Stochastic analysis of oscillatory hydraulic tomography

•Manipulating pumping rate frequency alone does not warrant estimate improvement.•MC simulation shows estimates from single and multi-freq tests are indistinguishable.•A dense wellfield or MC simulation is necessary to satisfy the ergodicity assumption. This paper investigates the effectiveness of different oscillatory hydraulic tomography (OHT) frequencies for estimating heterogeneous fields. The analysis first formulates the effects of uncharacterized aquifer responses, T, and S fields as the ensemble mean residual flux and residual storage terms in the stochastic unconditional and conditional mean equations. These terms persist unless the T, S, or head fields are specified everywhere. We then conducted OHT to estimate the T and S fields using Monte Carlo experiments. The experiments show that using the heads in response to periodic pumping with different frequencies or multifrequency, the estimates' performance metrics vary from one realization to others. The mean performance metrics over many realizations are, however, indistinguishable, despite the frequency. We attribute the variation in the performance metrics to the lack of parameter or state variable ergodicity. Lastly, we emphasize the importance of dense monitoring networks and a cost-effective data collection strategy to improve the resolution of characterizing aquifer heterogeneity.