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It is well known among regular beach goers that a sudden shoreline drawback is often a warning sign for an impending Tsunami. My understanding of Tsunamis is they they form as a result of the seafloor abruptly changing, causing a local vertical displacement of water at the site of above the disruption, which initiates the wave.

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How does this process ultimately result in the shoreline often receding prior to the Tsunami reaching the coast?

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It has nothing to do with the geological cause of the tsunami. Instead, it's a result of the way waves propagate. You can see the same effect on ordinary wind-generated ocean waves — the waterline draws back before each wave peak arrives and washes up the beach. Tsunamis are much bigger waves, in terms of both amplitude and wavelength, so the effect is more dramatic.

The particles in some surface waves, including wind waves and Rayleigh waves (a component of what is often called ground roll), have in a circular or elliptical motion — in the case of a wind wave the motion is clockwise if the wave is traveling from left to right (see this animated comparison for Rayleigh waves). The 'backwards' motion in the trough results in the drawback you are asking about.

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