A Short-Term Pumping Strategy for Hydraulic Tomography Based on the Successive Linear Estimator

In this study, the random finite element method, a finite element method with random field generation techniques, was applied to investigate the cross correlations between the observed head and hydraulic conductivity and specific storage at different locations and different times in pumping tests. The results show that the two cross correlations between the pumping well and the observation well reach their maximums before pumping reaches a steady state. Specifically, the cross correlation between the observed head and hydraulic conductivity is the greatest when the temporal derivative of the observed head does not change significantly, and that between the observed head and specific storage is the greatest when the temporal derivative (the rate) of the observed head is maximum. Based on the results of cross-correlation analysis, a short-term pumping strategy for hydraulic tomography is proposed to obtain the spatial distribution of hydraulic conductivity and specific storage using the successive linear estimator. Furthermore, this strategy was validated by Monte Carlo simulations. This paper points out that the sensitivity and cross-correlation analyses report the ensemble (averaged) behaviors of any heterogeneous aquifers, which is not necessarily suitable for one realization. Furthermore, Monte Carlo simulation is suggested for validating any groundwater inverse modeling result.