Although tsunamis are dispersive water waves, hazard maps for earthquake-generated tsunamis neglect dispersive effects because the spatial dimensions of tsunamis are much greater than the water depth, and dispersive effects are generally small. Furthermore, calculations that include non-dispersive effects tend to predict higher tsunamis than ones that include dispersive effects. Although non-dispersive models may overestimate the tsunami height, this conservative approach is acceptable in disaster management, where the goal is to save lives and protect property. However, we demonstrate that offshore frequency dispersion amplifies tsunamis caused by outer-rise earthquakes, which displace the ocean bottom downward in a narrow area, generating a dispersive short-wavelength and pulling-dominant (water withdrawn) tsunami. We compared observational evidence and calculations of tsunami for a 1933 Mw 8.3 outer-rise earthquake along the Japan Trench. Dispersive (Boussinesq) calculations predicted significant frequency dispersion in the 1933 tsunami. The dispersive tsunami deformation offshore produced tsunami inundation heights that were about 10% larger than those predicted by non-dispersive (long-wave) calculations. The dispersive tsunami calculations simulated the observed tsunami inundation heights better than did the non-dispersive tsunami calculations. Contrary to conventional practice, we conclude that dispersive calculations are essential when preparing deterministic hazard maps for outer-rise tsunamis.
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