THE ALL-SOURCE GREEN’S FUNCTION AND ITS APPLICATIONS TO TSUNAMI PROBLEMS

The classical Green’s function provides the global linear response to impulse forcing at a particular source location. It is a type of one-source-all-receiver Green’s function. This paper presents a new type of Green’s function, referred to as the all-source-one-receiver, or for short the all-source Green’s function (ASGF), in which the solution at a point of interest (POI) can be written in terms of global forcing without requiring the solution at other locations. The ASGF is particularly applicable to tsunami problems. The response to forcing anywhere in the global ocean can be determined within a few seconds on an ordinary personal computer or on a web server. The ASGF also brings in two new types of tsunami charts, one for the arrival time and the second for the gain, without assuming the location of the epicenter or reversibility of the tsunami travel path. Thus it provides a useful tool for tsunami hazard preparedness and to rapidly calculate the real-time responses at selected POIs for a tsunami generated anywhere in the world’s oceans.