Inverse modeling of aquifers usually involves identification of effective parameters such as transmissivities over a finite number of subregions, or zones. Theoretical restrictions on the maximum size of a zone for which such effective transmissivities can be properly defined and the desire to obtain a good resolution of the spatial variability of transmissivity may suggest that the aquifer be divided into numerous small zones. Considerations of parameter identifiability, on the other hand, may require that the number of unknown transmissivities be limited. To satisfy both requirements, an inverse approach has been developed in which the number of zones can be as large as deemed necessary on the basis of hydrogeological considerations. However, instead of trying to estimate a similar number of transmissivities, a smaller number of surrogate parameters, which are defined as linear combinations of the original log transmissivities, is estimated. The optimum number and definition of the surrogate parameters are determined through a singular value decomposition of a matrix arising from the linearization of the inverse problem. A "resolution matrix" and an "information density matrix" can also be obtained from the singular value decomposition. The resolution matrix is indicative of parameter identifiability and is valuable in deciding whether specific log-transmissivity zones should be lumped with their neighbors or left intact. The information density matrix shows how well the model can reproduce each measured hydraulic head value and may be used to determine the relative worth of each datum point for parameter estimation. This, in turn, may suggest discontinuing the collection of certain data and/or starting to collect data at other points in the aquifer. The methodology is illustrated by using data from the Avra Valley aquifer of southern Arizona.

This thesis l concerned with the mathematical modelling of open channel flows governed by the Saint-Venant equations, which are used as a prediction or identification tools. A survey of the literature in these fields identified the problems in need of Immediate research. Numerical test runs were then devised which led to projecting a clear picture as follows. The performance of twn widely used Implicit finite difference schemes, the 4-point box and 6-point staggered schemes were compared In a wide range of circumstances. it is concluded that both schemes produce 'very close results, but the staggered scheme is prone to convergence problems In some extreme cases. It was also noted that a sharp change in geometric configuration of compound channels produced discontinuous features on the aim ulated depth and discharge hydrographs. The inability of the staggered scheme In handling a head-discharge relationship as a downstream boundary condition was tackled by proposing and implementing a scheme of second order accuracy. As model data are generally corrupted withh errors and noise, their effects together with that of other factors on the Identified friction parameters we Investigated. The results demonstte the paramount Importance of the effect of a choice of objective function on the Identified parameters. While the individual values of the identified M2nning n may vary from one flood event to another, their mean is shown both numerically and rigorously to be dependent upon the choice of objective function. It is shown that an objective function formulated by using absolute errors performs ideally and produces reliable results even in the presence of autocorrelated Gaucian noise samples. The mean of the Identified parameters is also found to be adversely affected if the observation station is affected by localized disturbances. Sensitivity of objective functions to the variation In the value of the friction parameter Is also found to be an Important factor, as Insensitivity leads to ill-conditioning.

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In fractured rocks of low permeability, the hydraulic properties of the rock mass are strongly influenced by the connectivity and fracture geometry of the fracture system, the stiffness and deformational properties of fracture surfaces and the geostatic stresses. This dissertation demonstrates through theoretical analysis the sensitivity of fracture connectivity and flow rate to fracture radius, fracture density and measurement scale. Percolation factor and percolation frequency are suggested as indices of connectivity and flow rate. Models of hydromechanical coupling, normal closure and simple geometrical joint systems are proposed to study fracture porosity and fracture permeability and are compared with measured values from published papers. Fracture surface characteristics are expressed as indices of JRC and JCS. The relation between fracture aperture and geostatic stress is also examined. Based on the percolation process, a three dimensional discrete fracture model with statistical parameters of fracture geometry is developed to investigate the relations between the connectivity and flow rate and the percolation factor and percolation frequency. This model has the capability to generate a fracture network and to solve for steady state flow. The flow through each fracture is discretized by the boundary element method. By performing numerical simulation, the percolation threshold was found to be in the range of 0.9 to 2.4 for orthogonal joint sets. There is a rapid increase in flow rate with increasing fracture density or fracture length as the percolation factor reaches the percolation threshold. The percolation factor and percolation frequency are scale-dependent. A fracture network with large fractures and a high fracture density has a high percolation frequency and a high percolation factor. A network with high percolation frequency and percolation factor has a high flow rate. A constitutive model linking the initial conducting aperture, mechanical conducting aperture, JRC, JCS, geostatic stress and fracture geometries can be used to predict fracture porosity and fracture permeability in terms of depth. Preliminary comparison with field data shows that models comprising three orthogonal sets and disc-type fracture models can be used to simulate observed behavior. Fracture porosity and fracture permeability based on a model of three orthogonal sets can be used to predict flow through volcanic rocks. For sedimentary rocks a model incorporating a model of three orthogonal sets and one parallel set can be used with varying levels of confidence.

Water level recovery data collected in wells following controlled pumping tests are affected by both borehole and formation factors. The borehole factors comprise those effects attributed to the presence of the wellbore, such as step-increases in pumping rate, wellbore storage, well efficiency, and skin effects. The formation factors comprise those effects associated with the geologic environment in which an aquifer system occurs, such as variation of the coefficient of storage, and aquifer barrier boundaries. The recovery data should plot as a straight line on a semilogarithmic plot. Step-increases in the discharge rate during the pumping period cause the water level recovery plot to be concave downward. The curvature of the recovery data plot can be eliminated by applying a correction proposed by Harrill in 1970. However, the effect of step-increases in pumping rate on the recovery data is minimal so long as the duration of the pumping steps is less than about one-third of the total duration of pumping. The well efficiency and skin effects cause an additional component of drawdown in a pumped well, which is manifested as an initially rapid recovery rate after pumping stops. The effects of skin and well efficiency are usually dissipated within a few minutes after pumping stops. Wellbore storage effects can be critical in large diameter wells (wellbore radius greater than 0.5 feet) that penetrate aquifers with transmissivities less than about 2,700 feet squared per day. The time required to dissipate wellbore storage effects in the water level recovery data is inversely proportional to the aquifer transmissivity, and directly proportional to the borehole size. Variation of the coefficient of storage during the recovery period results in a semi-logarithmic recovery plot that is concave downward. The curvature of the recovery plot increases as the variation of the coefficient of storage increases. Variation in the coefficient of storage of one order of magnitude during the recovery period introduces an error of more than fifty percent in the transmissivity calculation at late recovery times. The recovery plot of data collected in a well influenced by a barrier boundary defines two straight line segments. The early-time straight line segment has a slope one-half that of the late-time straight line segment. Analysis of the early-time straight line yields the true aquifer transmissivity. Analysis and interpretation of water level recovery data collected in 59 wells following controlled pumping tests in aquifers of various rock types indicate that, in general, the shape of the recovery plot can be used to diagnose the presence of skin effects, low well efficiency, wellbore storage, and variation of the coefficient of storage. Analysis of data from seventeen wells in alluvial aquifers and thirteen wells in sandstone aquifers indicates that the concave downward recovery plot is the most common type of response curve. This shape of recovery curve indicates that the coefficient of storage is commonly smaller during the recovery period than during the drawdown period. Recovery data collected in twenty wells in fractured hard-rock aquifers indicate that the characteristic shape of the recovery plot predicted by Warren and Root in 1963 is generally diagnostic of flow in non-homogeneous, anisotropic, fractured aquifers. When the fracturing approaches being homogeneous and isotropic, the recovery plot can resemble data collected in non-fractured rocks. Recovery data from nine wells in composite limestone-sandstone aquifers indicate that the recovery plot is sometimes similar to the concave downward shape exhibited in sandstone and alluvial aquifers, and sometimes is similar to the shape predicted by Warren and Root for fractured rocks.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (M.S.)--Oregon State University, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 76-82). Also available on the World Wide Web.

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Thesis (M.S. - Hydrology and Water Resources)--University of Arizona, 1982. / Includes bibliographical references (leaves 73-75).