A temporal sampling strategy for hydraulic tomography analysis

Abstract

[1] 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.

Sampling schemes for hillslope hydrologic processes and stability analysis based on cross-correlation analysis

“…It is also clear that P at an observation location within the slope is not equally influenced by heterogeneous hydraulic conductivity values everywhere within the slope. This finding is consistent with those reported by Li and Yeh (), Mao et al (), and Sun et al ().…”

What does hydraulic tomography tell us about fractured geological media? A field study and synthetic experiments

“…12(b)) also reveals that the DH-2, the upper part of DH-15 and the pumped locations in tests 1, 3 and 4 are all connected via a low S s zone. Overall, the estimated S s values are generally negatively correlated with K values although their patterns are not identical as explained in Huang et al (2011) and Sun et al (2013).…”

“…For these analyses, the following sampling time strategy was used. According to Sun et al (2013), the drawdown at a well at the interpolated time at which drawdown is zero in CooperJacob's method is most correlated with S s over a large portion of the aquifer and late time drawdown data at the observation well are highly correlated to K over the entire aquifer. In addition, Yeh et al (2011) and Mao et al (2013) emphasized that the head change over at least two time step is necessary to determine S s term.…”

Image-guided inversion in steady-state hydraulic tomography

“…The SLE approach has proven to be an efficient tool in hydraulic tomography. Its success has been demonstrated in saturated flow synthetic tests [59,64]; [60,58]; [51], in variably-saturated flow synthetic tests [42], in pneumatic tomography [44], in sandbox experiments [3,32,40,41], and in field experiments [4,6,30,31,49].…”