Amplitude patterns of tsunami waves from submarine earthquakes

Abstract

Excitation of tsunamis by submarine faults is studied with the purpose of revealing the relations that exist between seismic and tsunamigenic source parameters. Evidence is produced to show that the far-field deep-water wave amplitudes are determined by the relation where δ and λ are the dip and slip angles, respectively, S0 = η0ξ0 is the tsunamigenic area, u0 is the fault dislocation, α is the group velocity of long gravity waves, and Ts(ϒ) is a calculable wave function that depends on the epicentral distance r, the mean ocean depth H, and the time t. The dependence of ε on the azimuth angle ϕ and on the linear dimensions of the source is embodied in F. We have applied the above relation to four North Pacific earthquakes for which the seismic source parameters were derived from analyses of 236 signals of mantle Love and Rayleigh waves. The corresponding values of ε were taken from observations of W. G. Van Dorn (1965). Solving for η0 and S0, we obtain, for example, a width of 20 km and a tsunamigenic area of about 1.2 × 104 km2 for the Alaskan earthquake of March 28, 1964. Conversely, the above equation can be used to estimate u0, provided that ε and S0 are known. Deep-water radiation patterns are derived: wave amplitudes in a direction normal to the fault exceed corresponding amplitudes in the fault's direction. Typical values for the ratio F (84°)/F(0°) are 2 : 1 for earthquakes with magnitude M ∼7¼, 5 : 1 for M ∼8, and 14 : 1 for M ∼8½. Observations tend to support these findings.