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Short answer: Both.

Long Answer: Many people would think that a tsunami is a transverse wave as they go up and down. But like all water waves a tsunami has elements of transverse wave motion and longitudinal wave motion. In a transverse wave the particles move perpendicular (at right angles) to wave direction. In a longitudinal wave the particles move parallel (in the same direction) to the wave direction. In water waves (including tsunami) the water particles move in a circular or elliptical pattern depending on the depth of the water. In the case of tsunami which can always be treated as shallow water waves, the motion is elliptical.

Note that this is only the case for non-breaking waves. As any wave (and particulalry a tsunami) breaks the pure wave behaviour will break down as the energy of the wave is transferred to the turbulent motion of the breaking wave or in some cases (as is common with tsunami) a bore, which is no longer a wave as all the wave energy has been turned into a forward moving 'wall' of water.

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