Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (M. Sc.)--University of Hong Kong, 2004. / Also available in print.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Available also in an electronic version.

Thesis (M. Sc.)--University of Hong Kong, 2004.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

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

Chebychev semi-discretizations for both ordinary and partial differential equations are explored. The Helmholtz, heat, Schrӧdinger and 15° migration equations are investigated. The Galerkin, pseudospectral and tau projection operators are employed, while the Crank-Nicolson scheme is used for the integration of the time (depth) dependence. The performance of the Chebychev scheme is contrasted with the performance of the finite difference scheme for Dirichlet and Neumann boundary conditions. Comparisons between all finite difference, Fourier and Chebychev migration algorithms are drawn as well. Chebychev expansions suffer from neither the artificial dispersion dispersion of finite difference approximations nor the demand for a periodic boundary structure of Fourier expansions. Thus, it is shown that finite difference schemes require at least one order of magnitude more points in order to match the accuracy level of the Chebychev schemes. In addition, the Chebychev migration algorithm is shown to be free of the wraparound problem, inherent in migration procedures based on Fourier transform. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M.App.Sc.) - Carleton University, 2007. / Includes bibliographical references (p. 115-119). Also available in electronic format on the Internet.