The excitation of tsunamis by deep earthquakes

Motivated by the detection of a millimetric tsunami following the deep earthquake of 2013 May 24 in the Sea of Okhotsk (depth 603 km; record moment M₀ = 3.95 × 10²⁸ dyn cm), we present a number of theoretical studies of the influence of source depth, z_s, on the excitation of tsunamis by dislocation sources. In the framework of the static deformation of an elastic half-space, we show that the energy available for tsunami excitation by a seismic source whose depth is significantly greater than source dimensions is expected to vary as M₀ ²/z_s ², in contrast to the classical scaling as M₀ ^4/3 for shallow sources. This is verified by numerical simulations based on the MOST algorithm, which also confirm the interpretation of the millimetric signals observed on DART sensors during the 2013 event. The normal-mode formalism, which considers tsunamis as a special branch of the spheroidal oscillations of the Earth in the presence of a water layer at its surface, also predicts an M₀ ²/z_s ² scaling for point source double-couples, and confirms millimetric amplitudes in the geometry of the DART buoys having recorded the 2013 Okhotsk tsunami. A general investigation of potential tsunami excitation as a function of depth for realistic intermediate and deep sources suggests the admittedly remote possibility of damaging events if deep earthquakes even greater than the 2013 event could occur at the bottom of Wadati-Benioff zones.