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We present the exact solution of the acoustic wave equation in the frequency domain in two space dimensions for a velocity that increases linearly with depth and a density that is a power law in depth. The geometric properties of the solution are described by the bipolar coordinate system. The asymptotic behaviour for large frequencies matches the result obtained by ray theory. The 3-D solution was already known.
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Kuvshinov et al. (2006) studied this question.
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