A simultaneous successive linear estimator and a guide for hydraulic tomography analysis

Self Cite

[1] In this study, we developed a stochastic estimator for characterizing the hydraulic heterogeneity in both unsaturated and saturated zones of unconfined aquifers using transient drawdown data from sequential pumping tests. This estimator was built upon the successive linear estimator by Yeh et al. (1996), the simultaneous successive linear estimator by Xiang et al. (2009), and the 3-D finite element program for flow and transport through heterogeneous media by Srivastava and Yeh (1992). The estimator was tested afterward using simulated data sets of sequential pumping tests in a synthetic unconfined aquifer where saturated conductivity, specific storage, saturated water content, and pore-size distribution parameter vary spatially in three dimensions. Test results show that the estimator is able to produce parameter fields that capture the overall 3-D pattern of the true heterogeneous parameter fields. We subsequently validated the estimated parameter fields by assessing their ability to predict drawdowns during an independent pumping test, which was not used during the estimation phase. Results of the validation show that the predicted drawdowns based on the estimated heterogeneous parameter fields are in close agreement with the true drawdowns. In addition, predicted drawdowns based on the parameter fields from the joint interpretation are superior to those based on the parameters estimated from the homogeneous conceptual model. Lastly, while many field experiments are necessary to fully assess the robustness of this estimator and sequential pumping tests, results of this study suggest they are a promising characterization technique for unconfined aquifers.

Section: Simultaneous Successive Linear Estimatormentioning

confidence: 99%

Section: Data Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Joint interpretation of sequential pumping tests in unconfined aquifers

Mao

Yeh

Wan

et al. 2013

Self Cite

Resolution analysis of tomographic slug test head data: Two‐dimensional radial case

Paradis

Gloaguen

Lefebvre

et al. 2015

Hydraulic tomography inverse problems, which are solved to estimate aquifer hydraulic properties between wells, are known to be ill-conditioned and a priori information is often added to regularize numerical inversion of head data. Because both head data and a priori information have effects on the inversed solution, assessing the meaningful information contained in head data alone is required to ensure comprehensive interpretation of inverse solutions, whether they are regularized or not. This study thus aims to assess the amount of information contained in tomographic slug tests head data to resolve heterogeneity in K h , K v /K h , and S s . Therefore, a resolution analysis based on truncated singular value decomposition of the sensitivity matrix with a noise level representative of field measurements is applied using synthetic data reflecting a known littoral aquifer. As an approximation of the hydraulic behavior of a real aquifer system, synthetic tomographic experiments and associated sensitivity matrices are generated using a radial flow model accounting for wellbore storage to simulate slug tests in a plane encompassing a stressed well and an observation well. Although fine-scale resolution of heterogeneities is limited by the diffusive nature of the groundwater flow equations, inversion of tomographic slug tests head data holds the potential to uniquely resolve coarse-scale heterogeneity in K h , K v /K h , and S s , as inscribed in the resolution matrix. This implies that tomographic head data can provide key information on aquifer heterogeneity and anisotropy, but that fine-scale information must be supplied by a priori information to obtain finer details.

Should hydraulic tomography data be interpreted using geostatistical inverse modeling? A laboratory sandbox investigation

Illman

Berg

Zhao

2015

The robust performance of hydraulic tomography (HT) based on geostatistics has been demonstrated through numerous synthetic, laboratory, and field studies. While geostatistical inverse methods offer many advantages, one key disadvantage is its highly parameterized nature, which renders it computationally intensive for large-scale problems. Another issue is that geostatistics-based HT may produce overly smooth images of subsurface heterogeneity when there are few monitoring interval data. Therefore, some may question the utility of the geostatistical inversion approach in certain situations and seek alternative approaches. To investigate these issues, we simultaneously calibrated different groundwater models with varying subsurface conceptualizations and parameter resolutions using a laboratory sandbox aquifer. The compared models included: (1) isotropic and anisotropic effective parameter models; (2) a heterogeneous model that faithfully represents the geological features; and (3) a heterogeneous model based on geostatistical inverse modeling. The performance of these models was assessed by quantitatively examining the results from model calibration and validation. Calibration data consisted of steady state drawdown data from eight pumping tests and validation data consisted of data from 16 separate pumping tests not used in the calibration effort. Results revealed that the geostatistical inversion approach performed the best among the approaches compared, although the geological model that faithfully represented stratigraphy came a close second. In addition, when the number of pumping tests available for inverse modeling was small, the geological modeling approach yielded more robust validation results. This suggests that better knowledge of stratigraphy obtained via geophysics or other means may contribute to improved results for HT.