A temporal sampling strategy for hydraulic tomography analysis

This paper investigates optimal sampling times of drawdowns for the analysis of hydraulic tomography (HT) survey. The investigation was carried out by analyzing the spatial and temporal evolution of cross-correlations between the head responses at an observation well and transmissivity (T) and storage coefficient (S) properties during a pumping test in homogeneous and heterogeneous aquifers. The analysis shows that the cross-correlation between the head and S values is limited to the region between the observation and the pumping well in the aquifers: It reaches the highest value near the early time (t(m)), and decays to zero afterwards. The time t(m) is approximately equal to the time t(0) at which the extrapolated drawdown from the first straight line portion of an observed drawdown-log time plot becomes zero. At early times, the high cross-correlation between the head and T is confined to the region between the observation and the pumping well. This region then evolves into two humps: One on each side of the circular region encompassing the observation well and the pumping well. The size of the two humps expands and their values reach the maximum as flow reach steady-state. As a consequence, we hypothesize that pairs of head data at t(0) and those at either the steady-state or a late time during an HT survey could yield the best estimates of the heterogeneous T and S fields. Results from numerical experiments have verified this hypothesis and demonstrated that this sampling strategy is generally applicable even when the boundary condition is unknown. We, therefore, recommend in principle that (1) carrying out pumping tests of HT surveys for sufficiently long period of time such that drawdown reaches the entire area of interest and (2) using a constant head or zero drawdown for all boundaries during the inverse modeling analysis.