Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions

Richards' equation (RE) is often used to model flow in unsaturated porous media. This model captures physical effects, such as sharp fronts in fluid pressures and saturations, which are present in more complex models of multiphase flow. The numerical solution of RE is difficult not only because of these physical effects but also because of the mathematical problems that arise in dealing with the nonlinearities. The method of lines has been shown to be very effective for solving RE in one space dimension. When solving RE in two space dimensions, direct methods for solving the linearized problem for the Newton step are impractical. In this work, we show how the method of lines and Newton-iterative methods, which solve linear equations with iterative methods, can be applied to RE in two space dimensions. We present theoretical results on convergence and use that theory to design an adaptive method for computation of the linear tolerance. Numerical results show the method to be effective and robust compared with an existing approach.     

Colonial auks and eiders as potential indicators of oil pollution

Colonial auk (Alcid) populations can be used as indicators of the effects of oil pollution on the seabirds of Canada's coastal zones. Of approximately 11 million breeding colonial alcids in Canada and in adjacent West Greenland waters, 87% are murres. Common Eiders may serve as the best indicators of the effects of oil pollution in Canada's western Arctic where colonial alcids are scarce.     

Seismic and electromagnetic controlled-source interferometry in dissipative media

Seismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an ‘interferometry‐by‐deconvolution’ approach which circumvents this assumption. The proposed method applies not only to seismic waves, but to any type of diffusion and/or wave field in a dissipative medium. This opens the way to applying interferometry to controlled‐source electromagnetic (CSEM) data. Interferometry‐by‐deconvolution replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications. We demonstrate this at the hand of numerically modeled CSEM data.     

Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems

Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.     

Prevention of Wellbore Clogging by Intermittent Abstraction

Wellfield “Tull en ’t Waal” (water utility Vitens Midden Nederland) suffers extensively from wellbore (or mechanical) clogging. To prevent this type of clogging, wells have been operated intermittently since August 2005 using a carrousel well operation schedule. Since the introduction of this schedule, wellbore clogging has become minimal.     

Equipartitioning is not sufficient for Green's function extraction

The extraction of the Earth's Green's function from field fluctuations is a rapidly growing area of research.The principle of Green's function extraction is often related to the requirement of equipartitioning,which stipulates that the energy of field fluctuations is distributed evenly in some sense.We show the meaning of equipartitioning for a variety of different formulations for Green's function retrieval.We show that equipartitioning is not a sufficient condition,and provide several examples that illustrate this point.We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green's function in seismology.The theory for Green's function extraction is usually based on a statistical theory that relies on ensemble averages.Since there is only one Earth,one usually replaces the ensemble average with a time average.We show that such a replacement only makes sense when attenuation is taken into account,and show how the theory for Green's function extraction for oscillating systems can be extended to incorporate attenuation.     

Modelling of differential single difference receiver clock bias for precise positioning

A receiver hardware delay should be seriously considered for time-transfer and determination of ionospheric delay corrections for wide area differential GPS positioning. A receiver hardware delay does not generally effect the common geo-position application, as suitable differences of observations are used, or equivalently, clock error parameters are introduced, epoch-wise, that also absorb the delays. This paper investigates the behavior of inter-frequency (or observation-type) receiver hardware delays by using a single difference (SD) model, which estimates the receiver delay along with the receiver clock error (and SD ambiguities of a reference satellite with carrier phase observations) for zero and short baselines. The purpose of this paper is to model the between-observation-type delays for the purpose of precise positioning, under practical circumstances. The focus is on data series of differential SD receiver clock biases, since they reflect the behavior of receiver hardware delays with time. A simple linear regression of the data series is employed to study the behavior, and test statistics are employed to assess both the significance of the parameters and the observations fit for the linear regression. The statistical analysis results indicate that almost all inter-observation type receiver delays can be modeled as the sum of a constant (offset) and a constant rate of change (slope). The analysis shows that the differential receiver delay is generally at the mm- to cm-level on phase, while at the dm-level on code for the equipment used in the experiments.     

Finite element methods for variable density flow and solute transport

Saltwater intrusion into coastal freshwater aquifers is an ongoing problem that will continue to impact coastal freshwater resources as coastal populations increase. To effectively model saltwater intrusion, the impacts of increased salt content on fluid density must be accounted for to properly model saltwater/freshwater transition zones and sharp interfaces. We present a model for variable density fluid flow and solute transport where a conforming finite element method discretization with a locally conservative velocity post-processing method is used for the flow model and the transport equation is discretized using a variational multiscale stabilized conforming finite element method. This formulation provides a consistent velocity and performs well even in advection-dominated problems that can occur in saltwater intrusion modeling. The physical model is presented as well as the formulation of the numerical model and solution methods. The model is tested against several 2-D and 3-D numerical and experimental benchmark problems, and the results are presented to verify the code.