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Cui T.,Massachusetts Institute of Technology | Ward N.D.,Otago Computational Modelling Group Ltd | Kaipio J.,University of Auckland
Journal of Hydrologic Engineering | Year: 2014

This study considers the estimation of aquifer parameters for a spatially heterogenous aquifer from pumping test data. An approach is proposed that is based on modeling the unknown parameters as smooth Markov random fields. The associated inverse problem is formulated using the Bayesian framework and the posterior probability distribution of parameters is explored using Markov chain Monte Carlo. The method is evaluated by a numerical simulation in which measurements are taken in four observation wells. Even such a minimalist example presents significant computational challenges. Therefore, to obtain a computationally feasible solution, a model reduction is carried out and the estimation problem is reduced from over 1,000 parameters to 40 parameters. The approximate posterior distribution is then sampled using an adaptive Markov chain Monte Carlo sampler in order to quantify parameter uncertainty. This paper compares the parameter with predictive uncertainty and discusses the consequences of the model reduction. © 2014 American Society of Civil Engineers.

Ward N.D.,Otago Computational Modelling Group Ltd | Falle S.,University of Leeds
Journal of Hydrologic Engineering | Year: 2013

Semianalytic formulas are obtained for flow to a well screened in a leaky aquifer that was overlain by an aquitard and phreatic aquifer and underlain by a second aquitard and leaky aquifer. Formulas are also obtained for the scenario in which the phreatic aquifer is hydraulically connected to a rectilinear stream. Adaptive mesh refinement is used to obtain highly resolved simulations for a meandering stream depletion problem that is both numerically challenging and has physically interesting features. The associated inverse problem is also considered, and a simple example is presented of synthetic pumping test data, which demonstrates that it can be very difficult to quantify the actual effects of pumping. The conclusion is that a framework for uncertainty quantification of aquifer parameters is necessary for objective determination of the parameters. ©2013 American Society of Civil Engineers.

Weggel J.R.,Drexel University | Ward N.D.,Otago Computational Modelling Group Ltd
Geotextiles and Geomembranes | Year: 2012

The equations for a numerical model that describes the accumulation of filter cake on a geotextile as flow passes through it are developed and solved numerically. The accumulation of both colloidal and settle-able particles is considered. The equations are first developed for a colloidal suspension and subsequently expanded to include settle-able particles having various settling velocities. Output from the numerical model includes: the flow rate through the geotextile/filter cake layers, the head drop through the layers, the cumulative volume of flow per unit area of geotextile and the rate of accumulation of the various size components of the filter cake. Important model parameters are Ψy 0/K which relates the permittivity of the geotextile times the water level at the start of the dewatering process to the permeability of the accumulating filter cake, gΨ 2/y 0, a dimensionless permittivity, the α i/e{open} values that determine how much each sediment size class contributes to the filter cake's thickness and the v i/K values that describe the settling velocities of each sediment size class. The size distribution of the particles in various layers within the filter cake can be determined from the model and an example solution is presented that shows how particle size distribution varies within the filter cake. Experiments to verify the theory are presented in Weggel and Dortch (this issue). © 2011 Elsevier Ltd.

Lahivaara T.,University of Eastern Finland | Dudley Ward N.F.,Otago Computational Modelling Group Ltd | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd | And 4 more authors.
Inverse Problems | Year: 2014

We study the inverse problem of estimating the pipeline location from ground-penetrating radar data in the context of Bayesian inversion. Maxwells equations are used to model the electromagnetic wave propagation, and are solved using a high-order discontinuous Galerkin method. The uncertainties related to the wave propagation in inhomogeneous background are taken into account by the Bayesian approximation error (BAE) approach. The inverse problem is solved using the full waveform data. Numerical simulations suggest that by using the BAE the model uncertainties can be taken satisfactorily into account, while at the same time making a significant reduction in the computational burden. Furthermore, the estimates for the location of the pipeline are feasible in the sense that the posterior model supports the actual location. © 2014 IOP Publishing Ltd.

Cui T.,Massachusetts Institute of Technology | Ward N.D.,Otago Computational Modelling Group Ltd
Journal of Hydrologic Engineering | Year: 2013

This study considers the problem of quantifying stream depletion from pumping test data. Bayesian inference is used to quantify the posterior uncertainty of parameters for a simple vertically heterogeneous aquifer model, in which the pumped semiconfined aquifer is separated by an aquiclude from a phreatic aquifer hydraulically connected to a stream. This study investigates the effects of using different data sets and shows that a single pumping test is generally not sufficient to determine stream depletion within reasonable limits. However, uncertainty quantification conducted within a Bayesian context reveals that by judicious design of aquifer tests, stream depletion can be accurately determined from data. © 2013 American Society of Civil Engineers.

Gulley A.K.,University of Auckland | Dudley Ward N.F.,Otago Computational Modelling Group Ltd. | Cox S.C.,Institute of Geological & Nuclear Sciences | Kaipio J.P.,University of Auckland
Journal of Hydrology | Year: 2013

The recent Canterbury/Christchurch earthquakes and aftershocks generated groundwater level responses throughout New Zealand. However, the greater part of damage has been sustained by the city of Christchurch which is built on a layered sequence of artesian aquifers. In this paper we focus on responses in these coastal aquifers. We quantify groundwater responses with a simple model which differentiates between immediate earthquake induced response (spike) and post-seismic change (offset). The most significant feature of our analysis is the consistent pattern of groundwater response to the earthquakes: deeper wells correlate with negative offset and shallower wells correlate with positive offset. This is consistent with the upwards vertical movement of water. We consider the hydrological and engineering consequences. © 2013 Elsevier B.V.

Lahivaara T.,University of Eastern Finland | Ward N.F.D.,Otago Computational Modelling Group Ltd | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd | And 3 more authors.
Inverse Problems | Year: 2014

Recently, it has been proposed that spontaneous seismic activity could be used in the estimation of hydrological parameters of aquifers such as permeability and storage. Approximate wave propagation models such as ray tracing, which are commonly used in hydrological parameter estimation with active sources and backscattering geometry, are not feasible with passive seismological imaging. With respect to full wave propagation models, the most accurate known model for aquifers is the poroelastic model while bedrock is usually modelled as an elastic medium. Using a poroelastic model in the forward model can be a computationally impractical choice. In this paper, we carry out a feasibility study in which we attempt to estimate the aquifer depth and water table using a highly approximate elastic model also for the aquifer. We adopt the Bayesian approximation error approach in which a statistical model is constructed for the errors that are induced by using model approximations such as sparse meshing and simplified physical models. We consider the problem in a simple two-dimensional geometry and show that straightforward adoption of approximate models leads to inconsistent parameter estimates, that is, the true parameters have essentially vanishing posterior density. On the other hand, using the Bayesian approximation error approach, the parameter estimates are consistent. © 2014 IOP Publishing Ltd.

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