Funding is requested for a fundamental research effort in the nature of seismological parameters controlling generation and propagation of far-field, i.e., transoceanic tsunamis. Specifically, we plan to carry out the following research: (i) develop a mantle magnitude Mm based on the measurement of Rayleigh waves at the very long but variable periods, in order to make feasible the one-station measurement of the seismic moment of a teleseismic earthquake in real time thereby providing adequate information for the possible issuance of tsunami warnings; (ii) research systematically the influence of a number of source parameters such as depth of focus, geometry of focal mechanism, geometry of rupture, etc., on the excitation of tsunamis by earthquake sources; we will focus primarily on the influence of crustal structure, and in particular of the presence of sedimentary layering, as well as on the effect of non-double- couple sources such as those involved in landslides and volcanic processes; (iii) use detailed rupture models to synthetize the tsunamis of individual earthquakes, including the so-called "tsunami earthquakes", whose tsunamis as much as 10 times greater than predicted from their seismic moments; and (iv) research the focusing and defocusing effects that variations in oceanic depth creates through lateral heterogeneity in tsunami velocities, and consequently refraction of tsunami rays. The proposed research constitutes a broad attempt at understanding the factors controlling the amplitude of the tsunami at its generation, and during its propagation, before run-up and resonance effects ass their final contribution to the amplitude measured at a tidal gauge station.