A three-dimensional finite-difference time-domain model has been developed to simulate the propagation of elastic waves in an elastic half space. The model incorporates a free-surface boundary condition for the surface of the half-space and a perfectly-matched layer absorbing boundary condition. This thesis includes a detailed description of the numerical model, a theoretical study of the stability of the finite-difference algorithm at a material interface, an analytical derivation of the elastic surface waves that arise at the surface of a solid medium, an extensive analysis of the interaction of elastic waves with buried land mines, a description of the resonant behavior of various mechanical objects, and results of experimental measurements of the elastic wave motion in a sand tank. The numerical model is primarily used to investigate the elastic wave motion in the ground and to explore the interaction of elastic waves with buried land mines. Various aspects of the mine-wave interaction have been studied. Simple mine models are used to explore the interaction with buried anti-personnel and anti-tank mines on a large scale. A more detailed mine-model is utilized to analyze the resonant behavior of buried mines. When elastic waves interact with a buried land mine, resonant oscillations occur at the location of the buried mine. These resonant oscillations enhance the mine's signature and distinguish it from clutter objects such as rocks. The resonance has been found to be largely dependent on the soil properties in the vicinity of the mine and on the burial depth of the mine. Although the numerical model is primarily used for the mine-detection problem, it is far more versatile and applicable to general problems in the field of elasticity. As an example for the model's versatility, the resonant motion of a tuning fork, as computed with the numerical model, is illustrated in this text.
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