Model for the Leading Waves of Tsunamis

We propose a model for the leading wave of tsunamis to explain why although the coastal manifestation of a tsunami is assumed solitary-wave-like it is most often accompanied by a shoreline which recedes first before advancing up the beach, suggesting a leading-depression N-wave. Far field, we use the Korteweg--de Vries equation, and find that N-waves of geophysical scale do not fission over transoceanic propagation distances. Near shore, we use shallow-water theory to calculate the evolution and runup of emerging non-breaking waves, and observe that they evolve according to Green's law. We discuss the effects of certain ground deformation parameters and provide one application by modeling the Nicaraguan tsunami of 1 September 1992.