A theory of the Earth's background free oscillations

Abstract

It has recently been established that the Earth's free oscillations are continuously excited by phenomena other than earthquakes and that these oscillations constitute the background noise in the normal mode band at quiet sites. On the basis of evidence that the excitation source is at or just above the Earth's surface, a normal mode theory of the Earth's free oscillations excited by random atmospheric loading is developed. The displacement field is expressed in the frequency domain in general terms of the cross‐spectral density of air pressure disturbance. For spatially homogeneous and isotropic disturbance the cross‐spectral density is approximated by the power spectral density and the coefficient of coherence with a coherence length much shorter than the wavelengths of normal modes. With this approximation the spectrum of ground acceleration is represented as the product of the pressure force term and the Earth response term. The final expression of the acceleration spectrum includes the effect of the gravity attraction of a disturbed air mass. A synthetic spectrum is calculated, using a power law decaying air pressure spectrum consistent with observations, assuming a frequency‐dependent coherence length of air pressure fluctuation, taking into account the effect of the gravity attraction of a disturbed air mass. This synthetic spectrum exhibits distinct peaks of fundamental modes and complex troughs consisting of overtone modes, in quantitative agreement with the peaks and troughs of the observed spectrum.