Plane-wave decomposition and slant stack transformation have recently gained much interest as viable routes to perform a variety of prestack processing tasks, such as velocity estimation, migration, filtering, deconvolution, and velocity inversion. To further complement the current advances, the problem of earth model parameter estimation and prestack structural imaging are addressed in this work. Unlike existing methods, the algorithms presented here make a novel and systematic use of the plane-wave domain to determine migration and interval velocities, interface dip angles and common-shot gather reflector images. To start, a method is developed to estimate migration velocities and interface dip angles in earth models composed of planar, dipping reflecting interfaces separating homogeneous layers, and where straight-ray travelpaths to the reflecting interfaces can be assumed. The method consists of transforming a common-shot gather into the plane-wave domain, where a semblance analysis search along cosinusoid trajectories is performed. Since the cosinusoid trajectories are functions of the migration velocity and interface dip angle, selection of the maximum semblance values yields the best estimates to the desired earth model parameters. To remove the straight-ray assumption of the velocity-dip analysis method, a recursive technique is developed to estimate interval velocities and interface dip angles via a ray tracing algorithm. This technique essentially generates plane-wave domain traveltimes for a range of interval velocities and interface dip angles, and computes the error between the generated and observed plane-wave traveltimes. The minimum error determines the best estimates of the earth model parameters. With the information attained in the velocity-dip analysis algorithm, a plane-wave based imaging method is developed to produce prestack common-shot gather images of the reflecting interfaces. The method consists of transforming a common-shot gather into the plane-wave domain, where a velocity-dip semblance analysis is performed. Then, the plane-wave components are downward extrapolated and recombined via a dip-incorporated inverse slant-stack transformation to produce the spherical-wave field that would have been recorded by receivers placed on the reflecting interfaces. The dip incorporation consists of redefining the angle of emergence of the plane waves. Finally, a simple mapping algorithm converts the offset and time coordinates of the reconstructed wave field to the true horizontal location and two-way vertical time of the reflection points. This results in the desired prestack migrated images of the reflecting interfaces. In this thesis, a novel algorithm to perform plane-wave decomposition via Fourier transforms is also proposed. This algorithm consists of the application of the double fast Fourier transform to the input data, followed by complex vector multiplications with essentially the Fourier representation of the Bessel function J0 . A numerical singularity is avoided by applying an analytical expression that approximately accounts for the singular point contribution. An inverse fast Fourier transform from frequency to time gives the desired plane-wave seismogram. The techniques proposed in this work have yielded encouraging results on synthetic and field data examples. The examples demonstrate, for the first time, the systematic use of the plane-wave domain in processing seismic reflection data from common-shot gather data to the plane-wave domain, to velocity and dip angle analysis and to prestack structural imaging. It is believed that the results from this work will help researchers as well as practising geophysicists to become better acquainted with plane-wave domain processing. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

This thesis investigates water particle kinematics and the wave forces exerted on a slender rigid vertical cylinder in regular bidirectional wave fields. The instrumented portion of this cylinder is partitioned into nine independent segments enabling measurement of the vertical profile of hydrodynamic loading both in-line and transverse to the direction of wave propagation. Experiments conducted at the Hydraulics Laboratory of the National Research Council in Ottawa are described and some results are compared with the predictions of a wave force model based on the Morison equation and linear fluid kinematics. The influence of the crossing angle between the two wave components on the forces experienced by the column is determined. These experiments consider short-crested wave behavior in intermediate and deep water resulting from the interaction of two identical regular wave trains crossing at angles of 30, 60 and 90 degrees. The limit corresponding to unidirectional monochromatic waves is also investigated to provide a reference condition for comparison with the short-crested results. Conditions at the location of maximum short-crested wave height are of primary interest, however, forces at locations between the anti-node and node of the flow are also examined. In all, water surface elevations, flow velocities, and wave forces were measured in 24 short-crested and 8 different long-crested wave conditions spanning the range of Keulegan-Carpenter number between 4 and 24. The results of this study confirm the findings of previous researchers that short -crested waves with a certain period travel faster and rise higher before breaking than do their long-crested counterparts, but that in-line wave forces are not necessarily increased. Lift force maxima equal to half the maximum in-line force were measured; these forces can contribute significantly to the magnitude and direction of the total force resultant. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Bibliography: pages 242-249. / We study the propagation and growth of acceleration waves in isotropic thermoelastic media subject to a broad class of thermomechanical constraints. The work is based on an existing thermodynamic theory of constrained thermoelastic materials presented by Reddy (1984) for both definite and non- conductors, but we differ by adopting a new definition of a constrained non-conductor and by investigating the consequences of isotropy. The set of constraints considered is not arbitrary but is large enough to include most constraints commonly found in practice. We also extend Reddy's (1984) work by including consideration of sets of constraints for which a set of vectors associated with the constraints is linearly dependent. These vectors play a significant role in the propagation conditions and in the growth equations described below. Propagation conditions (of Fresnel-Hadamard type) are derived for both homothermal and homentropic waves, and solutions for longitudinal and transverse principal waves are discussed. The derivations involve the determination of jumps in the time derivative of constraint multipliers which are required in the solution of the corresponding growth equations, and it is found that these multipliers cannot be separately determined if the set of constraint vectors mentioned above is linearly dependent. This difficulty forces us to restrict the constraint set for which the growth equations for homothermal and homentropic waves can be derived. The growth of plane, cylindrical and spherical waves is considered and solutions are discussed, concentrating on the influence of the constraints on the results.