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This thesis concerns the application of seismic interferometry to surface waves. Seismic interferometry is the process by which the wavefield between two recording locations is estimated, resulting in new recordings at one location as if a source had been placed at the other. Thus, in surface-wave interferometry, surface waves propagating between two receiver locations are estimated as if one receiver had recorded the response due to a source of surface-wave energy at the other receiver. In global and engineering seismology new surface-wave responses can allow for imaging of the subsurface, and in exploration seismology it has been proposed that these new surface-wave responses can allow for the prediction and removal of socalled ground-roll (surface waves that are treated as noise). This thesis presents a detailed analysis of surface-wave interferometry: using a combination of modelling studies, real-data studies, and theoretical analyses the processes involved in the application of interferometry to complex (both multi-mode and scattered) surface waves are revealed. These analyses identify why surface waves are often dominant in the application of interferometry, where errors may be introduced in the application of surface-wave interferometry, and how interferometry may be processed in such a way as to minimise those (and other) errors. This allows for the proposal of new data-processing strategies in the application of seismic interferometry to surface waves, potentially resulting in improved surface-wave estimates. Much of the work in this thesis focuses on the use of seismic interferometry to predict and subtract surface waves in land-seismic exploration surveys. Using insights from the presented analyses it is shown that seismic surface waves can be successfully predicted and removed from land-seismic data using an interferometric approach. However, the work in this thesis is not only limited to applications in exploration seismology. In addition to the ground-roll removal method, improved estimates of higher-mode and scattered surfaces waves may allow for more advanced imaging algorithms to be used in conjunction with seismic interferometry. Also, as a consequence of the analysis presented a Generalized Optical Theorem for Surface Waves is derived. This highlights a link between seismic interferometry and the optical theorem and may allow for further application of optical theorems in seismology.

The goal of this research project is to determine the fractal nature, if any, which certain surface water waves exhibit when viewed on a microscopic scale. We make use of the mathematical formulation of non-viscous fluids describing their physical properties. Using these expressions and including boundary conditions for free surfaces as well as taking the surface tension into consideration, we obtain a partial differential equation describing the dynamics of surface water waves. A brief introduction to the study of fractal geometry with several examples of well-known fractals is included. An important property of fractals is their non-integral dimension. Several methods of determining the dimension of a curve are described in this paper. Our wave equation is examined under different assumptions representing the conditions of a surface water wave near its breaking point. Solutions are developed using analytical and numerical methods. We determine the dimension of 'rough' solutions using one of the methods introduced and conclude that under certain conditions, surface water waves near their breaking point exhibit a fractal structure on a microscopic scale. / Graduation date: 1994

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