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In this paper, the kinematics of tsunami wave rays and fronts over an uneven bottom are studied. A formula for the wave height along a ray tube is obtained. An exact analytical solution for wave rays and fronts over a sloping bottom is derived. This solution makes possible to determine a tsunami wave height in an area with a sloping bottom from the initial source in the ray approximation. The distribution of wave-height maxima calculated in an area with a sloping bottom is compared to that obtained with a shallow-water model.doaj:c17045d75baf4b47aa4455326812e0ab fatcat:y36o4r3rlrcbtcoehfadoexawa