Geostatistical inverse modeling of transient pumping tests using temporal moments of drawdown

Abstract

[1] Pumping tests belong to the most common techniques of hydrogeological site assessment. While the steady state drawdown is determined by the distribution of transmissivity alone, the transient behavior is also influenced by the storativity field. In geostatistical inverse modeling the spatial distributions of both transmissivity and storativity are inferred from the drawdown curves and prior information on the spatial correlation of the parameter fields. So far, however, transient data have hardly been analyzed by geostatistical inverse methods because the computational effort is rather high. In the present study, we characterize the drawdown by its temporal moments. We present moment-generating equations and corresponding equations to compute the sensitivity of the temporal moments of drawdown with respect to the distributions of transmissivity and storativity. We utilize these equations to infer the transmissivity and storativity fields from transient pumping tests using the quasi-linear geostatistical approach of inverse modeling. Considering temporal moments rather than full drawdown curves drastically reduces the computational effort of the estimation procedure. In test cases we show that the first two temporal moments are sufficient to characterize the drawdown curves. We investigate how erroneous assumptions regarding the spatial variability of storativity affect the estimate of the transmissivity field, and we analyze the effect of truncating the measured drawdown curves.

Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

“…Second, the resulting spatiotemporal cross-covariance matrix is typically large and difficult to manipulate. In this study, we propose to assimilate temporal moments of the impulse response function of transient drawdown data (Harvey and Gorelick, 1995;Von Asmuth and Maas, 2001;Li et al, 2005;Bakker et al, 2008;Olsthoorn, 2008;Von Asmuth et al, 2008), rather than the hydraulic head data themselves.…”

Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area

“…Li et al (2005) has formulated the sensitivity of zeroth-order moments to a lnT value at a specific location, using the adjoint-state method (Sun, 1994). For the current estimate of T field required in the sensitivity analysis, we may use a uniform T field, since our priors are only for the global parameters (i.e., mean, variance, and scale) and we do not have any local information before the injection test.…”

“…The prior distributions of each parameter sufficiently cover possible values from the historical data at the site (Meyer et al, 2007) or literature values for similar geological formations (Rubin, 2003). The uniform distributions are considered to be less informative than Gaussian distributions, which have been commonly used in the Bayesian geostatistical inversion (Li et al, 2005). Three thousand sets of θ are generated from p(θ) using a quasi Monte-Carlo sampling method (Krommer and Ueberhuber, 1998).…”

“…According to Li et al (2005) and Zhu and Yeh (2006), the k-th-order temporal moment m k (x) for a pressure build-up curve s(x,t) is defined by…”

“…The particular difficulty in inverting injection-test or pumping-test data is the computational effort associated with a long time series. Li et al (2005) and Zhu and Yeh (2006) have applied temporal moments of drawdowns to estimate T and storativity S fields. The sandbox experiment by Liu et al (2007) has shown that the moment approach can successfully characterize a T field.…”