Free Oscillations: Frequencies and Attenuations

Abstract

The displacement at any point on the surface of the Earth can be quite complicated but can be thought of as a sum of discrete modes of oscillation, each mode having a characteristic frequency and decay rate which are dependent upon the structure of the Earth. The initial amplitudes of the modes of free oscillation depend upon the source of excitation which, in free-oscillation seismology (or “normal mode” seismology), is usually an earthquake. Earthquakes are typically of relatively short duration. For example, a magnitude 6.5 earthquake will rupture for perhaps ten seconds after which the Earth is in free oscillation. Away from the immediate vicinity of the earthquake, the motions of the Earth are small in amplitude and the total displacement at a recording site can be written simply as a sum of decaying cosinusoids: