Subsurface elastic wave energy focusing based on a time reversal concept
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In the context of wave propagation, time-reversal refers to the invariance of the wave equation when the direction of traversing the time line is reversed. To date, there have been several applications rooted in the time-reversal concept, primarily in acoustics and in electromagnetics, and in settings that typically involve closed, finite, domains. In recent times, the concept has been predominantly used for steering and focusing wave energy in medical therapeutics. The extension of the time-reversal concept to elastodynamics, particularly in unbounded domains, entails challenges: the presence of two velocities and two body wave types, the presence of surface waves, the unboundness of the host domain, and aperture constraints, all conspire to limit or weaken wave focusing. This dissertation concentrates on a computational study for assessing the feasibility of focusing elastic waves to one or multiple subsurface targets, based on the time-reversal concept. Of particular interest is the focusing of wave energy to subterranean geologic formations, embedded within heterogeneous hosts. The motivation stems from potential applications to wave-based enhanced oil recovery, though other applications also stand to benefit. We report on a study that systematically assesses each and every limitation that is present when a small number of surface motion records are time-reversed and broadcast back into a heterogenous halfspace, aimed at the illumination of subsurface targets. We report the results of numerical experiments in two and three dimensions, and the impact of the limitations on the focusing resolution. All in all, despite the difficulties imposed by the physical setting, we conclude that focusing of elastic wave energy is feasible and competitive when compared against inverse source methods with similar targeting or focusing goals.