Four distinct topics are covered in this dissertation. These topics can be grouped under the general heading of multicomponent seismology.
The first topic, deals with the generation of shear waves using vertical vibrators. Two methods were used to investigate this experimentally proven phenomenon. The first involves assuming the surface sources at some point can be modeled as vibrators with displacements in counterphase. The resulting far-field radiation pattern is then calculated. This shows the potential for strong vertically incident shear waves. The second method is based on simple mechanical models for vibrators that are allowed to interact over an elastic half-space. The theory for this method is developed fully and ready for numerical implementation.
The second topic deals with describing the composite earth as a generalized continuum. The method of Backus averaging, for a stack of finely layered media, is generalized to develop a new generalized continuum description. This development extends the averaging method to non-zero frequencies. The possibility of plane waves within this medium is investigated. This investigation show the plane waves in this type of media have the kinematic properties of waves in an elastic medium, but dynamic effects of absorption are and dispersion are present.
The third topic, involves a statistical method for finding the preferred frame of reference of an elastic tensor. The method is tested for the case of cubic symmetry and the preferred frame was extracted from a cubic elastic tensor represented in an arbitrary frame. Methods to extend the method to cases where the symmetry is unknown are presented.
The last topic, is concerned with a novel method of generating P- and S-wave synthetic seismograms using the state-space approach with coupled Goupillaud models. The method is implemented and synthetic seismograms generated showing good kinematic agreement to what is expected from the input model.
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