moment approach. Results of the investigation show that the temporal moment approach yields results similar to those from the approach that uses transient heads but at significantly less computational costs. Limitations using temporal moments are discussed subsequently.