National Oceanic and
Atmospheric Administration
United States Department of Commerce


FY 1979

Tsunami prediction using the reciprocal property of Green's functions

Loomis, H.G.

Mar. Geod., 2(1), 27–39, doi: 10.1080/15210607909379333 (1979)

Previously reported (Loomis, 1974) was the scheme of composing a tsunami by convoluting the source function with a family of previously calculated responses to unit impulse functions, which had been specified as initial conditions at points in the source region. A new application of an old idea makes this scheme considerably more useful. Namely, that the Green's function for the linear, oceanwide hydrodynamic equation is reciprocal in its space coordinates. The response at A due to a unit impulse at B is exactly the same as the response at B due to a unit impulse at A. This means that for a prediction at point A, it is necessary only to put a unit impulse at A, time-step the resulting disturbance throughout the ocean, and record the time history of the water level at each grid point in the ocean. This generates all of the Green's functions needed for any source area for a future tsunami prediction scheme at point A. These prerecorded functions are the Green's functions, and are available for simulating any tsunami at point A from any source region.

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