A theory of the Earth's background free oscillations

Abstract

[1] 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 crossspectral 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.

A numerical simulation of ionospheric and atmospheric variations associated with the Sumatra earthquake on December 26, 2004

“…The acoustic oscillations that are mainly confined to the tropospheremesosphere duct persist for about an hour (Walterscheid et al, 2003). Recent theoretical analyses with a realistic atmospheric temperature profile indicate that resonant waves with periods of 4.5, 3.8, and 3.2 min are known as the fundamental mode and the first and the second overtone modes, respectively (Kanamori and Mori, 1992;Kanamori et al, 1994;Lognonné et al, 1998;Nishida et al, 2000;Fukao et al, 2002). It is also known that some of the wave energy leaks into the upper thermosphere, producing oscillations with the same periods even in the entire thermosphere.…”

Three‐dimensional crustal S wave velocity structure in Japan using microseismic data recorded by Hi‐net tiltmeters

“…Following Fukao et al [2002] we assume homogeneous and isotropic excitation sources. We can write the synthetic cross spectra as equation (A10) and equation (A11) of Appendix A, based on the normal mode theory.…”

Clear evidence for the sign-reversal of the pressure admittance to gravity near 3mHz

“…This minimum in the vertical PSD and the difference between vertical and horizontal noise at these frequencies is nicely explained by the contributions from the atmosphere as described in detail by Zürn and Wielandt (2007) and . This special feature in the vertical noise PSD allows the clear detection of the Earth's background free oscillations ("Hum") in the vertical component records of many stations (e. g. Nawa et al, 1998;Suda et al 1998;Tanimoto et al 1998;Nishida et al 2002;Ekström, 2001;Fukao et al, 2002;Rhie and Romanowicz, 2004;Kurrle and Widmer-Schnidrig, 2006), while in contrast the horizontal hum can only be detected at barely a handful of them (Kurrle and Widmer-Schnidrig, 2008). Zürn and Wielandt (2007) were not able to directly demonstrate the reversal in the sign of the pressure admittance for vertical acceleration in real records.…”