Azimuthal Distribution of Dominant Periods of Tsunami Waves Formed by Coseismic Bottom Displacements

The stationary phase method is used to obtain a formula to calculate the frequency spectrum of tsunami waves for an ocean of constant depth based on the shape of the initial elevation of the water surface at the source. For a model source of a Gaussian shape (elliptical in plan), the dependence of the dominant period of tsunami waves on the azimuth angle is analytically investigated. A method is proposed for mapping a real tsunami source located in an ocean of variable depth on the spherical surface of the Earth onto an equivalent source in a basin of fixed depth with a flat bottom. An example is given calculating the period directivity diagram for the source of the Simushir tsunami of January 13, 2007.