Resolution and Ergodicity Issues of River Stage Tomography With Different Excitations

This study investigates spatiotemporal cross correlation between the observed head and the hydraulic diffusivity parameters in heterogeneous aquifers under static and migrating periodic excitations with different frequencies and other factors and a moving single excitation along a river boundary. Results of the cross-correlation analysis are verified by estimating the parameters in a synthetic heterogeneous aquifer under these excitations. For assuring the statistical significance of the results based on a single realization, Monte Carlo experiments of estimating the parameters with these excitations are conducted. The experiments also explore the relationship between the resolution of the estimated parameters and the distance from the excitation to the observation wells, the frequency, and amplitude of the excitation and the mean diffusivity of the aquifer. In addition, the relationship between the resolution of the estimates and monitoring network spatial density is investigated. Finally, the usefulness of moving single excitations, effects of frequencies of the periodic excitations under different situations, the density of monitoring network in term of correlation scale, and the ergodicity issue corresponding to the number of observation and size of simulation domain are discussed.